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The performance of density functional theory for the description of ground and excited state properties of inorganic and organometallic uranium compoundsDaniel Reta,1 Fabrizio Ortu,1 Simon Randall,1 David P. Mills,1 Nicholas F. Chilton,1 Richard E. P. Winpenny,1 Louise Natrajan,1 Bryan Edwards2 and Nikolas Kaltsoyannis1,*1 School of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, UK2 Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Oxford, Didcot OX11 0QX, UKAbstractMolecular uranium complexes are the most widely studied in actinide chemistry, and make a significant and growing contribution to inorganic and organometallic chemistry. However, reliable computational procedures to accurately describe the properties of such systems are not yet available. In this contribution, 18 experimentally characterized molecular uranium compounds, in oxidation states ranging from III to VI and with a variety of ligand environments, are studied computationally using density functional theory. The computed geometries and vibrational frequencies are compared with Xray crystallographic, and infrared and Raman spectroscopic data to establish which computational approach yields the closest agreement with experiment. NMR parameters and UVvis spectra are studied for three and five closedshell U(VI) compounds respectively. Overall, the most robust methodology for obtaining accurate geometries is the PBE functional with Grimme’s D3 dispersion corrections. For IR spectra, different approaches yield almost identical results, which makes the PBE functional with Grimme’s D3 dispersion corrections the best choice. However, for Raman spectra the dependence on functional is more pronounced and no such clear recommendation can be made. Similarly, for 1H, 13C NMR chemical shifts, no unequivocal recommendation emerges as to the best choice of density functional, although for spin-spin couplings, the LCωPBE functional with solvent corrections is the best approach. No form of timedependent density functional theory can be recommended for the simulation of the electronic absorption spectra of uranyl (VI) compounds; the orbitals involved in the transitions are not calculated correctly, and the energies are also typically unreliable. Two main approaches are adopted for the description of relativistic effects on the uranium centres: either a relativistic pseudopotential and associated valence basis set, or an all-electron basis set with the ZORA Hamiltonian. The former provides equal, if not better, agreement with experiment vs all-electron basis set calculations, for all properties investigated.IntroductionComputational quantum chemistry has matured rapidly in recent years, to the point that it is now central to many areas of research. It has benefitted from complementary developments in theoretical understanding and the availability of high performance computer systems. Many methods are well developed and understood for the treatment of systems containing only atoms with low to intermediate atomic numbers, and in favourable cases it is now possible to calculate structural, spectroscopic and thermodynamic properties that accurately rivals experiment. By contrast, the computational chemistry of systems containing atoms with large atomic numbers (especially the actinides) remains challenging. The two principal reasons for this are (i) relativistic effectsADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "ISBN" : "3527627499", "abstract" : "Relativistic Quantum Chemistry; Contents; Preface; 1 Introduction; 1.1 Philosophy of this Book; 1.2 Short Reader's Guide; 1.3 Notational Conventions and Choice of Units; Part I -- Fundamentals; 2 Elements of Classical Mechanics and Electrodynamics; 3 Concepts of Special Relativity; 4 Basics of Quantum Mechanics; Part II -- Dirac's Theory of the Electron; 5 Relativistic Theory of the Electron; 6 The Dirac Hydrogen Atom; Part III -- Four-Component Many-Electron Theory; 7 Quantum Electrodynamics; 8 First-Quantized Dirac-Based Many-Electron Theory; 9 Many-Electron Atoms.", "author" : [ { "dropping-particle" : "", "family" : "Reiher", "given" : "Markus.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolf", "given" : "Alexander", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2009" ] ] }, "number-of-pages" : "669", "publisher" : "Wiley-VCH", "title" : "Relativistic quantum chemistry: the fundamental theory of molecular science", "type" : "book" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "ISBN" : "1118688317", "abstract" : "1. Relativistic Configuration Interaction Calculations for Lanthanide and Actinide Anions / Donald R. Beck, Steven M. O'Malley and Lin Pan -- 2. Study of Actinides by Relativistic Coupled Cluster Methods / Ephraim Eliav and Uzi Kaldor -- 3. Relativistic All-Electron Approaches to the Study of f Element Chemistry / Trond Saue and Lucas Visscher -- 4. Low-Lying Excited States of Lanthanide Diatomics Studied by Four-Component Relativistic Configuration Interaction Methods / Hiroshi Tatewaki, Shigeyoshi Yamamoto and Hiroko Moriyama -- 5. The Complete-Active-Space Self-Consistent-Field Approach and Its Application to Molecular Complexes of the f-Elements / Andrew Kerridge -- 6. Relativistic Pseudopotentials and Their Applications / Xiaoyan Cao and Anna Weigand -- 7. Error-Balanced Segmented Contracted Gaussian Basis Sets : A Concept and Its Extension to the Lanthanides / Florian Weigend -- 8. Gaussian Basis Sets for Lanthanide and Actinide Elements : Strategies for Their Development and Use / Kirk A. Peterson and Kenneth G. Dyall -- 9. 4f, 5d, 6s, and Impurity-Trapped Exciton States of Lanthanides in Solids / Zoila Barandiara\u0301n and Luis Seijo -- 10. Judd-Ofelt Theory : The Golden (and the Only One) Theoretical Tool of f-Electron Spectroscopy / Lidia Smentek -- 11. Applied Computational Actinide Chemistry / Andre\u0301 Severo Pereira Gomes, Florent Re\u0301al, Bernd Schimmelpfennig, Ulf Wahlgren and Vale\u0301rie Vallet -- 12. Computational Tools for Predictive Modeling of Properties in Complex Actinide Systems / Jochen Autschbach, Niranjan Govind, Raymond Atta-Fynn, Eric J. Bylaska, John W. Weare and Wibe A. de Jong -- 13. Theoretical Treatment of the Redox Chemistry of Low Valent Lanthanide and Actinide Complexes / Christos E. Kefalidis, Ludovic Castro, Ahmed Yahia, Lionel Perrin and Laurent Maron -- 14. Computational Studies of Bonding and Reactivity in Actinide Molecular Complexes / Enrique R. Batista, Richard L. Martin and Ping Yang -- 15. The 32-Electron Principle : A New Magic Number / Pekka Pyykko\u0308, Carine Clavague\u0301ra and Jean-Pierre Dognon -- 16. Shell Structure, Relativistic and Electron Correlation Effects in f Elements and Their Importance for Cerium(III)-based Molecular Kondo System / Michael Dolg.", "author" : [ { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "editor" : [ { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "id" : "ITEM-2", "issued" : { "date-parts" : [ [ "2015" ] ] }, "number-of-pages" : "480", "publisher" : "Wiley-VCH", "title" : "Computational methods in lanthanide and actinide chemistry", "type" : "book" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[1,2]", "plainTextFormattedCitation" : "[1,2]", "previouslyFormattedCitation" : "[1,2]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[1,2] (the modification of energies and spatial extent of atomic orbital vs non-relativistic analogues, and spin-orbit coupling) have a significant effect on 5f element chemistry, and must be explicitly included in calculations, and (ii) the near degeneracy of several sets of valence atomic orbitals (5f, 6d, 7s and 7p) can lead to a plethora of closely-spaced electronic states which pose formidable electron correlation challenges.The principal workhorse of molecular computational chemistry in the 5f series is density functional theory (DFT).ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "ISSN" : "03060012", "author" : [ { "dropping-particle" : "", "family" : "Kaltsoyannis", "given" : "Nikolas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Society Reviews", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2003", "12", "18" ] ] }, "page" : "9-16", "publisher" : "Royal Society of Chemistry", "title" : "Recent developments in computational actinide chemistry", "type" : "article-journal", "volume" : "32" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "ISSN" : "0306-0012", "abstract" : "We briefly review advances in computational actinoid (An) chemistry during the past ten years in regard to two issues: the geometrical and electronic structures, and reactions. The former addresses the An\u2013O, An\u2013C, and M\u2013An (M is a metal atom including An) bonds in the actinoid molecular systems, including actinoid oxo and oxide species, actinoid\u2013carbenoid, dinuclear and diatomic systems, and the latter the hydration and ligand exchange, the disproportionation, the oxidation, the reduction of uranyl, hydroamination, and the photolysis of uranium azide. Concerning their relevance to the electronic structures and reactions of actinoids and their importance in the development of an advanced nuclear fuel cycle, we also mentioned the work on actinoid carbides and nitrides, which have been proposed to be candidates of the next generation of nuclear fuel, and the oxidation of PuOx, which is important to understand the speciation of actinoids in the environment, followed by a brief discussion on the urgent need for a heavier involvement of computational actinoid chemistry in developing advanced reprocessing protocols of spent nuclear fuel. The paper is concluded with an outlook.", "author" : [ { "dropping-particle" : "", "family" : "Wang", "given" : "Dongqi", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gunsteren", "given" : "Wilfred F.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Chai", "given" : "Zhifang", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Society Reviews", "id" : "ITEM-2", "issue" : "17", "issued" : { "date-parts" : [ [ "2012" ] ] }, "page" : "5836", "publisher" : "The Royal Society of Chemistry", "title" : "Recent advances in computational actinoid chemistry", "type" : "article-journal", "volume" : "41" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "ISSN" : "0009-2665", "author" : [ { "dropping-particle" : "", "family" : "Kov\u00e1cs", "given" : "Attila", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Konings", "given" : "Rudy J. M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gibson", "given" : "John K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Infante", "given" : "Ivan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gagliardi", "given" : "Laura", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Reviews", "id" : "ITEM-3", "issue" : "4", "issued" : { "date-parts" : [ [ "2015", "2", "25" ] ] }, "page" : "1725-1759", "publisher" : "American Chemical Society", "title" : "Quantum Chemical Calculations and Experimental Investigations of Molecular Actinide Oxides", "type" : "article-journal", "volume" : "115" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "ISSN" : "0001-4842", "abstract" : "Interest in the chemistry of the early actinide elements (notably uranium through americium) usually results either from the nuclear waste problem or the unique chemistry of these elements that result from 5f contributions to bonding. Computational actinide chemistry provides one useful tool for studying these processes. Theoretical actinide chemistry is challenging because three principal axes of approximation have to be optimized. These are the model chemistry (the choice of approximate electron\u2212electron correlation method and basis sets), the approximate relativistic method, and a method for modeling solvent (condensed phase) effects. In this Account, we arrange these approximations in a three-dimensional diagram, implying that they are relatively independent of each other. A fourth level of approximation concerns the choice of suitable models for situations too complex to treat in their entirety. We discuss test cases for each of these approximations. Gas-phase data for uranium fluorides and oxofluori...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Accounts of Chemical Research", "id" : "ITEM-4", "issue" : "1", "issued" : { "date-parts" : [ [ "2010", "1", "19" ] ] }, "page" : "19-29", "publisher" : "American Chemical Society", "title" : "Theoretical Actinide Molecular Science", "type" : "article-journal", "volume" : "43" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[3\u20136]", "plainTextFormattedCitation" : "[3\u20136]", "previouslyFormattedCitation" : "[3\u20136]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[3–6] However, there is by no means a standard approach to DFT calculations for molecular actinide species. For example, among the leading players, Liddle et al. favour the generalised gradient approximation (GGA) functional BP86ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1038/nchem.2279", "ISSN" : "1755-4330", "author" : [ { "dropping-particle" : "", "family" : "Gardner", "given" : "Benedict M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bal\u00e1zs", "given" : "G\u00e1bor", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scheer", "given" : "Manfred", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tuna", "given" : "Floriana", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McInnes", "given" : "Eric J. 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Here, we report the preparation of the terminal uranium(V) nitride complex [UN(Tren(TIPS))][Na(12-crown-4)(2)] {in which Tren(TIPS) = [N(CH(2)CH(2)NSiPr(i)(3))(3)](3-) and Pr(i) = CH(CH(3))(2)} by reaction of the uranium(III) complex [U(Tren(TIPS))] with sodium azide followed by abstraction and encapsulation of the sodium cation by the polydentate crown ether 12-crown-4. Single-crystal x-ray diffraction reveals a uranium-terminal nitride bond length of 1.825(15) angstroms (where 15 is the standard uncertainty). The structural assignment is supported by means of (15)N-isotopic labeling, electronic absorption spectroscopy, magnetometry, electronic structure calculations, elemental analyses, and liberation of ammonia after treatment with water.", "author" : [ { "dropping-particle" : "", "family" : "King", "given" : "David M", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tuna", "given" : "Floriana", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McInnes", "given" : "Eric J L", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McMaster", "given" : "Jonathan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lewis", "given" : "William", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Blake", "given" : "Alexander J", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Liddle", "given" : "Stephen T", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Science (New York, N.Y.)", "id" : "ITEM-2", "issue" : "6095", "issued" : { "date-parts" : [ [ "2012", "8", "10" ] ] }, "page" : "717-20", "publisher" : "American Association for the Advancement of Science", "title" : "Synthesis and structure of a terminal uranium nitride complex.", "type" : "article-journal", "volume" : "337" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[7,8]", "plainTextFormattedCitation" : "[7,8]", "previouslyFormattedCitation" : "[7,8]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[7,8] and Gagliardi et al. also often use GGAs.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1038/nchem.2009", "ISSN" : "1755-4330", "author" : [ { "dropping-particle" : "", "family" : "Anderson", "given" : "Nickolas H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Odoh", "given" : "Samuel O.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Yao", "given" : "Yiyi", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Williams", "given" : "Ursula J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schaefer", "given" : "Brian A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kiernicki", "given" : "John J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lewis", "given" : "Andrew J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Goshert", "given" : "Mitchell D.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Fanwick", "given" : "Phillip E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schelter", "given" : "Eric J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Walensky", "given" : "Justin R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gagliardi", "given" : "Laura", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bart", "given" : "Suzanne C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Nature Chemistry", "id" : "ITEM-1", "issue" : "10", "issued" : { "date-parts" : [ [ "2014", "7", "27" ] ] }, "page" : "919-926", "publisher" : "Nature Research", "title" : "Harnessing redox activity for the formation of uranium tris(imido) compounds", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/jp504147s", "ISSN" : "1932-7447", "abstract" : "The self-assembly of uranyl-peroxide nanocapsules in aqueous solution is unique in uranium chemistry and has potential applications in the fabrication and reprocessing of actinide-based materials. We present the first study of these species in aqueous solution by means of classical molecular dynamics simulations. To this end, we parametrized a uranyl-peroxide force field from interaction energies computed with second order M\u00f8ller\u2013Plesset perturbation theory and fit to a Born\u2013Huggins\u2013Mayer potential. Bonded parameters were fit from density functional theory calculations. The solvent and counterion structures surrounding four different systems ([(UVIO2)]2+, [(UVIO2)2(\u03bc2-O2)]2+, [(UVIO2)5(\u03bc2-O2)5], and [(UVIO2)20(\u03bc2-O2)30]20-) were studied in aqueous solution. The largest studied system is predicted to encapsulate an ice-like water cluster.", "author" : [ { "dropping-particle" : "", "family" : "Mir\u00f3", "given" : "Pere", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vlaisavljevich", "given" : "Bess", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dzubak", "given" : "Allison L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hu", "given" : "Shuxian", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Burns", "given" : "Peter C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Cramer", "given" : "Christopher J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Spezia", "given" : "Riccardo", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gagliardi", "given" : "Laura", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry C", "id" : "ITEM-2", "issue" : "42", "issued" : { "date-parts" : [ [ "2014", "10", "23" ] ] }, "page" : "24730-24740", "publisher" : "American Chemical Society", "title" : "Uranyl\u2013Peroxide Nanocapsules in Aqueous Solution: Force Field Development and First Applications", "type" : "article-journal", "volume" : "118" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[9,10]", "plainTextFormattedCitation" : "[9,10]", "previouslyFormattedCitation" : "[9,10]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[9,10] By contrast, the Los Alamos team routinely employs hybrid DFT (primarily B3LYP),ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/C3SC52030G", "abstract" : "Evidence for metal\u2013carbon orbital mixing in thorocene and uranocene was determined from DFT calculations and carbon K-edge X-ray absorption spectra (XAS) collected with a scanning transmission X-ray microscope (STXM). Both the experimental and computational results showed that the 5f orbitals engaged in significant \u03b4-type mixing with the C8H82\u2212 ligands, which increased as the 5f orbitals dropped in energy on moving from Th4+ to U4+. The first experimental evidence for extensive \u03d5-orbital interactions has been provided by the C K-edge XAS analysis of thorocene; however, \u03d5-type covalency in uranocene was negligible. The results highlighted two contrasting trends in orbital mixing from one pair of highly symmetric molecules, and showed that covalency does not increase uniformly for different molecular orbital interactions with later actinides.", "author" : [ { "dropping-particle" : "", "family" : "Minasian", "given" : "Stefan G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Keith", "given" : "Jason M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Batista", "given" : "Enrique R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Boland", "given" : "Kevin S.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Clark", "given" : "David L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kozimor", "given" : "Stosh A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Martin", "given" : "Richard L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shuh", "given" : "David K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tyliszczak", "given" : "Tolek", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Sci.", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2014" ] ] }, "page" : "351-359", "publisher" : "The Royal Society of Chemistry", "title" : "New evidence for 5f covalency in actinocenes determined from carbon K-edge XAS and electronic structure theory", "type" : "article-journal", "volume" : "5" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/ja2105015", "ISSN" : "0002-7863", "abstract" : "Chlorine K-edge X-ray absorption spectroscopy (XAS) and ground-state and time-dependent hybrid density functional theory (DFT) were used to probe the electronic structures of Oh-MCl62\u2013 (M = Ti, Zr, Hf, U) and C4v-UOCl5\u2013, and to determine the relative contributions of valence 3d, 4d, 5d, 6d, and 5f orbitals in M\u2013Cl bonding. Spectral interpretations were guided by time-dependent DFT calculated transition energies and oscillator strengths, which agree well with the experimental XAS spectra. The data provide new spectroscopic evidence for the involvement of both 5f and 6d orbitals in actinide\u2013ligand bonding in UCl62\u2013. For the MCl62\u2013, where transitions into d orbitals of t2g symmetry are spectroscopically resolved for all four complexes, the experimentally determined Cl 3p character per M\u2013Cl bond increases from 8.3(4)% (TiCl62\u2013) to 10.3(5)% (ZrCl62\u2013), 12(1)% (HfCl62\u2013), and 18(1)% (UCl62\u2013). Chlorine K-edge XAS spectra of UOCl5\u2013 provide additional insights into the transition assignments by lowering the symmetry...", "author" : [ { "dropping-particle" : "", "family" : "Minasian", "given" : "Stefan G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Keith", "given" : "Jason M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Batista", "given" : "Enrique R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Boland", "given" : "Kevin S.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Clark", "given" : "David L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Conradson", "given" : "Steven D.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kozimor", "given" : "Stosh A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Martin", "given" : "Richard L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schwarz", "given" : "Daniel E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shuh", "given" : "David K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wagner", "given" : "Gregory L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wilkerson", "given" : "Marianne P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolfsberg", "given" : "Laura E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Yang", "given" : "Ping", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of the American Chemical Society", "id" : "ITEM-2", "issue" : "12", "issued" : { "date-parts" : [ [ "2012", "3", "28" ] ] }, "page" : "5586-5597", "publisher" : "American Chemical Society", "title" : "Determining Relative f and d Orbital Contributions to M\u2013Cl Covalency in MCl ₆ ^2\u2013 (M = Ti, Zr, Hf, U) and UOCl ₅ ^\u2013 Using Cl K-Edge X-ray Absorption Spectroscopy and Time-Dependent Density Functional Theory", "type" : "article-journal", "volume" : "134" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[11,12]", "plainTextFormattedCitation" : "[11,12]", "previouslyFormattedCitation" : "[11,12]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[11,12] an approach also adopted by Maron et al.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/C5SC02150B", "ISSN" : "2041-6520", "abstract" : "New tris-amidinate actinide (Th, U) complexes containing a rare O-bound terminal phosphaethynolate (OCP\u2212) ligand were synthesized and fully characterized. The cyanate (OCN\u2212) and thiocyanate (SCN\u2212) analogs were prepared for comparison and feature a preferential N-coordination to the actinide metals. The Th(amid)3(OCP) complex reacts with Ni(COD)2 to yield the heterobimetallic adduct (amid)3Th(\u03bc-\u03b71(O):\u03b72(C,P)-OCP)Ni(COD) featuring an unprecedented reduced (OCP\u2212) bent fragment bridging the two metals.", "author" : [ { "dropping-particle" : "", "family" : "Camp", "given" : "Cl\u00e9ment", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Settineri", "given" : "Nicholas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lef\u00e8vre", "given" : "Julia", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jupp", "given" : "Andrew R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Goicoechea", "given" : "Jos\u00e9 M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Maron", "given" : "Laurent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Arnold", "given" : "John", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Sci.", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "2015" ] ] }, "page" : "6379-6384", "publisher" : "The Royal Society of Chemistry", "title" : "Uranium and thorium complexes of the phosphaethynolate ion", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[13]", "plainTextFormattedCitation" : "[13]", "previouslyFormattedCitation" : "[13]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[13] who exclusively use B3PW91. Research in our group has employed both GGAADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/anie.201411250", "author" : [ { "dropping-particle" : "", "family" : "Arnold", "given" : "Polly L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Prescimone", "given" : "Alessandro", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Farnaby", "given" : "Joy H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mansell", "given" : "Stephen M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Parsons", "given" : "Simon", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaltsoyannis", "given" : "Nikolas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Angew. Chem. Int. Ed.", "id" : "ITEM-1", "issue" : "23", "issued" : { "date-parts" : [ [ "2015", "6", "1" ] ] }, "page" : "6735-6739", "publisher" : "WILEY\u2010VCH Verlag", "title" : "Characterizing Pressure-Induced Uranium C\uf8ffH Agostic Bonds", "type" : "article-journal", "volume" : "54" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1039/C5SC01248A", "abstract" : "Reaction of [Th(I)(NR2)3] (R = SiMe3) (2) with KECPh3 (E = O, S) affords the thorium chalcogenates, [Th(ECPh3)(NR2)3] (3, E = O; 4, E = S), in moderate yields. Reductive deprotection of the trityl group from 3 and 4 by reaction with KC8, in the presence of 18-crown-6, affords the thorium oxo complex, [K(18-crown-6)][Th(O)(NR2)3] (6), and the thorium sulphide complex, [K(18-crown-6)][Th(S)(NR2)3] (7), respectively. The natural bond orbital and quantum theory of atoms-in-molecules approaches are employed to explore the metal\u2013ligand bonding in 6 and 7 and their uranium analogues, and in particular the relative roles of the actinide 5f and 6d orbitals.", "author" : [ { "dropping-particle" : "", "family" : "Smiles", "given" : "Danil E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wu", "given" : "Guang", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaltsoyannis", "given" : "Nikolas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hayton", "given" : "Trevor W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Sci.", "id" : "ITEM-2", "issue" : "7", "issued" : { "date-parts" : [ [ "2015" ] ] }, "page" : "3891-3899", "publisher" : "The Royal Society of Chemistry", "title" : "Thorium\u2013ligand multiple bonds via reductive deprotection of a trityl group", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[14,15]", "plainTextFormattedCitation" : "[14,15]", "previouslyFormattedCitation" : "[14,15]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[14,15] and hybridADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/C5DT04317D", "abstract" : "The enthalpies of the reactions AnO2+ \u2192 AnO+ + O and AnO2+ + H2O \u2192 AnO2(H2O)+, and those of the isomerisation of the latter to AnO(OH)2+, have been calculated for An = Pa\u2013Pu. The data match previous experimental and computational values very closely, and the computed enthalpy for the isomerisation of PaO2(H2O)+ to PaO(OH)2+, requested by the authors of Inorg. Chem., 2015, 54, 7474, is found to be 0.8 kJ mol\u22121. The NPA, NBO and QTAIM approaches are used to probe covalency in the An\u2013Oyl bond of AnO2(H2O)+, and all metrics agree that these bonds become increasingly covalent as the 5f series is crossed, providing rationalisation for the increasingly endothermic isomerisation reactions. QTAIM analysis indicates that the AnO and An\u2013OH bonds in the oxide hydroxide isomers also become increasingly covalent as the 5f series is crossed.", "author" : [ { "dropping-particle" : "", "family" : "Kaltsoyannis", "given" : "Nikolas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Dalton Trans.", "id" : "ITEM-1", "issue" : "7", "issued" : { "date-parts" : [ [ "2016" ] ] }, "page" : "3158-3162", "publisher" : "The Royal Society of Chemistry", "title" : "Covalency hinders AnO ₂ (H ₂ O) ⁺ \u2192 AnO(OH) ₂ ⁺ isomerisation (An = Pa\u2013Pu)", "type" : "article-journal", "volume" : "45" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[16]", "plainTextFormattedCitation" : "[16]", "previouslyFormattedCitation" : "[16]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[16] functionals. Meta variants of both GGAs and hybrids are gaining popularity, such as in the recent TPSS/TPSSh work of Kerridge et al.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/acs.inorgchem.5b01219", "ISSN" : "0020-1669", "abstract" : "The molecular structures of a series of uranyl (UO22+) complexes in which the uranium center is equatorially coordinated by a first-row species are calculated at the density functional theory level and binding energies deduced. The resulting electronic structures are investigated using a variety of density-based analysis techniques in order to quantify the degree of covalency in the equatorial bonds. It is shown that a consideration of the properties of both the one-electron and electron-pair densities is required to understand and rationalize the variation in axial bonding effected by equatorial complexation. Strong correlations are found between density-based measures of the covalency and equatorial binding energies, implying a stabilizing effect due to covalent interaction, and it is proposed that uranyl U\u2013Oyl stretching vibrational frequencies can serve as an experimental probe of equatorial covalency.", "author" : [ { "dropping-particle" : "", "family" : "Pietro", "given" : "Poppy", "non-dropping-particle" : "Di", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kerridge", "given" : "Andrew", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "2016", "1", "19" ] ] }, "page" : "573-583", "publisher" : "American Chemical Society", "title" : "U\u2013O _yl Stretching Vibrations as a Quantitative Measure of the Equatorial Bond Covalency in Uranyl Complexes: A Quantum-Chemical Investigation", "type" : "article-journal", "volume" : "55" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[17]", "plainTextFormattedCitation" : "[17]", "previouslyFormattedCitation" : "[17]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[17] and Pandey,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1016/j.inoche.2013.09.020", "ISSN" : "13877003", "abstract" : "Geometry and bonding energy analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}] were investigated with the DFT, DFT-D3 and DFT-D3(BJ) methods using density functionals (BLYP, BP86, PW91, PBE, revPBE and TPSS). The BLYP functional yields a UN bond distance of 1.788\u00c5 for the model complex [NU{N(CH2CH2NSiMe3)3}] which is in close agreement with the experimental value of the UN bond distance of 1.799(7) \u00c5 for [NU{N(CH2CH2NSiiPr3)3}]. The calculated Mayer bond order (2.95) and Gopinathan\u2013Jug bond order (3.18) indicate that the UN bond in this complex is essentially UN triple bonds. The electrostatic interaction is significantly smaller than the covalent bonding. The bond dissociation energy (BDE) is largest for the functional PBE and smallest for the functional TPSS. The DFT-D3 dispersion corrections are 5.3kcal/mol (BLYP) and 5.0kcal/mol (TPSS).", "author" : [ { "dropping-particle" : "", "family" : "Pandey", "given" : "Krishna K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry Communications", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "4-6", "title" : "The effect of density functional and dispersion interaction on structure and bonding analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}]: A theoretical study", "type" : "article-journal", "volume" : "37" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[18]", "plainTextFormattedCitation" : "[18]", "previouslyFormattedCitation" : "[18]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[18] and the M06 calculations of Steele et al.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp401875f", "ISSN" : "1089-5639", "abstract" : "The measured redox potential of an actinide at an electrode surface involves the transfer of a single electron from the electrode surface on to the actinide center. Before electron transfer takes place, the complexing ligands and molecules of solvation need to become structurally arranged such that the electron transfer is at its most favorable. Following the electron transfer, there is further rearrangement to obtain the minimum energy structure for the reduced state. As such, there are three parts to the total energy cycle required to take the complex from its ground state oxidized form to its ground state reduced form. The first part of the energy comes from the structural rearrangement and solvation energies of the actinide species before the electron transfer or charge transfer process; the second part, the energy of the electron transfer; the third part, the energy required to reorganize the ligands and molecules of solvation around the reduced species. The time resolution of electrochemical techniq...", "author" : [ { "dropping-particle" : "", "family" : "Steele", "given" : "Helen M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Guillaumont", "given" : "Dominique", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Moisy", "given" : "Philippe", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "21", "issued" : { "date-parts" : [ [ "2013", "5", "30" ] ] }, "page" : "4500-4505", "publisher" : "American Chemical Society", "title" : "Density Functional Theory Calculations of the Redox Potentials of Actinide(VI)/Actinide(V) Couple in Water", "type" : "article-journal", "volume" : "117" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[19]", "plainTextFormattedCitation" : "[19]", "previouslyFormattedCitation" : "[19]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[19] It is therefore not uncommon that a random selection of three different papers on molecular actinide chemistry will report the results of DFT calculations from three different rungs of Perdew’s “Jacob’s ladder”,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.1904565", "abstract" : "We present the case for the nonempirical construction of density functional approximations for the exchange-correlation energy by the traditional method of \u201cconstraint satisfaction\u201d without fitting to data sets, and present evidence that this approach has been successful on the first three rungs of \u201cJacob\u2019s ladder\u201d of density functional approximations [local spin-density approximation (LSD), generalized gradient approximation (GGA), and meta-GGA]. We expect that this approach will also prove successful on the fourth and fifth rungs (hyper-GGA or hybrid and generalized random-phase approximation). In particular, we argue for the theoretical and practical importance of recovering the correct uniform density limit, which many semiempirical functionals fail to do. Among the beyond-LSD functionals now available to users, we recommend the nonempirical Perdew\u2013Burke\u2013Ernzerhof (PBE) GGA and the nonempirical Tao\u2013Perdew\u2013Staroverov\u2013Scuseria (TPSS) meta-GGA, and their one-parameter hybrids with exact exchange. TPSS im...", "author" : [ { "dropping-particle" : "", "family" : "Perdew", "given" : "John P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ruzsinszky", "given" : "Adrienn", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tao", "given" : "Jianmin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Staroverov", "given" : "Viktor N.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "Gustavo E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Csonka", "given" : "G\u00e1bor I.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "6", "issued" : { "date-parts" : [ [ "2005", "8", "8" ] ] }, "page" : "062201", "publisher" : "American Institute of PhysicsAIP", "title" : "Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits", "type" : "article-journal", "volume" : "123" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[20]", "plainTextFormattedCitation" : "[20]", "previouslyFormattedCitation" : "[20]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[20] yet there is little evidence that conclusions concerning molecular actinide chemistry are functional independent.With this in mind, we were keen to establish the best DFT methodology for studying molecular uranium inorganic and organometallic complexes, and here report the results of a wideranging investigation. We have conducted extensive calculations on 18 uranium compounds, featuring the metal in a variety of oxidation states and ligand environments, for which there is a range of high quality experimental data available with which we can compare our results. The properties we have studied include molecular geometries and vibrational frequencies (XRD, IR and Raman data) and, for closed shell U(VI) species, NMR parameters and electronic excitations (UVvis data). All of these types of data are routinely acquired by experimental molecular actinide chemists, and are often reported in conjunction with supporting DFT results. We shall see that for some properties there are clearcut recommendations as to the best DFT approach to adopt, whereas for others the picture is either much less clear, or just depressing. We expect that the actinide, and wider, community will find our work, and conclusions, highly valuable. Target compounds REF _Ref457550072 \h \* MERGEFORMAT Figure 1 introduces the compounds investigated in this work, and indicates the references from which we draw experimental data. The list contains representative examples of the rich variety of molecular uranium complexes, and the compounds considered display a wide range of physical properties. The structural and spectroscopic of all of these complexes have been experimentally well characterized. Our classification of the different compounds is done on the basis of the oxidation state of the uranium centre, which also provides the framework for the discussion throughout this work. Compounds 1 – 3, 4 – 8, 9 and 10 – 16 feature a U(III), U(IV), U(V) and U(VI) centre with three, two, one and zero unpaired electrons in the 5f orbitals, respectively. Compounds 17 – 18, by contrast to the other compounds, are dimeric species with formally one unpaired electron on each of the two paramagnetic U(V) centres. An additional feature that varies throughout the list of compounds is the charge. Most of them are neutral, apart from compound 10 which has a -1 charge, compounds 9 and 17 which are dianions and compound 13 which carries a -4 charge.Figure SEQ Figure \* ARABIC 1. Schematic representation of the 18 uranium compounds investigated. The numbering scheme is used throughout the work, and superscripts indicate the sources of the experimental data. Each column features a different oxidation state of the uranium centre, including monomeric U(III), U(IV), U(V), U(VI) and dimeric U(V)–U(V). The circles indicate the system of colours that has been used throughout this work to refer to each group of molecules. MethodologyOne of the aims of this work is to determine which quantum chemistry approach(es) offer(s) the most reliable description of molecular uranium compounds. Several programs exist with which this evaluation could be performed, with differing performance in terms of functionality, computational cost and accuracy of the results, and we have selected two of the key players to study the different properties; Gaussian09 version D.01ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "author" : [ { "dropping-particle" : "", "family" : "Frisch", "given" : "M. J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Trucks", "given" : "G. W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schlegel", "given" : "H. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "G. E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Robb", "given" : "M. 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The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.", "author" : [ { "dropping-particle" : "", "family" : "Adamo", "given" : "Carlo", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Barone", "given" : "Vincenzo", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "13", "issued" : { "date-parts" : [ [ "1999", "4", "1" ] ] }, "page" : "6158-6170", "publisher" : "AIP Publishing", "title" : "Toward reliable density functional methods without adjustable parameters: The PBE0 model", "type" : "article-journal", "volume" : "110" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[51]", "plainTextFormattedCitation" : "[51]", "previouslyFormattedCitation" : "[51]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[51] B3LYPADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.464913", "ISSN" : "00219606", "abstract" : "Recent developments in density functional theory have transformed the entire field of quantum chemistry. This paper provides a perspective on Becke's landmark papers in 1992 and 1993 that led to the popular density functionals such as B3LYP.", "author" : [ { "dropping-particle" : "", "family" : "Becke", "given" : "Axel D", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "J Chem Phys", "id" : "ITEM-1", "issue" : "7", "issued" : { "date-parts" : [ [ "1993" ] ] }, "page" : "5648-5652", "title" : "Density functional thermochemistry. III. The role of exact exchange", "type" : "article-journal", "volume" : "98" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[52]", "plainTextFormattedCitation" : "[52]", "previouslyFormattedCitation" : "[52]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[52] and TPSShADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1103/PhysRevLett.91.146401", "author" : [ { "dropping-particle" : "", "family" : "Tao", "given" : "Jianmin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Perdew", "given" : "John P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Staroverov", "given" : "Viktor N.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "Gustavo E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Review Letters", "id" : "ITEM-1", "issue" : "14", "issued" : { "date-parts" : [ [ "2003", "9", "30" ] ] }, "page" : "146401-146404", "publisher" : "American Physical Society", "title" : "Climbing the Density Functional Ladder: Nonempirical Meta\u2013Generalized Gradient Approximation Designed for Molecules and Solids", "type" : "article-journal", "volume" : "91" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[50]", "plainTextFormattedCitation" : "[50]", "previouslyFormattedCitation" : "[50]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[50] hybrid functionals and the LC-ωPBEADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.2409292", "ISSN" : "0021-9606", "PMID" : "17190549", "abstract" : "Common approximate exchange-correlation functionals suffer from self-interaction error, and as a result, their corresponding potentials have incorrect asymptotic behavior. The exact asymptote can be imposed by introducing range separation into the exchange component and replacing the long-range portion of the approximate exchange by the Hartree-Fock counterpart. The authors show that this long-range correction works particularly well in combination with the short-range variant of the Perdew-Burke-Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, here denoted LC-omegaPBE, is remarkably accurate for a broad range of molecular properties, such as thermochemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer.", "author" : [ { "dropping-particle" : "", "family" : "Vydrov", "given" : "Oleg A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "Gustavo E", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of chemical physics", "id" : "ITEM-1", "issue" : "23", "issued" : { "date-parts" : [ [ "2006", "12", "21" ] ] }, "page" : "234109-9", "publisher" : "AIP Publishing", "title" : "Assessment of a long-range corrected hybrid functional.", "type" : "article-journal", "volume" : "125" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1063/1.2244560", "ISSN" : "0021-9606", "PMID" : "16942321", "abstract" : "We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.", "author" : [ { "dropping-particle" : "", "family" : "Vydrov", "given" : "Oleg A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Heyd", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "V", "family" : "Krukau", "given" : "Aliaksandr", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "Gustavo E", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of chemical physics", "id" : "ITEM-2", "issue" : "7", "issued" : { "date-parts" : [ [ "2006", "8", "21" ] ] }, "page" : "074106-9", "title" : "Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals.", "type" : "article-journal", "volume" : "125" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1063/1.2723119", "ISSN" : "0021-9606", "PMID" : "17461616", "abstract" : "In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.", "author" : [ { "dropping-particle" : "", "family" : "Vydrov", "given" : "Oleg A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Scuseria", "given" : "Gustavo E", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Perdew", "given" : "John P", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of chemical physics", "id" : "ITEM-3", "issue" : "15", "issued" : { "date-parts" : [ [ "2007", "4", "21" ] ] }, "page" : "154109-9", "title" : "Tests of functionals for systems with fractional electron number.", "type" : "article-journal", "volume" : "126" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[53\u201355]", "plainTextFormattedCitation" : "[53\u201355]", "previouslyFormattedCitation" : "[53\u201355]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[53–55] long range-corrected functional. Additionally, for each functional empirical dispersion corrections as proposed by GrimmeADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/wcms.30", "ISSN" : "17590876", "author" : [ { "dropping-particle" : "", "family" : "Grimme", "given" : "Stefan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Wiley Interdisciplinary Reviews: Computational Molecular Science", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "2011", "3", "16" ] ] }, "page" : "211-228", "title" : "Density functional theory with London dispersion corrections", "type" : "article-journal", "volume" : "1" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1002/jcc.20078", "ISSN" : "0192-8651", "PMID" : "15224390", "abstract" : "An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The \"double counting\" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.", "author" : [ { "dropping-particle" : "", "family" : "Grimme", "given" : "Stefan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of computational chemistry", "id" : "ITEM-2", "issue" : "12", "issued" : { "date-parts" : [ [ "2004", "9" ] ] }, "page" : "1463-73", "title" : "Accurate description of van der Waals complexes by density functional theory including empirical corrections.", "type" : "article-journal", "volume" : "25" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1002/jcc.20495", "ISSN" : "0192-8651", "PMID" : "16955487", "abstract" : "A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.", "author" : [ { "dropping-particle" : "", "family" : "Grimme", "given" : "Stefan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of computational chemistry", "id" : "ITEM-3", "issue" : "15", "issued" : { "date-parts" : [ [ "2006", "11", "30" ] ] }, "page" : "1787-99", "title" : "Semiempirical GGA-type density functional constructed with a long-range dispersion correction.", "type" : "article-journal", "volume" : "27" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[56\u201358]", "plainTextFormattedCitation" : "[56\u201358]", "previouslyFormattedCitation" : "[56\u201358]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[56–58] have been included when available (hereafter referred to as “D3”). Finally, UV-vis spectra were studied by means of time dependent DFT (TD-DFT) for those closedshell molecules with available experimental data. In this case, in addition to the previously mentioned functionals, we also considered the popular CAMB3LYP.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1016/j.cplett.2004.06.011", "ISSN" : "00092614", "abstract" : "A new hybrid exchange\u2013correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree\u2013Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the standard error function with parameter 0.33.", "author" : [ { "dropping-particle" : "", "family" : "Yanai", "given" : "Takeshi", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tew", "given" : "David P", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Handy", "given" : "Nicholas C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics Letters", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2004" ] ] }, "page" : "51-57", "title" : "A new hybrid exchange\u2013correlation functional using the Coulomb-attenuating method (CAM-B3LYP)", "type" : "article-journal", "volume" : "393" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[59]", "plainTextFormattedCitation" : "[59]", "previouslyFormattedCitation" : "[59]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[59] Note that all these functionals were investigated when using Gaussian09; initial attempts to use functionals other than the pure-exchange PBE with ADF resulted in persistent Self-Consistent Field (SCF) convergence problems and slow performance. Thus, throughout the text when referring to ADF results, only data from the PBE functional are discussed.An underlying feature common to all our systems is the need to include relativistic effects due to the uranium centre; these have been accounted for by means of either relativistic pseudopotentialsADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/cr2001383", "ISSN" : "0009-2665", "author" : [ { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Cao", "given" : "Xiaoyan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Reviews", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2012", "1", "11" ] ] }, "page" : "403-480", "publisher" : "American Chemical Society", "title" : "Relativistic Pseudopotentials: Their Development and Scope of Applications", "type" : "article-journal", "volume" : "112" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[60]", "plainTextFormattedCitation" : "[60]", "previouslyFormattedCitation" : "[60]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[60] or the scalar relativistic ZORA Hamiltonian.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.472460", "abstract" : "In this paper we will calculate the effect of spin\u2013orbit coupling on properties of closed shell molecules, using the zero\u2010order regular approximation to the Dirac equation. Results are obtained using density functionals including density gradient corrections. Close agreement with experiment is obtained for the calculated molecular properties of a number of heavy element diatomic molecules.", "author" : [ { "dropping-particle" : "", "family" : "Lenthe", "given" : "E.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Snijders", "given" : "J. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "E. J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "15", "issued" : { "date-parts" : [ [ "1996" ] ] }, "page" : "6505-6516", "publisher" : "American Institute of Physics", "title" : "The zero\u2010order regular approximation for relativistic effects: The effect of spin\u2013orbit coupling in closed shell molecules", "type" : "article-journal", "volume" : "105" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1063/1.467943", "ISSN" : "0021-9606", "abstract" : "In this paper we will discuss relativistic total energies using the zeroth order regular approximation (ZORA). A simple scaling of the ZORA one\u2010electron Hamiltonian is shown to yield energies for the hydrogenlike atom that are exactly equal to the Dirac energies. The regular approximation is not gauge invariant in each order, but the scaled ZORA energy can be shown to be exactly gauge invariant for hydrogenic ions. It is practically gauge invariant for many\u2010electron systems and proves superior to the (unscaled) first order regular approximation for atomic ionization energies. The regular approximation, if scaled, can therefore be applied already in zeroth order to molecular bond energies. Scalar relativistic density functional all\u2010electron and frozen core calculations on diatomics, consisting of copper, silver, and gold and their hydrides are presented. We used exchange\u2010correlation energy functionals commonly used in nonrelativistic calculations; both in the local\u2010density approximation (LDA) and including...", "author" : [ { "dropping-particle" : "", "family" : "Lenthe", "given" : "E.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "E. 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To zeroth order, the expansions give second order differential equations (just like the Schr\u00f6dinger equation), which already contain the most important relativistic effects, including spin\u2013orbit coupling. One of the zero order Hamiltonians is identical to the one obtained earlier by Chang, Pelissier, and Durand [Phys. Scr. 34, 394 (1986)]. Self\u2010consistent all\u2010electron and frozen\u2010core calculations are performed as well as first order perturbation calculations for the case of the uranium atom using these Hamiltonians. They give very accurate results, especially for the one\u2010electron energies and densities of the valence orbitals.", "author" : [ { "dropping-particle" : "", "family" : "Lenthe", "given" : "E.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "E. J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Snijders", "given" : "J. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-3", "issue" : "6", "issued" : { "date-parts" : [ [ "1993", "9", "15" ] ] }, "page" : "4597-4610", "publisher" : "American Institute of Physics", "title" : "Relativistic regular two\u2010component Hamiltonians", "type" : "article-journal", "volume" : "99" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1002/(SICI)1097-461X(1996)57:3<281::AID-QUA2>3.0.CO;2-U", "ISSN" : "0020-7608", "author" : [ { "dropping-particle" : "", "family" : "Lenthe", "given" : "E.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Leeuwen", "given" : "R.", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "E. J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Snijders", "given" : "J. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-4", "issue" : "3", "issued" : { "date-parts" : [ [ "1996", "2", "5" ] ] }, "page" : "281-293", "publisher" : "John Wiley & Sons, Inc.", "title" : "Relativistic regular two-component Hamiltonians", "type" : "article-journal", "volume" : "57" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[42\u201345]", "plainTextFormattedCitation" : "[42\u201345]", "previouslyFormattedCitation" : "[42\u201345]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[42–45] Spin-orbit coupling (SOC) calculations are indicated whenever they are performed. The description of the uranium centres depends on the program used: in Gaussian09, the inner uranium electrons were described with the ECP60MWBADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.466847", "ISSN" : "00219606", "abstract" : "We present nonrelativistic and quasirelativistic energy\u2010adjusted pseudopotentials, the latter augmented by spin\u2013orbit operators, as well as optimized (12s11p10d8f)/ [8s7p6d4f]\u2010Gaussian\u2010type orbitals (GTO) valence basis sets for the actinide elements actinium through lawrencium.Atomic excitation and ionizationenergies obtained by the use of these pseudopotentials and basis sets in self\u2010consistent field (SCF) calculations differ by less than 0.2 eV from corresponding finite\u2010difference all\u2010electron results. Large\u2010scale multiconfiguration self\u2010consistent field (MCSCF), multireference configuration interaction (MRCI), and multireference averaged coupled\u2010pair functional (MRACPF) calculations for thorium and thorium monoxide yield results in satisfactory agreement with available experimental data. Preliminary results from spin\u2013orbit configuration interaction calculations for the low\u2010lying electronic states of thorium monoxide are also reported.", "author" : [ { "dropping-particle" : "", "family" : "Ku\u0308chle", "given" : "W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dolg", "given" : "M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Stoll", "given" : "H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Preuss", "given" : "H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "10", "issued" : { "date-parts" : [ [ "1994" ] ] }, "page" : "7535-7542", "publisher" : "AIP Publishing", "title" : "Energy-adjusted pseudopotentials for the actinides. Parameter sets and test calculations for thorium and thorium monoxide", "type" : "article-journal", "volume" : "100" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1063/1.1521431", "ISSN" : "00219606", "abstract" : "Gaussian (14s13p10d8f6g)/[6s6p5d4f3g] atomic natural orbital valence basis sets have been generated for relativistic energy-consistent small-core actinide pseudopotentials of the Stuttgart\u2013Bonn variety. Effective valence spin\u2013orbit operators supplementing the scalar-relativistic pseudopotentials have been derived from multiconfiguration Dirac\u2013Hartree\u2013Fock reference data. Pseudopotentials, basis sets and spin\u2013orbit operators have been used to determine the first and second ionization potentials of all actinide elements at the multiconfiguration self-consistent field and multireference averaged coupled-pair functional level. Comparison is made to results obtained from large-scale calculations using uncontracted basis sets up to i -type functions and extrapolation to the basis set limit as well as to experimental data. Molecular calibration studies using the coupled-cluster singles, doubles, and perturbative triples approach are reported for the ground states of AcH, AcO, AcF, and ThO.", "author" : [ { "dropping-particle" : "", "family" : "Cao", "given" : "Xiaoyan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Stoll", "given" : "Hermann", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-2", "issue" : "2", "issued" : { "date-parts" : [ [ "2003" ] ] }, "page" : "487-496", "publisher" : "AIP Publishing", "title" : "Valence basis sets for relativistic energy-consistent small-core actinide pseudopotentials", "type" : "article-journal", "volume" : "118" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1016/j.theochem.2003.12.015", "ISSN" : "01661280", "abstract" : "Gaussian (14s13p10d8f6g)/[10s9p5d4f3g] valence basis sets using a segmented contraction scheme have been derived for relativistic energy-consistent small-core actinide pseudopotentials of the Stuttgart-K\u00f6ln variety. The present basis sets are only slightly larger than previously published (14s13p10d8f6g)/[6s6p5d4f3g] atomic natural orbital basis sets, which use a generalized contraction scheme, and achieve a similar accuracy in atomic and molecular calculations. For calibration purposes multi-configuration self-consistent field and subsequent multi-reference averaged coupled-pair functional calculations are presented for the first to fourth ionization potentials of all actinide elements. In addition, results of molecular calibration studies using the coupled-cluster singles, doubles and perturbative triples approach as well as gradient-corrected density functional theory are reported for the monohydrides, monoxides and monofluorides of actinium and lawrencium.", "author" : [ { "dropping-particle" : "", "family" : "Cao", "given" : "Xiaoyan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Molecular Structure: THEOCHEM", "id" : "ITEM-3", "issue" : "1", "issued" : { "date-parts" : [ [ "2004" ] ] }, "page" : "203-209", "title" : "Segmented contraction scheme for small-core actinide pseudopotential basis sets", "type" : "article-journal", "volume" : "673" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[61\u201363]", "plainTextFormattedCitation" : "[61\u201363]", "previouslyFormattedCitation" : "[61\u201363]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[61–63] relativistic pseudopotential, and the valence electrons with the associated segmented basis set,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.1521431", "ISSN" : "00219606", "abstract" : "Gaussian (14s13p10d8f6g)/[6s6p5d4f3g] atomic natural orbital valence basis sets have been generated for relativistic energy-consistent small-core actinide pseudopotentials of the Stuttgart\u2013Bonn variety. Effective valence spin\u2013orbit operators supplementing the scalar-relativistic pseudopotentials have been derived from multiconfiguration Dirac\u2013Hartree\u2013Fock reference data. Pseudopotentials, basis sets and spin\u2013orbit operators have been used to determine the first and second ionization potentials of all actinide elements at the multiconfiguration self-consistent field and multireference averaged coupled-pair functional level. Comparison is made to results obtained from large-scale calculations using uncontracted basis sets up to i -type functions and extrapolation to the basis set limit as well as to experimental data. Molecular calibration studies using the coupled-cluster singles, doubles, and perturbative triples approach are reported for the ground states of AcH, AcO, AcF, and ThO.", "author" : [ { "dropping-particle" : "", "family" : "Cao", "given" : "Xiaoyan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Stoll", "given" : "Hermann", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "2003" ] ] }, "page" : "487-496", "publisher" : "AIP Publishing", "title" : "Valence basis sets for relativistic energy-consistent small-core actinide pseudopotentials", "type" : "article-journal", "volume" : "118" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[62]", "plainTextFormattedCitation" : "[62]", "previouslyFormattedCitation" : "[62]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[62] while in ADF, the internal ZORA/QZ4P/U basis set was used. The choice was guided by extensive previous works on the use and effect of pseudopotentials.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp909576w", "ISSN" : "1089-5639", "abstract" : "Density functional theory (DFT) calculations using relativistic effective core potentials (RECPs) have emerged as a robust and fast method of calculating the structural parameters and energy changes of the thermochemical reactions of actinide complexes. A comparative investigation of the performance of the Stuttgart small-core and large-core RECPs in DFT calculations has been carried out. The vibrational frequencies and reaction enthalpy changes of several uranium(VI) compounds computed using these RECPs were compared to those obtained using DFT and a four-component one-electron scalar relativistic approximation of the full Dirac equation with large all-electron basis sets (AE). The relativistic AE method is a full solution of the Dirac equation with all spin components separated out. This method gives the \u201ccorrect\u201d answer (with respect to scalar relativity) which should be closest to experimental values when an adequate density functional is used and in the absence of significant spin\u2212orbit effects. The ...", "author" : [ { "dropping-particle" : "", "family" : "Odoh", "given" : "Samuel O.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "4", "issued" : { "date-parts" : [ [ "2010", "2", "4" ] ] }, "page" : "1957-1963", "publisher" : " American Chemical Society", "title" : "Performance of Relativistic Effective Core Potentials in DFT Calculations on Actinide Compounds", "type" : "article-journal", "volume" : "114" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/jp801124u", "ISSN" : "1089-5639", "abstract" : "We have investigated the performance of DFT in U(VI) chemistry. A large, representative selection of functionals has been tested, in combination with two ECPs developed in Stuttgart that have different-sized cores (60 and 78 electrons for U). In addition, several tests were undertaken with another 14 electron pseudopotential, which was developed in Los Alamos. The experimental database contained vibrational wavenumbers, thermochemical data, and 19F chemical shifts for molecules of the type UF6\u2212nCln. For the prediction of vibrational wavenumbers, the large-core RECP (14 electrons) gives results that are at least as good as those obtained with the small-core RECP (32 electrons). GGA functionals are as successful as hybrid GGA for vibrational spectroscopy; typical errors are only a few percent with the Stuttgart pseudopotentials. For thermochemistry, hybrid versions of DFT are more successful than GGA, LDA, or meta-GGA. Marginally better results are obtained with a 32 electron ECP than with 14; since the exp...", "author" : [ { "dropping-particle" : "", "family" : "Iche\u0301-Tarrat", "given" : "Nathalie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Marsden", "given" : "Colin J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "33", "issued" : { "date-parts" : [ [ "2008", "8" ] ] }, "page" : "7632-7642", "publisher" : " American Chemical Society", "title" : "Examining the Performance of DFT Methods in Uranium Chemistry: Does Core Size Matter for a Pseudopotential?", "type" : "article-journal", "volume" : "112" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1021/JP053522F", "abstract" : "The title compounds, [AnO2(H2O)5]n+, n = 1 or 2 and An = U, Np, and Pu, are studied using relativistic density functional theory (DFT). Three rather different relativistic methods are used, small-core effective core potentials (SC-ECP), a scalar four-component all-electron relativistic method, and the zeroeth-order regular approximation. The methods provide similar results for a variety of properties, giving confidence in their accuracy. Spin-orbit and multiplet corrections to the AnVI/AnV reduction potential are added in an approximate fashion but are found to be essential. Bulk solvation effects are modeled with continuum solvation models (CPCM, COSMO). These models are tested by comparing explicit (cluster), continuum, and mixed cluster/continuum solvation models as applied to various properties. The continuum solvation models are shown to accurately account for the effects of the solvent, provided that at least the first coordination sphere is included. Reoptimizing the structures in the presence of t...", "author" : [ { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-3", "issue" : "48", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "10961\u201310974", "publisher" : "American Chemical Society", "title" : "Density Functional Studies of Actinyl Aquo Complexes Studied Using Small-Core Effective Core Potentials and a Scalar Four-Component Relativistic Method", "type" : "article-journal", "volume" : "109" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[64\u201366]", "plainTextFormattedCitation" : "[64\u201366]", "previouslyFormattedCitation" : "[64\u201366]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[64–66] The lighter atoms (H, C, N, O, F, Na, Si, P, S, Cl) were described with the Dunning-type cc-pVDZADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.456153", "ISSN" : "00219606", "abstract" : "In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Alml\u00f6f, Taylor, and co\u2010workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree\u2013Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen\u2010containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Alml\u00f6f and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%\u201397% of the total (HF+1+2) correlation energy for the atoms neon through boron.", "author" : [ { "dropping-particle" : "", "family" : "Dunning", "given" : "Thom H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "1989" ] ] }, "page" : "1007-1024", "publisher" : "AIP Publishing", "title" : "Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen", "type" : "article-journal", "volume" : "90" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[67]", "plainTextFormattedCitation" : "[67]", "previouslyFormattedCitation" : "[67]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[67] basis in Gaussian09, and the iodine atoms in compounds 5 and 6 with the ECP46MWBADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "abstract" : "Quasi-relativistic energy-adjusted ab initio pseudopotentials for the elements of groups 13\u201317 up to atomic number 53 (I) are presented together with corresponding energy-optimized valence basis sets. Test calculations for atomic excitation and ionization energies show the reliability of the derived pseudopotentials and basis sets.", "author" : [ { "dropping-particle" : "", "family" : "Bergner", "given" : "Andreas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dolg", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "K\u00fcchle", "given" : "Wolfgang", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Stoll", "given" : "Hermann", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Preu\u00df", "given" : "Heinzwerner", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Molecular Physics", "id" : "ITEM-1", "issue" : "6", "issued" : { "date-parts" : [ [ "1993" ] ] }, "page" : "1431-1441", "publisher" : "Taylor & Francis Group", "title" : "Ab initio energy-adjusted pseudopotentials for elements of groups 13\u201317", "type" : "article-journal", "volume" : "80" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[68]", "plainTextFormattedCitation" : "[68]", "previouslyFormattedCitation" : "[68]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[68] relativistic pseudopotential and the associated (14s10p3d1f)/[3s3p2d1f] VTZ basis set.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.1337864", "ISSN" : "0021-9606", "abstract" : "We propose large-core correlation-consistent (cc) pseudopotential basis sets for the heavy p-block elements Ga\u2013Kr and In\u2013Xe. The basis sets are of cc-pVTZ and cc-pVQZ quality, and have been optimized for use with the large-core (valence-electrons only) Stuttgart\u2013Dresden\u2013Bonn (SDB) relativistic pseudopotentials. Validation calculations on a variety of third-row and fourth-row diatomics suggest them to be comparable in quality to the all-electron cc-pVTZ and cc-pVQZ basis sets for lighter elements. Especially the SDB-cc-pVQZ basis set in conjunction with a core polarization potential (CPP) yields excellent agreement with experiment for compounds of the later heavy p-block elements. For accurate calculations on Ga (and, to a lesser extent, Ge) compounds, explicit treatment of 13 valence electrons appears to be desirable, while it seems inevitable for In compounds. For Ga and Ge, we propose correlation consistent basis sets extended for (3d) correlation. For accurate calculations on organometallic complexes o...", "author" : [ { "dropping-particle" : "", "family" : "Martin", "given" : "Jan M. L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Sundermann", "given" : "Andreas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "8", "issued" : { "date-parts" : [ [ "2001", "2", "22" ] ] }, "page" : "3408-3420", "publisher" : "American Institute of PhysicsAIP", "title" : "Correlation consistent valence basis sets for use with the Stuttgart\u2013Dresden\u2013Bonn relativistic effective core potentials: The atoms Ga\u2013Kr and In\u2013Xe", "type" : "article-journal", "volume" : "114" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[69]", "plainTextFormattedCitation" : "[69]", "previouslyFormattedCitation" : "[69]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[69] Using an ECP28MDFADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP065887L", "abstract" : "A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X12\u03a03/2 states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core\u2212valence correlation, relativistic effects (scalar and spin\u2212orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 \u00c5 and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 \u00c5, presumably due to an underestimation of molecular spin\u2212orbit coupling effects. Spectroscopic constants for the spin\u2212orbit excited X22\u03a01/2 states are also reported for each species. The predicted...", "author" : [ { "dropping-particle" : "", "family" : "Peterson", "given" : "Kirk A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shepler", "given" : "Benjamin C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Detlev", "given" : "Figgen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Stoll", "given" : "Hermann", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "51", "issued" : { "date-parts" : [ [ "2006" ] ] }, "page" : "13877\u201313883", "publisher" : "American Chemical Society", "title" : "On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions", "type" : "article-journal", "volume" : "110" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[70]", "plainTextFormattedCitation" : "[70]", "previouslyFormattedCitation" : "[70]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[70] and the same VTZ basis set provides nearly identical molecular structures. In ADF the internal ZORA/DZP basis set with the keyword “core small” was used for the lighter atoms, and the ZORA/TZP/I basis set for iodine.All optimized geometries have been obtained using the default convergence criteria. The crystal structure was always used as input for geometry optimizations and geometries converged with a different functional were never used as starting point for problematic cases, in order to facilitate a clean comparison of the different methods. For a given functional, geometries optimized with dispersion corrections did use those structures converged without corrections as a starting point; test calculations showed, however, that using either the nonD3 structures or crystal structures as starting points yielded the same D3 geometries. No symmetry was imposed for any calculations, i.e. the C1 point group was always employed. Solvent effects were included, where required, by means of the Polarizable Continuum Model (PCM) using the default parameters as implemented in Gaussian09, specifying in each case the appropriate solvent.Explicit calculations of the Hessian to characterize the stationary points on the Potential Energy Surfaces (PES) and model the IR spectra were performed using the default convergence criteria. However, more often than not we needed to carry out a vibrational frequency calculation at an intermediate point and use these forces in subsequent calculations to achieve full convergence for the geometries. In some cases (particularly the U(III) and U(V)-U(V) compounds) this had to be repeated several times. Raman intensities were also computed using the default criteria using the same functionals and basis sets used for geometry optimizations.The performance of standard DFT methods to reproduce NMR parameters of closed-shell uranium compounds has been investigated in a subset of our molecules; the chemical shifts and spinspin coupling constants of compounds 11 – 13 were modelled using the default criteria and approaches.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/j100002a024", "ISSN" : "0022-3654", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "1995", "1" ] ] }, "page" : "606-611", "publisher" : "American Chemical Society", "title" : "Calculation of NMR Shielding Tensors Using Gauge-Including Atomic Orbitals and Modern Density Functional Theory", "type" : "article-journal", "volume" : "99" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1002/(SICI)1097-461X(1996)60:3<753::AID-QUA4>3.0.CO;2-W", "ISSN" : "0020-7608", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-2", "issue" : "3", "issued" : { "date-parts" : [ [ "1996", "11", "5" ] ] }, "page" : "753-766", "publisher" : "John Wiley & Sons, Inc.", "title" : "The calculation of NMR shielding tensors based on density functional theory and the frozen-core approximation", "type" : "article-journal", "volume" : "60" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1002/(SICI)1097-461X(1997)61:6<899::AID-QUA3>3.0.CO;2-R", "ISSN" : "0020-7608", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-3", "issue" : "6", "issued" : { "date-parts" : [ [ "1997" ] ] }, "page" : "899-918", "publisher" : "John Wiley & Sons, Inc.", "title" : "Calculation of NMR shielding tensors based on density functional theory and a scalar relativistic Pauli-type Hamiltonian. The application to transition metal complexes", "type" : "article-journal", "volume" : "61" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[71\u201373]", "plainTextFormattedCitation" : "[71\u201373]", "previouslyFormattedCitation" : "[71\u201373]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[71–73] The same set of functionals and basis sets as used for the calculation of vibrational and Raman intensities, were employed to calculate the NMR properties as well as the specialized IGLOIIADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1007/978-3-642-75932-1_3", "author" : [ { "dropping-particle" : "", "family" : "Kutzelnigg", "given" : "Werner", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Fleischer", "given" : "Ulrich", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schindler", "given" : "Michael", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "NMR Basic Principles and Progress, vol 23", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1990" ] ] }, "page" : "165-262", "publisher" : "Springer", "publisher-place" : "Berlin, Heidelberg", "title" : "The IGLO-Method: Ab-initio Calculation and Interpretation of NMR Chemical Shifts and Magnetic Susceptibilities", "type" : "chapter" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[74]", "plainTextFormattedCitation" : "[74]", "previouslyFormattedCitation" : "[74]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[74] and jcplADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/jcc.20030", "ISSN" : "0192-8651", "author" : [ { "dropping-particle" : "", "family" : "Chong", "given" : "Delano P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lenthe", "given" : "Erik", "non-dropping-particle" : "Van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gisbergen", "given" : "Stan", "non-dropping-particle" : "Van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "Evert Jan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Computational Chemistry", "id" : "ITEM-1", "issue" : "8", "issued" : { "date-parts" : [ [ "2004", "6" ] ] }, "page" : "1030-1036", "publisher" : "Wiley Subscription Services, Inc., A Wiley Company", "title" : "Even-tempered slater-type orbitals revisited: From hydrogen to krypton", "type" : "article-journal", "volume" : "25" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/ct900535d", "ISSN" : "1549-9618", "abstract" : "A benchmark study for relativistic density functional calculations of NMR spin\u2212spin coupling constants has been performed. The test set contained 47 complexes with heavy metal atoms (W, Pt, Hg, Tl, Pb) with a total of 88 coupling constants involving one or two heavy metal atoms. One-, two-, three-, and four-bond spin\u2212spin couplings have been computed at different levels of theory (nonhybrid vs hybrid DFT, scalar vs two-component relativistic). The computational model was based on geometries fully optimized at the BP/TZP scalar relativistic zeroth-order regular approximation (ZORA) and the conductor-like screening model (COSMO) to include solvent effects. The NMR computations also employed the continuum solvent model. Computations in the gas phase were performed in order to assess the importance of the solvation model. The relative median deviations between various computational models and experiment were found to range between 13% and 21%, with the highest-level computational model (hybrid density functio...", "author" : [ { "dropping-particle" : "", "family" : "Moncho", "given" : "Salvador", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Autschbach", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Chemical Theory and Computation", "id" : "ITEM-2", "issue" : "1", "issued" : { "date-parts" : [ [ "2010", "1", "12" ] ] }, "page" : "223-234", "publisher" : " American Chemical Society", "title" : "Relativistic Zeroth-Order Regular Approximation Combined with Nonhybrid and Hybrid Density Functional Theory: Performance for NMR Indirect Nuclear Spin\u2212Spin Coupling in Heavy Metal Compounds", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[75,76]", "plainTextFormattedCitation" : "[75,76]", "previouslyFormattedCitation" : "[75,76]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[75,76] basis sets in Gaussian09 and ADF, respectively. Within Gaussian09, the effect of triple- and quadrupole-ζ polarized (cc-pVTZADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.456153", "ISSN" : "00219606", "abstract" : "In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Alml\u00f6f, Taylor, and co\u2010workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree\u2013Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen\u2010containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Alml\u00f6f and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%\u201397% of the total (HF+1+2) correlation energy for the atoms neon through boron.", "author" : [ { "dropping-particle" : "", "family" : "Dunning", "given" : "Thom H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "1989" ] ] }, "page" : "1007-1024", "publisher" : "AIP Publishing", "title" : "Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen", "type" : "article-journal", "volume" : "90" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[67]", "plainTextFormattedCitation" : "[67]", "previouslyFormattedCitation" : "[67]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[67] and cc-pVQZ,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.456153", "ISSN" : "00219606", "abstract" : "In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Alml\u00f6f, Taylor, and co\u2010workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree\u2013Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen\u2010containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Alml\u00f6f and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%\u201397% of the total (HF+1+2) correlation energy for the atoms neon through boron.", "author" : [ { "dropping-particle" : "", "family" : "Dunning", "given" : "Thom H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "1989" ] ] }, "page" : "1007-1024", "publisher" : "AIP Publishing", "title" : "Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen", "type" : "article-journal", "volume" : "90" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[67]", "plainTextFormattedCitation" : "[67]", "previouslyFormattedCitation" : "[67]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[67] respectively) quality basis sets on hydrogen and carbon atoms was studied for PBE functional. We also investigate the effect of including relativistic effect via scalar ZORAADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.478680", "abstract" : "We present a new relativistic formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors. The formulation makes use of gauge-including atomic orbitals and is based on density functional theory. The relativistic effects are included by making use of the zeroth-order regular approximation. This formulation has been implemented and the 199Hg NMR shifts of HgMe2, HgMeCN, Hg(CN)2, HgMeCl, HgMeBr, HgMeI, HgCl2, HgBr2, and HgI2 have been calculated using both experimental and optimized geometries. For experimental geometries, good qualitative agreement with experiment is obtained. Quantitatively, the calculated results deviate from experiment on average by 163 ppm, which is approximately 3% of the range of 199Hg NMR. The experimental effects of an electron donating solvent on the mercury shifts have been reproduced with calculations on HgCl2(NH3)2, HgBr2(NH3)2, and HgI2(NH3)2. In addition, it is shown that the mercury NMR shieldings are sensitive to geometry with changes for HgCl2 of a...", "author" : [ { "dropping-particle" : "", "family" : "Wolff", "given" : "S. K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "T.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "van", "family" : "Lenthe", "given" : "E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "E. J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "16", "issued" : { "date-parts" : [ [ "1999" ] ] }, "page" : "7689-7698", "publisher" : "American Institute of Physics", "title" : "Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance", "type" : "article-journal", "volume" : "110" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[77]", "plainTextFormattedCitation" : "[77]", "previouslyFormattedCitation" : "[77]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[77] or ZORA + SOCADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.476630", "abstract" : "A formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors, based on density functional theory (DFT), is presented. Scalar-relativistic and spin-orbit coupling effects are taken into account, and a Fermi-contact term is included in the NMR shielding tensor expression. Gauge-including atomic orbitals (GIAO) and a frozen-core approximation are used. This formulation has been implemented, and 1H and 13C NMR shifts of hydrogen and methyl halides have been calculated and show good agreement with experiment. 13C NMR shifts of 5d transition metal carbonyls have been calculated and show improved agreement with experiment over previous scalar-relativistic calculations. For the metal carbonyls it is shown explicitly that the combination of spin-orbit coupling and magnetic field mixes spin triplet states into the ground state, inducing a spin density that then interacts with the nuclei of the metal carbonyl via the Fermi-contact term. Results indicate that the Fermi-contact contribution ...", "author" : [ { "dropping-particle" : "", "family" : "Wolff", "given" : "S. K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "T.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "3", "issued" : { "date-parts" : [ [ "1998" ] ] }, "page" : "895-907", "publisher" : "American Institute of Physics", "title" : "Calculation of DFT-GIAO NMR shifts with the inclusion of spin-orbit coupling", "type" : "article-journal", "volume" : "109" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[78]", "plainTextFormattedCitation" : "[78]", "previouslyFormattedCitation" : "[78]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[78] in ADF2016.Time dependent DFT was employed to model UV-vis spectra of compounds 10, 11 and 13 – 15, using the default criteria. Given that they are all closed-shell molecules, only singlet-singlet excitations were computed. In addition to the standard functionals, CAMB3LYP was also investigated, in all cases using the same basis sets as for the geometry optimizations. For [UO2Cl4]2- and compound 14, the effect of diffuse functions was also investigated by using aug-cc-pVDZADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.464303", "ISSN" : "0021-9606", "abstract" : "Correlation consistent and augmented correlation consistent basis sets have been determined for the second row atoms aluminum through argon. The methodology, originally developed for the first row atoms [T. H. Dunning, Jr., J. Chem. Phys. 90, (1989)] is first applied to sulfur. The exponents for the polarization functions (dfgh) are systematically optimized for a correlated wave function (HF+1+2). The (sp) correlation functions are taken from the appropriate HF primitive sets; it is shown that these functions differ little from the optimum functions. Basis sets of double zeta [4s3p1d], triple zeta [5s4p2d1f], and quadruple zeta [6s5p3d2f1g] quality are defined. Each of these sets is then augmented with diffuse functions to better describe electron affinities and other molecular properties: s and p functions were obtained by optimization for the anion HF energy, while an additional polarization function for each symmetry present in the standard set was optimized for the anion HF+1+2 energy. The results for...", "author" : [ { "dropping-particle" : "", "family" : "Woon", "given" : "David E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dunning", "given" : "Thom H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "1993", "1", "15" ] ] }, "page" : "1358-1371", "publisher" : "American Institute of Physics", "title" : "Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon", "type" : "article-journal", "volume" : "98" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[79]", "plainTextFormattedCitation" : "[79]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[79] for light atoms. REF _Ref475365656 \h \* MERGEFORMAT Table 1 presents the approaches that have been followed to model each of the experimentally available data types, depending on whether or not the uranium centre has any unpaired electrons, i.e. the closed-shell U(VI) complexes (10 – 16) and the (open-shell) molecules (1 – 9, 17, 18).Compounds 10 – 16Compounds 1 – 9, 17, 18XRD – IR – RamanNMRUV-visXRD – IR – RamanProgram / Method / Basis setGaussian /DFT /Dunning-ECPGaussian /DFT /Dunning-ECPGaussian /TD-DFT /Dunning-ECPGaussian /DFT /Dunning-ECPGaussian /DFT /IGLOII-ECPADF /DFT /Slater-scalar ZORAADF /DFT /Slater-scalar ZORAADF /TD-DFT /Slater- scalar ZORAADF /DFT /Slater-scalar ZORAADF /DFT /Slater-spin orbit ZORATable SEQ Table \* ARABIC 1. Summary of employed computational approaches depending on the experimental data being modelled.The Computational Shared Facility of The University of Manchester was employed to carry out all of the calculations here discussed. MatplotlibADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1109/MCSE.2007.55", "ISSN" : "1521-9615", "author" : [ { "dropping-particle" : "", "family" : "Hunter", "given" : "John D.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Computing in Science & Engineering", "id" : "ITEM-1", "issue" : "3", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "90-95", "publisher" : "AIP Publishing", "title" : "Matplotlib: A 2D Graphics Environment", "type" : "article-journal", "volume" : "9" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[80]", "plainTextFormattedCitation" : "[80]", "previouslyFormattedCitation" : "[79]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[80] and Python2.7 were used to display the data. The graphical program Inkscape was used to compile the figures.Results and discussion Molecular geometriesAll the compounds shown in REF _Ref457550072 \h \* MERGEFORMAT Figure 1 have a well-established molecular geometry obtained from Xray diffraction (XRD) experiments. The agreement between these data and the predicted geometries obtained computationally has been addressed using the Root-Mean-Square Deviation (RMSD) between the two sets of atomic positions (excluding hydrogen atoms). This value (in ?) measures the average distance between corresponding pairs of atoms in the optimized and experimental structures. In order to ensure that the rotation applied to superimpose the two structures yields the lowest possible RMSD value, we follow the algorithm proposed by KabschADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1107/S0567739476001873", "ISSN" : "0567-7394", "abstract" : "A simple procedure is derived which determines a best rotation of a given vector set into a second vector set by minimizing the weighted sum of squared deviations. The method is generalized for any given metric constraint on the transformation.", "author" : [ { "dropping-particle" : "", "family" : "Kabsch", "given" : "W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "IUCr", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Acta Crystallographica Section A", "id" : "ITEM-1", "issue" : "5", "issued" : { "date-parts" : [ [ "1976", "9", "1" ] ] }, "page" : "922-923", "publisher" : "International Union of Crystallography", "title" : "A solution for the best rotation to relate two sets of vectors", "type" : "article-journal", "volume" : "32" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1107/S0567739478001680", "ISSN" : "0567-7394", "abstract" : "A method is discussed for obtaining the best proper rotation to relate two sets of vectors.", "author" : [ { "dropping-particle" : "", "family" : "Kabsch", "given" : "W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "IUCr", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Acta Crystallographica Section A", "id" : "ITEM-2", "issue" : "5", "issued" : { "date-parts" : [ [ "1978", "9", "1" ] ] }, "page" : "827-828", "publisher" : "International Union of Crystallography", "title" : "A discussion of the solution for the best rotation to relate two sets of vectors", "type" : "article-journal", "volume" : "34" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[81,82]", "plainTextFormattedCitation" : "[81,82]", "previouslyFormattedCitation" : "[80,81]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[81,82] and implemented by Kroman and Bratholm.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.5281/zenodo.46697", "author" : [ { "dropping-particle" : "", "family" : "Kroman", "given" : "J. C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bratholm", "given" : "A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2016" ] ] }, "number" : "GitHub: Calculate RMSD for two XYZ structures", "page" : "", "title" : "GitHub: Calculate RMSD for two XYZ structures", "type" : "article" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[83]", "plainTextFormattedCitation" : "[83]", "previouslyFormattedCitation" : "[82]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[83] Thus, the smaller the RMSD value, the more similar are the optimized and experimental structures.Geometry optimizations using a pseudopotential for the uranium centres were carried out using the PBE, PBE0, TPSS, TPSSh, B3LYP and LCωPBE functionals within the Gaussian09 program. PBE calculations were also carried out using Slater all-electron basis sets and scalar ZORA relativistic corrections within the ADF2016 code. Additionally, each calculation was carried out including Grimme’s D3 dispersion corrections (indicated by the suffix -D3). For all cases, we explicitly calculated the Hessian to ensure that all frequencies are real and that the forces are zero, to ensure that we located a stationary minimum. For each compound, this results in 11 optimized structures obtained using a pseudopotential (note that Grimme parameters are not defined for the TPSSh functional in Gaussian09) and 2 optimized structures obtained using Slater basis sets and the ZORA Hamiltonian. This yields a maximum of 234 possible optimized structures considering both approaches. Detailed information on the performance of both approaches, indicating whether they converged properly or not (and the reason) depending on the functional used and compound studied can be found in Table SI 1 and Table SI 2 of section 1 of the SI. Summarising, with Gaussian09 we were able to obtain 148 correctly converged results out of the 198 possible structures (75%). For ADF, of the possible 36 optimized structures, 29 (80%) structures converged correctly. Therefore, a total of 177 out of 234 structures (76%) were characterized as stationary points on their potential energy surfaces. REF _Ref457993826 \h \* MERGEFORMAT Figure 2 presents the RMSD values for the 18 compounds as determined by Gaussian09; the closer the data point lies to the middle of the figure, the better the agreement between theory and experiment. Note that not all compounds have data for all functionals, compound 10 being the most extreme case as no structure was converged. It is worth noting that this is not the case for compound 9, despite the similarity between them. Only for half of the compounds (4 – 6 and 11 – 16) did all functionals provide a converged structure. For the rest of them, the most common behaviour is a generally good convergence with PBE and TPSSh, a less efficient performance for PBE0, TPSS and B3LYP and a persistent failure of LC-ωPBE. This reveals that the computational description of the structural features in these compounds is sensitive to characteristics such as oxidation state and charge. A similar plot to REF _Ref457993826 \h \* MERGEFORMAT Figure 2 obtained using Slater basis set and ZORA Hamiltonian, can be found in Figure SI 1 of section 2 of the SI. A comparison between the two figures indicates that the use of pseudopotentials for the uranium atoms provides very similar results to those obtained with all electron basis sets.Figure SEQ Figure \* ARABIC 2. Polar plot of structural differences (RMSD values in ?) between the XRD and DFTcomputed structures for the 18 investigated compounds, as obtained with the chosen functionals using Gaussian09. The suffix “-D3” after the employed functional indicates the use of Grimme dispersion corrections for the optimization of the geometries.A general conclusion from REF _Ref457993826 \h \* MERGEFORMAT Figure 2 is that the performance across all the different compounds with the six density functionals is in reasonable agreement with experiment, rarely exceeding an RMSD of 0.6 ?. In fact, the mean and standard deviation for all 177 results is 0.3±0.2 ?. Also, for a given compound, the converged structures generally lie in a narrow range of RMSD values. This is not the case for compounds 2 and 5, for which the RMSD values are considerably dispersed. Apart from compound 10, compounds 1 – 3 were the most difficult to converge, especially compound 3 for which only the TPSSh functional provided a true minimum. Of similar difficulty is compound 18; attempts to locate a stationary point were unsuccessful with any functional other than the pure exchange PBE, in either singlet or triplet multiplicities. As already noted, compound 10 is the most problematic case, as no converged structure was obtained using a pseudopotential. However, all-electron basis set calculations did provide converged structures with RMSD values around 0.25 ? (see Figure SI 1 of section 2 of the SI). In general it seems that there is no pattern to the performance of the various methods that can be associated with a particular oxidation state or molecular charge. REF _Ref459026275 \h \* MERGEFORMAT Figure 3a and b present the RMSD values (in ?) as a function of the employed functional rather than as a function of the compound investigated, aiming to highlight the different performance of each functional. In REF _Ref459026275 \h \* MERGEFORMAT Figure 3a the order of the compounds and the colour assignment for the oxidation states are the same as in REF _Ref457550072 \h \* MERGEFORMAT Figure 1 and REF _Ref457993826 \h \* MERGEFORMAT Figure 2. In REF _Ref459026275 \h \* MERGEFORMAT Figure 3b the numbers appearing beneath the functional indicate the number of stationary points located with it. These complementary plots reveal that: i) the inclusion of dispersion corrections systematically reduces the range of RMSD values, as found in previous worksADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/om500624x", "ISSN" : "0276-7333", "abstract" : "The challenge of differentiating the chemistry of two closely related Lewis acidic metals in heterobimetallic complexes was addressed by studying hydrogenolysis and C\u2013H bond activation reactions of bimetallic rare-earth hydride complexes. Hydrogenolysis of equimolar amounts of Cp*2Lu(\u03b73-C3H5) (1-Lu) and Cp*2Y(\u03b73-C3H5) (1-Y) (Cp* = C5Me5) forms a mixture of hydride complexes, the heterobimetallic compound Cp*2Lu(H)2YCp*2 (2-Lu/Y) and the homobimetallic compounds (Cp*2LuH)2 (2-Lu/Lu) and (Cp*2YH)2 (2-Y/Y). This mixture can be analyzed and differentiated by 1H NMR spectroscopy due to the I = 1/2 89Y nucleus to reveal these three products in a ratio of approximately 86:10:4, respectively. Heating this mixture leads to C\u2013H bond activation and formation of tuckover hydride complexes, the heterobimetallic compounds Cp*2Y(\u03bc-H)(\u03bc-\u03b71:\u03b75-CH2C5Me4)LuCp* (3-Y/Lu) and Cp*2Lu(\u03bc-H)(\u03bc-\u03b71:\u03b75-CH2C5Me4)YCp* (3-Lu/Y) and the homobimetallic compounds Cp*2Lu(\u03bc-H)(\u03bc-\u03b71:\u03b75-CH2C5Me4)LuCp* (3-Lu/Lu) and Cp*2Y(\u03bc-H)(\u03bc-\u03b71:\u03b75-CH2C5Me4)...", "author" : [ { "dropping-particle" : "", "family" : "Fieser", "given" : "Megan E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mueller", "given" : "Thomas J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bates", "given" : "Jefferson E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziller", "given" : "Joseph W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Furche", "given" : "Filipp", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Evans", "given" : "William J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Organometallics", "id" : "ITEM-1", "issue" : "14", "issued" : { "date-parts" : [ [ "2014", "7", "28" ] ] }, "page" : "3882-3890", "publisher" : "American Chemical Society", "title" : "Differentiating Chemically Similar Lewis Acid Sites in Heterobimetallic Complexes: The Rare-Earth Bridged Hydride (C ₅ Me ₅ ) ₂ Ln(\u03bc-H) ₂ Ln\u2032(C ₅ Me ₅ ) ₂ and Tuckover Hydride (C ₅ Me ₅ ) ₂ Ln(\u03bc-H)(\u03bc-\u03b7 ¹ :\u03b7 ⁵ -CH ₂ C ₅ Me ₄ )Ln\u2032(C ₅ Me ₅ ) Systems", "type" : "article-journal", "volume" : "33" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/ic300029d", "ISSN" : "0020-1669", "abstract" : "The pentagonal K10[(UO2)5(\u03bc-O2)5(C2O4)5] species have been identified as the building blocks of uranyl-peroxide nanocapsules. The computed complexation energies of different alkali cations (Li+, Na+, K+, Rb+, and Cs+) with [(UO2)5(\u03bc-O2)5(O2)5]10\u2013 and [(UO2)20(\u03bc-O2)30]20\u2013 species suggest a strong cation templating effect. In the studied species, the largest complexation energy occurs for the experimentally used alkali cations (Na+ and K+).", "author" : [ { "dropping-particle" : "", "family" : "Miro", "given" : "Pere", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bo", "given" : "Carles", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-2", "issue" : "6", "issued" : { "date-parts" : [ [ "2012", "3", "19" ] ] }, "page" : "3840-3845", "publisher" : "American Chemical Society", "title" : "Uranyl-Peroxide Nanocapsules: Electronic Structure and Cation Complexation in [(UO ₂ ) ₂₀ (\u03bc-O ₂ ) ₃₀ ] ^20\u2013", "type" : "article-journal", "volume" : "51" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1016/j.inoche.2013.09.020", "ISSN" : "13877003", "abstract" : "Geometry and bonding energy analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}] were investigated with the DFT, DFT-D3 and DFT-D3(BJ) methods using density functionals (BLYP, BP86, PW91, PBE, revPBE and TPSS). The BLYP functional yields a UN bond distance of 1.788\u00c5 for the model complex [NU{N(CH2CH2NSiMe3)3}] which is in close agreement with the experimental value of the UN bond distance of 1.799(7) \u00c5 for [NU{N(CH2CH2NSiiPr3)3}]. The calculated Mayer bond order (2.95) and Gopinathan\u2013Jug bond order (3.18) indicate that the UN bond in this complex is essentially UN triple bonds. The electrostatic interaction is significantly smaller than the covalent bonding. The bond dissociation energy (BDE) is largest for the functional PBE and smallest for the functional TPSS. The DFT-D3 dispersion corrections are 5.3kcal/mol (BLYP) and 5.0kcal/mol (TPSS).", "author" : [ { "dropping-particle" : "", "family" : "Pandey", "given" : "Krishna K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry Communications", "id" : "ITEM-3", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "4-6", "title" : "The effect of density functional and dispersion interaction on structure and bonding analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}]: A theoretical study", "type" : "article-journal", "volume" : "37" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[18,84,85]", "plainTextFormattedCitation" : "[18,84,85]", "previouslyFormattedCitation" : "[18,83,84]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[18,84,85] ii) that the PBE functional provides the most robust (larger number of converged structures) and consistent approach (narrower range of RMSD values centred on ~0.3 ?) for describing the molecular structures, iii) the B3LYP results are similar to those obtained with PBE, but the number of converged structures is smaller, iv) PBE0 and LC-ωPBE have the smallest number of converged structures (and those obtained with PBE0 have a much smaller spread than the ones associated with LC-ωPBE), and v) TPSS, TPSSh and LC-ωPBE yield the most widely distributed sets of results.Finally, solvent effects were included for the PBE functional within Gaussian09, as presented in Table SI 3 in section 1 of the SI. The generally small RMSD values between gasphase and solution geometries across the series of compounds allows us to conclude that the inclusion of a solvent model for structural optimization does not greatly impact the comparison with XRD data, for the investigated compounds. Thus, implicit solvent effects will not be discussed any further. However, it should be noted that for aqueous uranyl(VI), the combination of explicit water molecules in the first coordination sphere with PCM solvation has previously produced results in better agreement with experiment.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP000519H", "abstract" : "The structures and vibrational frequencies of UO2(H2O)52+, NpO2(H2O)52+, and PuO2(H2O)52+ corresponding to An(VI) oxidation states and UO2(H2O)5+, Np(H2O)5+, and Pu(H2O)5+ corresponding to An(V) have been calculated using density functional theory (DFT) and relativistic effective core potentials (RECPs). The resulting structures are compared to EXAFS solution studies, and the Raman and IR vibrational frequencies of the actinyl unit are compared to experimental studies in solution. Free energies for reactions in solution are computed by combining thermodynamic free energies in the gas phase with a dielectric continuum model to treat solvent effects. The hydrolysis reaction of UO2(H2O)52+ to form UO2(H2O)4(OH)+ and the reactions for removing or adding a water to the first shell in UO2(H2O)52+ are examined using this approach. Multiplet and spin\u2212orbit effects not included in a single-configuration DFT wave function are incorporated by model spin\u2212orbit CI calculations. PuO2q+ is used as a model for the aquo c...", "author" : [ { "dropping-particle" : "", "family" : "Hay", "given" : "P. Jeffrey", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Martin", "given" : "Richard L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "26", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "6259\u20136270", "publisher" : "American Chemical Society", "title" : "Theoretical Studies of the Properties and Solution Chemistry of AnO22+ and AnO2+ Aquo Complexes for An = U, Np, and Pu", "type" : "article-journal", "volume" : "104" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/IC035450H", "abstract" : "We have studied the solvation of uranyl, UO22+, and the reduced species UO(OH)2+ and U(OH)22+ systematically using three levels of approximation:\u2009 direct application of a continuum model (M1); explicit quantum-chemical treatment of the first hydration sphere (M2); a combined quantum-chemical/continuum model approach (M3). We have optimized complexes with varying numbers of aquo ligands (n = 4\u22126) and compared their free energies of solvation. Models M1 and M2 have been found to recover the solvation energy only partially, underestimating it by \u223c100 kcal/mol or more. With our best model M3, the calculated hydration free energy \u0394hG\u00b0 of UO22+ is about \u2212420 kcal/mol, which shifts to about \u2212370 kcal/mol when corrected for the expected error of the model. This value agrees well with the experimentally determined interval, \u2212437 kcal/mol < \u0394hG\u00b0 < \u2212318 kcal/mol. Complexes with 5 and 6 aquo ligands have been found to be about equally favored with models M2 and M3. The same solvation models have been applied to a two...", "author" : [ { "dropping-particle" : "V.", "family" : "Moskaleva", "given" : "Lyudmila", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kr\u00fcger", "given" : "Sven", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Sp\u00f6rl", "given" : "Andreas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "R\u00f6sch", "given" : "Notker", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-2", "issue" : "13", "issued" : { "date-parts" : [ [ "2004" ] ] }, "page" : "4080-4090", "publisher" : "American Chemical Society", "title" : "Role of Solvation in the Reduction of the Uranyl Dication by Water:\u2009 A Density Functional Study", "type" : "article-journal", "volume" : "43" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1021/JP061851H", "abstract" : "The structures and vibrational frequencies of UO2(H2O)42+ and UO2(H2O)52+ have been calculated using density functional theory and are in reasonable agreement with experiment. The energies of various reactions were calculated at the density functional theory (DFT) and MP2 levels; the latter provides the best results. Self-consistent reaction field calculations in the PCM and SCIPCM approximations predicted the free energy of the water exchange reaction, UO2(H2O)42+ + H2O \u2194 UO2(H2O)52+. The calculated free energies of reaction are very sensitive to the choice of radii (O and H) and isodensity values in the PCM and SCIPCM models, respectively. Results consistent with the experimental HEXS value of \u22121.19 \u00b1 0.42 kcal/mol (within 1\u22123 kcal/mol) are obtained with small cavities. The structures and vibrational frequencies of the clusters with second solvation shell waters:\u2009 UO2(H2O)4(H2O)82+, UO2(H2O)4(H2O)102+, UO2(H2O)4(H2O)112+, UO2(H2O)5(H2O)72+, and UO2(H2O)5(H2O)102+, were calculated and are in better agree...", "author" : [ { "dropping-particle" : "", "family" : "Gutowski", "given" : "Keith E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dixon", "given" : "David. A", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-3", "issue" : "28", "issued" : { "date-parts" : [ [ "2006" ] ] }, "page" : "8840\u20138856", "publisher" : "American Chemical Society", "title" : "Predicting the Energy of the Water Exchange Reaction and Free Energy of Solvation for the Uranyl Ion in Aqueous Solution", "type" : "article-journal", "volume" : "110" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1021/ar800271r", "ISSN" : "0001-4842", "abstract" : "Interest in the chemistry of the early actinide elements (notably uranium through americium) usually results either from the nuclear waste problem or the unique chemistry of these elements that result from 5f contributions to bonding. Computational actinide chemistry provides one useful tool for studying these processes. Theoretical actinide chemistry is challenging because three principal axes of approximation have to be optimized. These are the model chemistry (the choice of approximate electron\u2212electron correlation method and basis sets), the approximate relativistic method, and a method for modeling solvent (condensed phase) effects. In this Account, we arrange these approximations in a three-dimensional diagram, implying that they are relatively independent of each other. A fourth level of approximation concerns the choice of suitable models for situations too complex to treat in their entirety. We discuss test cases for each of these approximations. Gas-phase data for uranium fluorides and oxofluori...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Accounts of Chemical Research", "id" : "ITEM-4", "issue" : "1", "issued" : { "date-parts" : [ [ "2010", "1", "19" ] ] }, "page" : "19-29", "publisher" : " American Chemical Society", "title" : "Theoretical Actinide Molecular Science", "type" : "article-journal", "volume" : "43" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[86\u201389]", "plainTextFormattedCitation" : "[86\u201389]", "previouslyFormattedCitation" : "[85\u201388]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[86–89]Figure SEQ Figure \* ARABIC 3. RMSD values (?) between XRD and DFTcomputed structures, as given by the different functionals used. Note that PBE was used in both the Gaussian09 and ADF programs a) Bar plot of RMSD values at the optimized geometries obtained without (o, ?) or with (?, *) dispersion corrections, respectively. b) Polar plot of RMSD values for each functional employed. Beneath each functional the number of converged structures is indicated. Note that the maximum possible number is 18, except for PBE for which it is 36.In summary, our recommendation is that the most robust approach to obtain reliable geometries is to employ the PBE functional with dispersion corrections, and to use a pseudopotential to account for scalar relativistic effects (as such calculations are typically less computationally demanding than all-electron calculations with a relativistic Hamiltonian, provided that all other parameters (system size, code, machine etc) are similar.Infra-red and Raman spectraFor each of the geometries obtained, calculation of analytical Hessians and hence vibrational frequencies was performed at the stationary point. REF _Ref459044970 \h \* MERGEFORMAT Figure 4 presents the IR spectra obtained for compound 1 and exemplifies the very similar plots produced for the rest of the compounds, to be found in section 3 of the SI (Figures SI 2-15). These plots consist of three subplots, presenting the same data in different ways so as to facilitate their interpretation. The upper left subplot introduces all the IR spectra overlapped, while the upper right subplot splits those and presents them in two groups; the ones obtained without the inclusion of dispersion corrections and the ones with them. It also includes the most relevant signals obtained experimentally. Finally, the lower subplots present the separated IR spectra according to the functional used. Obviously, the functionals that failed to provide a converged geometry do not have IR spectra. Figure SEQ Figure \* ARABIC 4. Comparison of IR spectra obtained with the investigated functionals using Gaussian09 for compound 1. Similar plots can be found in section 3 of the SI for the rest of the molecules. Upper left plot shows all obtained IR overlapped. Upper right plot is split in two to see the influence of including dispersion corrections (suffix “-D3”) and presents the experimental signals (and corresponding height) (weak, medium, strong and very strong) as vertical lines. Lower figure compares each functional; blank boxes highlight for which functionals it proved impossible to obtain converged geometries.The IR spectra do not depend strongly on the choice of functional, which agrees with previous studies on model actinide compounds,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp801124u", "ISSN" : "1089-5639", "abstract" : "We have investigated the performance of DFT in U(VI) chemistry. A large, representative selection of functionals has been tested, in combination with two ECPs developed in Stuttgart that have different-sized cores (60 and 78 electrons for U). In addition, several tests were undertaken with another 14 electron pseudopotential, which was developed in Los Alamos. The experimental database contained vibrational wavenumbers, thermochemical data, and 19F chemical shifts for molecules of the type UF6\u2212nCln. For the prediction of vibrational wavenumbers, the large-core RECP (14 electrons) gives results that are at least as good as those obtained with the small-core RECP (32 electrons). GGA functionals are as successful as hybrid GGA for vibrational spectroscopy; typical errors are only a few percent with the Stuttgart pseudopotentials. For thermochemistry, hybrid versions of DFT are more successful than GGA, LDA, or meta-GGA. Marginally better results are obtained with a 32 electron ECP than with 14; since the exp...", "author" : [ { "dropping-particle" : "", "family" : "Iche\u0301-Tarrat", "given" : "Nathalie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Marsden", "given" : "Colin J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "33", "issued" : { "date-parts" : [ [ "2008", "8" ] ] }, "page" : "7632-7642", "publisher" : " American Chemical Society", "title" : "Examining the Performance of DFT Methods in Uranium Chemistry: Does Core Size Matter for a Pseudopotential?", "type" : "article-journal", "volume" : "112" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[65]", "plainTextFormattedCitation" : "[65]", "previouslyFormattedCitation" : "[65]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[65] and extends the conclusion to long-range corrected functionals. Note, however, that for those model compounds, other studies conclude that GGA functionals provide better geometries and IR frequencies than hybrid counterparts.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/ar800271r", "ISSN" : "0001-4842", "abstract" : "Interest in the chemistry of the early actinide elements (notably uranium through americium) usually results either from the nuclear waste problem or the unique chemistry of these elements that result from 5f contributions to bonding. Computational actinide chemistry provides one useful tool for studying these processes. Theoretical actinide chemistry is challenging because three principal axes of approximation have to be optimized. These are the model chemistry (the choice of approximate electron\u2212electron correlation method and basis sets), the approximate relativistic method, and a method for modeling solvent (condensed phase) effects. In this Account, we arrange these approximations in a three-dimensional diagram, implying that they are relatively independent of each other. A fourth level of approximation concerns the choice of suitable models for situations too complex to treat in their entirety. We discuss test cases for each of these approximations. Gas-phase data for uranium fluorides and oxofluori...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Accounts of Chemical Research", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2010", "1", "19" ] ] }, "page" : "19-29", "publisher" : " American Chemical Society", "title" : "Theoretical Actinide Molecular Science", "type" : "article-journal", "volume" : "43" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/JP012301G", "abstract" : "In this paper, we present a theoretical investigation of structural and vibrational properties of selected gas-phase UX3 (X = F, Cl, Br, and I) and U(CH3)3 molecules by density functional methodologies or with a post Hartree\u2212Fock MP2 perturbative approach. Relativistic scalar corrections have been explicitly included either by a frozen core approximation with a quasi-relativistic treatment (QR) of the valence electron shells or by energy-adjusted large core quasi-relativistic effective core potential (QRECP) scheme. The influence of the size of the core (large core, LC, or small core, SC) as well as of the addition of polarization functions has also been examined on one derivative, i.e., UCl3. MP2/LC-QRECP optimized geometries and vibrational frequencies are found in good agreement with the available estimated or experimental data. Among the different DFT approaches, the best agreement is obtained for DFT/QR computations which reproduce the experimental (or estimated) C3v molecular structures of all the s...", "author" : [ { "dropping-particle" : "", "family" : "Joubert", "given" : "Laurent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Maldivi", "given" : "Pascale", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "39", "issued" : { "date-parts" : [ [ "2001" ] ] }, "page" : "9068\u20139076", "publisher" : "American Chemical Society", "title" : "A Structural and Vibrational Study of Uranium(III) Molecules by Density Functional Methods", "type" : "article-journal", "volume" : "105" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1002/chem.200601244", "ISSN" : "09476539", "author" : [ { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vo", "given" : "Thach N.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Eur. J.", "id" : "ITEM-3", "issue" : "17", "issued" : { "date-parts" : [ [ "2007", "6", "4" ] ] }, "page" : "4932-4947", "publisher" : "WILEY\u2010VCH Verlag", "title" : "A Comparative Relativistic DFT and Ab Initio Study on the Structure and Thermodynamics of the Oxofluorides of Uranium(IV), (V) and (VI)", "type" : "article-journal", "volume" : "13" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1021/JP053522F", "abstract" : "The title compounds, [AnO2(H2O)5]n+, n = 1 or 2 and An = U, Np, and Pu, are studied using relativistic density functional theory (DFT). Three rather different relativistic methods are used, small-core effective core potentials (SC-ECP), a scalar four-component all-electron relativistic method, and the zeroeth-order regular approximation. The methods provide similar results for a variety of properties, giving confidence in their accuracy. Spin-orbit and multiplet corrections to the AnVI/AnV reduction potential are added in an approximate fashion but are found to be essential. Bulk solvation effects are modeled with continuum solvation models (CPCM, COSMO). These models are tested by comparing explicit (cluster), continuum, and mixed cluster/continuum solvation models as applied to various properties. The continuum solvation models are shown to accurately account for the effects of the solvent, provided that at least the first coordination sphere is included. Reoptimizing the structures in the presence of t...", "author" : [ { "dropping-particle" : "", "family" : "Shamov", "given" : "Grigory A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-4", "issue" : "48", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "10961\u201310974", "publisher" : "American Chemical Society", "title" : "Density Functional Studies of Actinyl Aquo Complexes Studied Using Small-Core Effective Core Potentials and a Scalar Four-Component Relativistic Method", "type" : "article-journal", "volume" : "109" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[66,89\u201391]", "plainTextFormattedCitation" : "[66,89\u201391]", "previouslyFormattedCitation" : "[66,88\u201390]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[66,89–91] For our results, differences in the principal features are barely distinguishable between the different functionals. This is not unexpected given the similarities of the geometries obtained from the different functionals; the RMSD values between the computed structures rarely exceed 0.2 ?, although in the worst case scenarios such as TPSS vs PBE for compound 2 and TPSSh vs B3LYP for compound 5, the corresponding RMSD values are rather larger, 1.06 and 0.61 ?, respectively. If one checks the influence on the predicted IR spectra, it is very minor.When comparing predicted and computed spectra, a general observation is that for all functionals investigated, the lower energy region (from 0 to ~750 cm-1) is described more poorly vs experiment than other energetic regions. As a specific example, let us consider compound 1 ( REF _Ref459044970 \h \* MERGEFORMAT Figure 4) to further discuss specific features. The most significant vibrational modes associated with the U-N-Si2 stretching are well captured by all functionals, although the most energetic experimental vibrational modes have intensities which are underestimated by all functionals. Above ~3000 cm-1, the lack of experimental data prevents addressing how meaningful the predicted features are, by contrast to compound 2 (Figure SI 3). Compound 5 (Figure SI 5) displays the most significant differences between computed spectra; notably, PBE functional predicts an intense peak at ~1500 cm-1, which matches very well with the experimental value. Finally, for compounds 11 and 13, the computed frequencies are generally overestimated (in wavenumber) with respect to experiment. We conclude that as different approaches provide very similar IR spectra, the PBE functional appears the best choice because of its reliability in obtaining molecular structures. This supports earlier studies on U(VI) complexes which concluded that relativistic DFT is a robust approach for geometries and IR spectra,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/(SICI)1096-987X(19990115)20:1<70::AID-JCC9>3.0.CO;2-F", "ISSN" : "0192-8651", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hay", "given" : "P. Jeffrey", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Martin", "given" : "Richard L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Computational Chemistry", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "1999", "1", "15" ] ] }, "page" : "70-90", "publisher" : "John Wiley & Sons, Inc.", "title" : "Density functional calculations on actinide compounds: Survey of recent progress and application to [UO2X4]2- (X=F, Cl, OH) and AnF6 (An=U, Np, Pu)", "type" : "article-journal", "volume" : "20" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/IC980057A", "abstract" : "The title compound, uranyl(VI) tetrahydroxide [UO2(OH)4]2-, has been studied in detail using density functional theory (DFT) in the first systematic theoretical study of the compound. Scalar relativistic effects are included approximately by replacing the uranium core with a relativistic effective core potential. A total of nine stable structures have been characterized. Four of them (I\u2212IV) possess the usual linear uranyl bond, and rapid exchange between these conformations is expected at finite temperatures. The uranyl and U\u2212OH bond lengths of the minimum energy structure, I, are calculated as 1.842 and 2.334 \u00c5, respectively. This compares well with the experimental crystal structure values of 1.824(3) \u00c5 and 2.258(3) \u00c5, respectively. The existence of stable structures with a bent uranyl bond (\u201ccis-uranyl\u201d) is predicted for the first time (structures V\u2212IX). These conformers are only 18\u221219 kcal/mol higher in energy than the global energy minimum, and their uranyl bond angles cover a range of 113\u2212132\u00b0. Harm...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hay", "given" : "P. Jeffrey", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Martin", "given" : "Richard L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-2", "issue" : "17", "issued" : { "date-parts" : [ [ "1998" ] ] }, "page" : "4442\u20134451", "publisher" : "American Chemical Society", "title" : "Theoretical Study of Stable Trans and Cis Isomers in [UO2(OH)4]2- Using Relativistic Density Functional Theory", "type" : "article-journal", "volume" : "37" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1021/IC9910615", "abstract" : "The title compounds, the uranium (VI) fluoride chlorides (UF6-nCln, n = 0\u22126) and methoxyuranium (VI) fluorides [UF6-n(OCH3)n, n = 0\u22125], have been studied using relativistic density functional theory. Applying the B3LYP hybrid functional and an effective core potential on uranium, equilibrium geometries have been calculated for these molecules. In addition, harmonic vibrational frequencies have been computed for the chloride fluorides. Calculated frequencies have been compared to experiment where possible. All experimentally observed bands have been assigned, based on these calculations. The average deviation between theoretical and experimental frequencies is 15.6 cm-1 for 23 experimental modes. Theory always underestimates the experimental frequencies. This can be explained by the calculated bond lengths that are somewhat too long. The electronic structure of the uranium (VI) chloride fluorides has been investigated using scalar relativistic calculations and the PW91 functional. Periodic trends in the ro...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-3", "issue" : "6", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "1265\u20131274", "publisher" : "American Chemical Society", "title" : "Mixed Uranium Chloride Fluorides UF6-nCln and Methoxyuranium Fluorides UF6-n(OCH3)n:\u2009 A Theoretical Study of Equilibrium Geometries, Vibrational Frequencies, and the Role of the f Orbitals", "type" : "article-journal", "volume" : "39" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[92\u201394]", "plainTextFormattedCitation" : "[92\u201394]", "previouslyFormattedCitation" : "[91\u201393]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[92–94] and extends the conclusions to open-shell uranium systems.In the same manner as for the IR spectra, calculation of third derivatives was performed to obtain Raman spectra. The experimental Raman spectra for compounds 6 and 16 are presented in section 7 of the SI. At variance with the previous results, analytical solutions could not be calculated by all functionals in the Gaussian09 code. In fact, for TPSS and TPSSh, the numerical approach had to be taken by making use of the freq=NRaman keyword. For the LC-ωPBE functional, Raman spectra could not be obtained. REF _Ref459047626 \h \* MERGEFORMAT Figure 5 introduces the calculated Raman spectra for compound 6, presented in a similar manner to the IR results. The rest of the calculated Raman spectra can be found in section 4 of the SI (Figures SI 16 – 21). By contrast with the IR spectra, for the Raman spectra the choice of the functional has a larger impact on the relative positions of the signals. Additionally, the overall agreement with experiment is much poorer, with calculation predicting important features where experiment is silent. This is particularly true for the higher energy regions.Therefore, there is no clear recommendation as to which functional to use when seeking accurate Raman spectra, although PBE generally performs a little better than the other functionals tested.Figure SEQ Figure \* ARABIC 5. Comparison of Raman spectra as obtained with the investigated functionals using Gaussian09 for compound 6. Similar plots can be found in section 4 of the SI for the rest of the molecules. Upper left plot shows all obtained spectra overlapped. Upper right plot is split in two to see the influence of including dispersion corrections (suffix “-D3”) and presents the reported experimental signals (and corresponding heights, counts relative to the signal with the largest amount of counts) as vertical lines. Lower figure compares each functional; blank boxes highlight for which functionals it proved impossible to obtain converged geometries . NMR spectraDFT-based calculations have proved capable of correctly reproducing chemical shifts of diamagnetic uranium compounds,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP001143A", "abstract" : "In this and a subsequent article, the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. In the given first paper, various issues are explored that are related to this goal. It is shown that both the relativistic DFT-ZORA (zeroth-order regular approximation, as developed for NMR properties by Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689) and the older quasi-relativistic (QR) DFT methods are applicable to these compounds. Another popular relativistic method, the use of relativistic effective core potentials (ECP) for the calculation of ligand NMR parameters, is tested as well. It is demonstrated that the ECP approach is beyond its limits for the very heavy actinide compounds. Comparing the ZORA and Pauli approaches, it is found that Pauli is more accurate for the 1H NMR in UF6-n(OCH3)n compounds whereas ZORA is m...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolff", "given" : "Stephen K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "J. Phys. Chem. A", "id" : "ITEM-1", "issue" : "35", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "8244\u20138255", "publisher" : "American Chemical Society", "title" : "NMR Shielding Calculations across the Periodic Table:\u2009 Diamagnetic Uranium Compounds. 1. Methods and Issues", "type" : "article-journal", "volume" : "104" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/IC020370J", "abstract" : "In this and a previous article (J. Phys. Chem. A 2000, 104, 8244), the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. Two relativistic DFT methods are used, ZORA (\u201czeroth-order regular approximation\u201d) and the quasirelativistic (QR) method. In the given second paper, NMR shieldings and chemical shifts are calculated and discussed for a wide range of compounds. The molecules studied comprise uranyl complexes, [UO2Ln]\u00b1q; UF6; inorganic UF6 derivatives, UF6-nCln, n = 0\u22126; and organometallic UF6 derivatives, UF6-n(OCH3)n, n = 0\u22125. Uranyl complexes include [UO2F4]2-, [UO2Cl4]2-, [UO2(OH)4]2-, [UO2(CO3)3]4-, and [UO2(H2O)5]2+. For the ligand NMR, moderate (e.g., 19F NMR chemical shifts in UF6-nCln) to excellent agreement [e.g., 19F chemical shift tensor in UF6 or 1H NMR in UF6-n(OCH3)n] has been found between theory and experiment. The methods have been used ...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-2", "issue" : "25", "issued" : { "date-parts" : [ [ "2002" ] ] }, "page" : "6560\u20136572", "publisher" : "American Chemical Society", "title" : "NMR Shielding Calculations across the Periodic Table:\u2009 Diamagnetic Uranium Compounds. 2. Ligand and Metal NMR", "type" : "article-journal", "volume" : "41" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[95,96]", "plainTextFormattedCitation" : "[95,96]", "previouslyFormattedCitation" : "[94,95]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[95,96] although particular difficulties for 19F chemical shifts have been reported,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp801124u", "ISSN" : "1089-5639", "abstract" : "We have investigated the performance of DFT in U(VI) chemistry. A large, representative selection of functionals has been tested, in combination with two ECPs developed in Stuttgart that have different-sized cores (60 and 78 electrons for U). In addition, several tests were undertaken with another 14 electron pseudopotential, which was developed in Los Alamos. The experimental database contained vibrational wavenumbers, thermochemical data, and 19F chemical shifts for molecules of the type UF6\u2212nCln. For the prediction of vibrational wavenumbers, the large-core RECP (14 electrons) gives results that are at least as good as those obtained with the small-core RECP (32 electrons). GGA functionals are as successful as hybrid GGA for vibrational spectroscopy; typical errors are only a few percent with the Stuttgart pseudopotentials. For thermochemistry, hybrid versions of DFT are more successful than GGA, LDA, or meta-GGA. Marginally better results are obtained with a 32 electron ECP than with 14; since the exp...", "author" : [ { "dropping-particle" : "", "family" : "Iche\u0301-Tarrat", "given" : "Nathalie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Marsden", "given" : "Colin J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "33", "issued" : { "date-parts" : [ [ "2008", "8" ] ] }, "page" : "7632-7642", "publisher" : " American Chemical Society", "title" : "Examining the Performance of DFT Methods in Uranium Chemistry: Does Core Size Matter for a Pseudopotential?", "type" : "article-journal", "volume" : "112" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[65]", "plainTextFormattedCitation" : "[65]", "previouslyFormattedCitation" : "[65]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[65] raising some contradictions.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1016/j.chemphys.2004.10.041", "ISSN" : "03010104", "abstract" : "The 19F NMR nuclear shieldings of fluoride ligands in uranium complexes UFnCl6\u2212n (n=1\u20136) have been studied quantum chemically, using different exchange-correlation functionals and a relativistic small-core pseudopotential on uranium. In contrast to a recent study [G. Schreckenbach, S.W. Wolff, T. Ziegler, J. Phys. Chem. A 104 (2000) 8244] we find that pseudopotential methods are well suited for calculations of ligand chemical shifts in actinide compounds, provided that a sufficiently small core-size definition is used. With modern relativistic small-core pseudopotentials and gradient-corrected density functionals we obtain results of the same accuracy as were found with all-electron density functional ZORA or Pauli calculations. The unusually large dependence of the shifts on the exchange-correlation functional is discussed in the context of the description of \u03c3- and \u03c0-bonding, and also with respect to the accuracy of the optimized structures.", "author" : [ { "dropping-particle" : "", "family" : "Straka", "given" : "Michal", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaupp", "given" : "Martin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "45-56", "title" : "Calculation of 19F NMR chemical shifts in uranium complexes using density functional theory and pseudopotentials", "type" : "article-journal", "volume" : "311" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1002/qua.20350", "ISSN" : "00207608", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-2", "issue" : "4", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "372-380", "publisher" : "Wiley Subscription Services, Inc., A Wiley Company", "title" : "Density functional calculations of ¹⁹ F and ²³⁵ U NMR chemical shifts in uranium (VI) chloride fluorides UF6\u2212 <i>n</i> Cl <i>n</i> : Influence of the relativistic approximation and role of the exchange-correlation functional", "type" : "article-journal", "volume" : "101" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[97,98]", "plainTextFormattedCitation" : "[97,98]", "previouslyFormattedCitation" : "[96,97]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[97,98] On the other hand, paramagnetic systems remain an issue due to the inherent deficiencies of DFT to treat systems with pronounced multireference character and important relativistic contributions. Recent theoretical and computational efforts provide appropriate descriptions for such complex problems,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/acs.jpclett.5b00932", "ISSN" : "1948-7185", "abstract" : "Paramagnetic effects on NMR shifts (pNMR) for paramagnetic metal complexes are calculated from first-principles, without recourse to spin Hamiltonian parameters. A newly developed code based on complete active space (CAS) and restricted active space (RAS) techniques in conjunction with treating spin\u2013orbit (SO) coupling via state interaction is applied to 13C NMR shifts of actinyl tris-carbonate complexes, specifically [UO2(CO3)3]5\u2013 and [NpO2(CO3)3]4\u2013. The experimental pNMR shifts as well as the sizable difference of the 13C NMR shift for these iso-electronic species are well reproduced by the calculations. Approximations to the pNMR shift equations using spin Hamiltonian parameters or the magnetic susceptibility are calculated for the same systems at the same level of theory, and it is shown how the approximations relate to the ab initio data.", "author" : [ { "dropping-particle" : "", "family" : "Gendron", "given" : "Fr\u00e9d\u00e9ric", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Sharkas", "given" : "Kamal", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Autschbach", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry Letters", "id" : "ITEM-1", "issue" : "12", "issued" : { "date-parts" : [ [ "2015", "6", "18" ] ] }, "page" : "2183-2188", "publisher" : "American Chemical Society", "title" : "Calculating NMR Chemical Shifts for Paramagnetic Metal Complexes from First-Principles", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/acs.jctc.6b00462", "ISSN" : "1549-9618", "abstract" : "Ligand paramagnetic NMR (pNMR) chemical shifts of the 5f1 complexes UO2(CO3)35\u2013 and NpO2(CO3)34\u2013, and of the 5f2 complexes PuO2(CO3)34\u2013 and (C5H5)3UCH3 are investigated by wave function theory calculations, using a recently developed sum-over-states approach within complete active space and restricted active space paradigm including spin\u2013orbit (SO) coupling [J. Phys. Chem. Lett. 2015, 20, 2183-2188]. The experimental 13C pNMR shifts of the actinyl tris-carbonate complexes are well reproduced by the calculations. The results are rationalized by visualizing natural spin orbitals (NSOs) and spin-magnetizations generated from the SO wave functions, in comparison with scalar relativistic spin densities. The analysis reveals a complex balance between spin-polarization, spin and orbital magnetization delocalization, and spin-compensation effects due to SO coupling. This balance creates the magnetization due to the electron paramagnetism around the nucleus of interest, and therefore the pNMR effects. The calculat...", "author" : [ { "dropping-particle" : "", "family" : "Gendron", "given" : "Fr\u00e9d\u00e9ric", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Autschbach", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Chemical Theory and Computation", "id" : "ITEM-2", "issue" : "11", "issued" : { "date-parts" : [ [ "2016", "10", "6" ] ] }, "page" : "5309\u20135321", "publisher" : "American Chemical Society", "title" : "Ligand NMR Chemical Shift Calculations for Paramagnetic Metal Complexes: 5f1 vs 5f2 Actinides", "type" : "article-journal", "volume" : "12" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[99,100]", "plainTextFormattedCitation" : "[99,100]", "previouslyFormattedCitation" : "[98,99]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[99,100] but they rely on wavefunction-based methods and they are therefore out the scope of this work. We now present the 1H and 13C NMR results on the closed shell target molecules for which experimental data are available, i.e. compounds 11 – 13. The approaches employed are given in REF _Ref475365656 \h \* MERGEFORMAT Table 1.All calculations have been performed with the same functional used to optimize the geometry. Thus, when discussing the results obtained with B3LYP, for example, it is implicit that the geometry used is the one obtained with B3LYP functional. For both Gaussian09 and ADF, each calculation has been carried out with two basis sets; the same basis set used to optimize the structures and additionally the IGLOII basis sets for hydrogen and carbon atoms in the case of Gaussian09 and jcpl in the case of ADF2016, which have been explicitly developed for NMR properties. The interest of comparing the results from Gaussian09 and ADF2016 is that it allows us to address the effect of including relativistic effects either with a pseudopotential (Gaussian09) or by means of scalar ZORA Hamiltonian alone or together with spin-orbit coupling (ADF2016) on the chemical shifts and spin-spin couplings.The deviation from experiment is calculated as the difference between the experimental and calculated isotropic shifts, all referenced to the tetramethlysilane (TMS) standard. The TMS molecule has been treated at the same level of theory (code, functional, basis set) as the one used to treat the uranium complex in each case. Section 5 of the SI presents a detailed explanation of how the different absolute and relative errors were calculated. As a large amount of data is involved, only the mean and standard deviation of those differences together with the corresponding relative errors are presented. Note that these means have been calculated using the absolute values of the differences between experiment and theory, to avoid error cancellation. In order to avoid oversimplification of the discussion arising from consideration of only comparative averages, and to help discern which approach behaves best for the series of investigated compounds, Tables SI 4 – 7 in section 5 of the SI provide the smallest and largest relative errors for each experimental signal together with the associated method. Solvent effects have been included by the PCM; note that these are single point calculations in which the PCM is used at the geometry of the gasphase calculation. We concluded in section 4.1 that the inclusion of solvent effects makes virtually no difference to the geometry but, as a test case, have calculated the deviations from experiment of the 1H chemical shifts of compound 11 (vide infra) at the geometries optimized without and with inclusion of the solvent. At the PBE (cc-pVDZ basis set) PCM level, these are 0.40 and 0.40 for the 1.73 ppm signal and 0.24 and 0.20 for the 5.81 ppm signal, i.e. the minor differences in the underlying geometry have similarly minimal effect on the computed NMR pound 11Compound 11ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "abstract" : "Reaction of the uranyl \u03b2-ketoiminate complex UO2(tBuacnac)2 (1) (tBuacnac = tBuNC(Ph)CHC(Ph)O) with Me3SiI, in the presence of Ph3P, results in the reductive silylation of the uranyl moiety and formation of the U(V) bis-silyloxide complex [Ph3PI][U(OSiMe3)2I4] (2). Subsequent reaction of 2 with Lewis bases, such as 2,2\u2032-bipyridine (bipy), 1,10-phenanthroline (phen), and tetrahydrofuran (THF), results in a further reduction of the metal center and isolation of the U(IV) complexes U(OSiMe3)2I2(bipy)2 (3), U(OSiMe3)2I2(phen)2 (4), and [U(OSiMe3)2I(THF)4][I3] (5), respectively.", "author" : [ { "dropping-particle" : "", "family" : "Brown", "given" : "Jessie L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mokhtarzadeh", "given" : "Charles C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lever", "given" : "Jeremie M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wu", "given" : "Guang", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hayton", "given" : "Trevor W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "2011" ] ] }, "page" : "5105\u20135112", "publisher" : "American Chemical Society", "title" : "Facile Reduction of a Uranyl(VI) \u03b2-Ketoiminate Complex to U(IV) Upon Oxo Silylation", "type" : "article-journal", "volume" : "50" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[28]", "plainTextFormattedCitation" : "[28]", "previouslyFormattedCitation" : "[28]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[28] has a 1H NMR spectrum in C6D6 with two distinct signals, a singlet at 1.73 ppm, assigned to the methyl groups of the tBu moiety, and another at 5.81 ppm, associated with the γ-carbon of the ketoiminate ring. The 13C NMR spectrum measured in CD2Cl2 shows four distinct signals at 33.6, 102.9, 171.8 and 173.4 ppm. REF _Ref461445089 \h \* MERGEFORMAT Table 2 presents the deviations of the calculated chemical shifts. Examining first the 1H shifts obtained with Gaussian09, we can see that the average absolute error from experiment and the corresponding standard deviation, considering all 22 calculations, is 0.42 ± 0.03 and 0.17 ± 0.09 ppm for the 1.73 and 5.81 ppm experimental signals, respectively. These values correspond to relative errors of 24 and 3%, respectively. The same set of calculations was carried out using the IGLOII basis set, obtaining for the same experimental signals the following mean and standard deviations, 0.13 ± 0.05 and 0.28 ± 0.09. The change of basis set thus results in a much smaller relative error of 8% for the hydrogens of the methyl groups of the tBu moiety and a similar relative error (5%) for the γ-carbon hydrogens, i.e. the IGLOII basis sets are superior for calculation of these 1H chemical shifts. For the pVDZ basis set, the methods that yield the smallest absolute error from the two experimental signals are PBE0 with solvent at the geometry optimized without dispersion corrections (i.e. PBE0-PCM, 0.37 ppm, δx = 21.4 %) and PBE0 without solvent at the optimized geometry with dispersion corrections (i.e. PBE0-D3, 0.01 ppm, δx = 0.2 %). Similarly, the largest absolute errors arise from LC-ωPBE without solvent at the optimized geometry with dispersion corrections (i.e. LC-ωPBE-D3, 0.50 ppm, δx = 29.0 %) and B3LYP with no solvent and no dispersion corrections (i.e. B3LYP, 0.31 ppm, δx = 5.3 %). For the IGLOII basis set, B3LYP and TPSS with no solvent and no dispersion corrections yield the smallest deviations (0.09 and -0.14 ppm for both signals, respectively) while the largest absolute errors are found when using LC-ωPBE without solvent at the geometry optimized with dispersion corrections (i.e. LC-ωPBE-D3, 0.26 ppm) and PBE0 with solvent and dispersion corrections (i.e. PBE0-D3-PCM, 0.47 ppm). This data can be found in Table SI 4 in section 5.1 of the SI.For similar discussion of the 13C values, the reader is referred to Table SI 4, where a more explicit description of the averaged relative error and the methods that provide the smallest and largest relative errors for each signal can be found. However, it is worth mentioning that the differential effect of considering different basis sets seems to dilute when averaging over all experimental signals, even making the results from the IGLOII basis set slightly worse, at variance with the 1H case.Hence a clear recommendation as to which method is best suited is not so straightforward. That said, we can safely say that for the 13C chemical shifts, PBE0 and TPSS often perform the worst.Gaussian 09a)ADFb)Exp. δ (ppm)?x ? ± σδx (%)?x δx (%)1H1.730.42 ± 0.0324.20.3419.90.13 ± 0.057.80.179.95.81 0.17 ± 0.093.10.183.00.28 ± 0.094.80.274.6? ± σ of δx (%)13.6 ± 10.611.4 ± 11.96.3 ± 1.57.3 ± 3.713C33.64.38 ± 2.5113.01.815.45.12 ± 1.7215.23.069.1102.96.46 ± 3.536.33.043.03.24 ± 2.683.14.234.1171.82.39 ± 2.181.43.191.97.65 ± 4.344.55.233.0173.42.50 ± 1.901.49.305.48.51 ± 4.064.98.815.1? ± σ of δx (%)5.5 ± 4.83.9 ± 1.86.9 ± 4.85.3 ± 2.6a) 1H results are averaged over the 22 calculations: 6 functionals, 2 geometries each (except TPSSh), with/without solvent each. For 13C solvent was not considered.b) Results at PBE geometry only.Table SEQ Table \* ARABIC 2. Summary of calculated 1H and 13C NMR shifts (ppm) for compound 11. ?x (Hz) and δx represents the absolute and relative error, respectively. ? ± σ stands for the mean and standard deviation of the absolute errors. The order of the signals is as reported in refADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "abstract" : "Reaction of the uranyl \u03b2-ketoiminate complex UO2(tBuacnac)2 (1) (tBuacnac = tBuNC(Ph)CHC(Ph)O) with Me3SiI, in the presence of Ph3P, results in the reductive silylation of the uranyl moiety and formation of the U(V) bis-silyloxide complex [Ph3PI][U(OSiMe3)2I4] (2). Subsequent reaction of 2 with Lewis bases, such as 2,2\u2032-bipyridine (bipy), 1,10-phenanthroline (phen), and tetrahydrofuran (THF), results in a further reduction of the metal center and isolation of the U(IV) complexes U(OSiMe3)2I2(bipy)2 (3), U(OSiMe3)2I2(phen)2 (4), and [U(OSiMe3)2I(THF)4][I3] (5), respectively.", "author" : [ { "dropping-particle" : "", "family" : "Brown", "given" : "Jessie L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mokhtarzadeh", "given" : "Charles C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lever", "given" : "Jeremie M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wu", "given" : "Guang", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hayton", "given" : "Trevor W.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-1", "issue" : "11", "issued" : { "date-parts" : [ [ "2011" ] ] }, "page" : "5105\u20135112", "publisher" : "American Chemical Society", "title" : "Facile Reduction of a Uranyl(VI) \u03b2-Ketoiminate Complex to U(IV) Upon Oxo Silylation", "type" : "article-journal", "volume" : "50" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[28]", "plainTextFormattedCitation" : "[28]", "previouslyFormattedCitation" : "[28]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[28] for that paper’s compound 1. For the Gaussian09 results for each signal, the first row gives the results obtained with the pVDZ basis set, while the second row collects those for the IGLOII basis set. For the ADF results for each signal, the first row presents the results obtained with scalar ZORA, while the second row gives ZORA+SOC data, using the internal jcpl (for C and H) basis set. The relative error is calculated with respect to the averaged value of the absolute error (deviation). ? ± σ in the last row refers to the mean and standard deviation for all relative errors.Let us now discuss the effect of all-electron basis sets and relativistic effects (i.e. ZORA Hamiltonian, at either the scalar only or scalar + SOC levels) on the calculated chemical shifts. This has been probed using the ADF programme with the PBE functional, at the unique PBE optimized geometry and therefore geometry effects are not considered here. These results can be found in the rightmost part of REF _Ref460861816 \h \* MERGEFORMAT Table 2 from which the differential effect of considering scalar ZORA or ZORA + SOC is not that large. Note, however, that the inclusion of SOC effects reduces the standard deviation of the relative errors, particularly for 1H chemical shifts. A comparison of the mean and standard deviation of the relative errors ? ± σ of δx (%) results from Gaussian09 and ADF2016 in REF _Ref460861816 \h \* MERGEFORMAT Table 2 indicates that the use of a pseudopotential on the metal centre provides similar results to those obtained with all electron basis sets. The effect of different basis sets on the calculation of chemical shifts considering relativistic effects via ZORA or ZORA+SOC can be seen by comparing these data with Table SI 5 in section 5.1 the SI. One can see that for 1H chemical shifts, the use of jcpl improves agreement markedly, but for 13C it is practically negligible. It is worth noting that the largest deviation, no matter the approach taken, is associated with the 1H of the tert-butyl pound 12Compound 12ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/chem.201300071", "ISSN" : "09476539", "author" : [ { "dropping-particle" : "", "family" : "Cooper", "given" : "Oliver J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mills", "given" : "David P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McMaster", "given" : "Jonathan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tuna", "given" : "Floriana", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McInnes", "given" : "Eric. J. L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lewis", "given" : "William", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Blake", "given" : "Alexander J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Liddle", "given" : "Stephen T.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Eur. J.", "id" : "ITEM-1", "issue" : "22", "issued" : { "date-parts" : [ [ "2013", "5", "27" ] ] }, "page" : "7071-7083", "publisher" : "WILEY\u2010VCH Verlag", "title" : "The Nature of the U=C Double Bond: Pushing the Stability of High-Oxidation-State Uranium Carbenes to the Limit", "type" : "article-journal", "volume" : "19" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[30]", "plainTextFormattedCitation" : "[30]", "previouslyFormattedCitation" : "[30]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[30] has 10 and 16 distinct signals for 1H and 13C chemical shifts respectively, in addition to different spin-spin couplings. These can be found in the supplementary information of reference ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/chem.201300071", "ISSN" : "09476539", "author" : [ { "dropping-particle" : "", "family" : "Cooper", "given" : "Oliver J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mills", "given" : "David P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McMaster", "given" : "Jonathan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tuna", "given" : "Floriana", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McInnes", "given" : "Eric. J. L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lewis", "given" : "William", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Blake", "given" : "Alexander J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Liddle", "given" : "Stephen T.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Eur. J.", "id" : "ITEM-1", "issue" : "22", "issued" : { "date-parts" : [ [ "2013", "5", "27" ] ] }, "page" : "7071-7083", "publisher" : "WILEY\u2010VCH Verlag", "title" : "The Nature of the U=C Double Bond: Pushing the Stability of High-Oxidation-State Uranium Carbenes to the Limit", "type" : "article-journal", "volume" : "19" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[30]", "plainTextFormattedCitation" : "[30]", "previouslyFormattedCitation" : "[30]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[30] (compound 3). From this, we chose the JHH=7.6, JHH=9.2, JPH=35.64 and JPC=135.87 (Hz) signals to compare with our computed results. The first two couplings are associated with 4H from p-Ph-CH and 8H from m-Ph-CH; the third coupling corresponds to the doublet PH and the last one to CHP2. First, let us discuss the chemical shifts. REF _Ref461441583 \h \* MERGEFORMAT Table 3 presents the deviations from experiment of the calculated chemical shifts and the relative error of their averaged value as calculated with Gaussian09. We start by discussing the effect of the two basis sets employed by considering the mean and standard deviation of the relative errors (? ± σ of δx (%) at the bottom of REF _Ref461441583 \h \* MERGEFORMAT Table 3). As was observed for compound 11, 1H chemical shifts are better described with IGLOII, although here the difference with respect to pVDZ is less pronounced (10.6 ± 6.7 vs 9.2 ± 9.0 for pVDZ and IGLOII, respectively). 13C chemical shifts are better described with the pVDZ basis set. Overall, the agreement with experiment is reasonable, within a ~12% error, although it is worth mentioning that the smallest signals suffer from a large deviation. In order to gain further insight the reader is referred to Table SI 5 in section 5.2 of the SI, where a more detailed description of the methods that perform the best and worst for each signal is presented.Overall, for compound 12, the recommendation of which approach to take to properly describe chemical shifts using Gaussian09 is as unclear as for compound 11.The inclusion of relativistic effects via ZORA or ZORA+SOC was also investigated, both for the chemical shifts and spin-spin couplings, using PBE within ADF. The results are similar to those obtained with Gaussian09, and hence are presented in Table SI 8 in section 5 of the SI. The inclusion of relativistic effects by means of scalar or spin-orbit ZORA affects much more the description of 13C than 1H chemical shifts; thus, ZORA + SOC reduces the mean and standard deviation of the relative errors (1H and 13C together) from 12.1 ± 22.5 to 8.7 ± 8.5 (when using jcpl basis set), as can be observed from the ? ± σ of δx (%) values of REF _Ref482182976 \h \* MERGEFORMAT Table 5; more details can be found in Table SI 8. Comparison of the ? ± σ of δx (%) values obtained with Gaussian09 and ADF2016 permits addressing the effect of using a relativistic pseudopotential or relativistic Hamiltonian plus all electron basis set, respectively. These are very similar, with an almost identical value for the 1H chemical shifts and a noticeably better agreement with experiment of the ZORA + SOC jcpl basis set results for the 13C shifts. Exp. δ (ppm)?x ? ± σδx (%)Exp. δ (ppm)?x ? ± σδx (%)1H13C1.480.15 ± 0.059.97.095.6 ± 3.478.80.47 ± 0.0531.56.9 ± 4.297.02.390.23 ± 0.039.820.372.2 ± 0.310.70.13 ± 0.045.43.9 ± 0.619.42.460.40 ± 0.0616.020.681.8 ± 0.38.90.06 ± 0.052.33.6 ± 0.618.02.810.79 ± 0.0628.021.062.2 ± 0.310.60.52 ± 0.0618.54.1 ± 0.519.44.530.35 ± 0.137.721.453.2 ± 0.515.10.13 ± 0.112.95.2 ± 0.724.36.900.62 ± 0.119.025.593.4 ± 1.413.30.90 ± 0.0913.15.6 ± 1.322.17.000.19 ± 0.172.875.421.8 ± 1.12.40.58 ± 0.158.35.6 ±2.47.57.130.33 ± 0.144.6127.82.8 ± 2.02.20.10 ± 0.081.56.0 ± 3.54.77.280.57 ± 0.147.9129.13.1 ± 2.22.40.18 ± 0.102.57.7 ± 4.15.97.820.80 ± 0.1410.2129.63.1 ± 2.22.40.45 ± 0.125.77.4 ± 4.15.7130.93.0 ± 1.92.38.7 ± 4.06.7132.44.0 ± 2.22.96.0 ± 4.14.5134.42.4 ± 1.61.86.6 ± 3.44.9135.32.5 ± 1.51.88.4 ± 3.26.2136.65.3 ± 3.03.93.1 ± 2.12.3144.61.5 ± 1.01.010.3 ± 1.77.2? ± σ of δx (%)10.6 ± 6.710.0 ± 18.39.2 ± 9.015.9 ± 22.1Table SEQ Table \* ARABIC 3. Summary of calculated 1H and 13C NMR shifts (ppm) for compound 12 as calculated using Gaussian09. ?x (ppm) and δx represents the absolute and relative error, respectively. ? ± σ stand for the mean and standard deviation of the absolute errors. The order of the signals is the same as the one reported in the SI for compound 3 inADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1002/chem.201300071", "ISSN" : "09476539", "author" : [ { "dropping-particle" : "", "family" : "Cooper", "given" : "Oliver J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Mills", "given" : "David P.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McMaster", "given" : "Jonathan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tuna", "given" : "Floriana", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "McInnes", "given" : "Eric. J. 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J.", "id" : "ITEM-1", "issue" : "22", "issued" : { "date-parts" : [ [ "2013", "5", "27" ] ] }, "page" : "7071-7083", "publisher" : "WILEY\u2010VCH Verlag", "title" : "The Nature of the U=C Double Bond: Pushing the Stability of High-Oxidation-State Uranium Carbenes to the Limit", "type" : "article-journal", "volume" : "19" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[30]", "plainTextFormattedCitation" : "[30]", "previouslyFormattedCitation" : "[30]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[30]. The leftmost values correspond to 1H NMR and the rightmost values to 13C NMR. For each signal, the first row presents the results obtained with the pVDZ basis set, while the second row is for IGLOII basis set. The relative error is calculated with respect to the averaged value of the absolute error (deviation). ? ± σ in the last row refers to the mean and standard deviation for all relative errors for 1H and 13C, using the pVDZ and IGLOII basis sets, respectively.Now let us discuss the spin-spin coupling constants presented in REF _Ref461443442 \h \* MERGEFORMAT Table 4. Technical details can be found in section 10 of the SI. There is a clear dependence of the agreement on the experimental signal considered, and the consistency of results between Gaussian09 and ADF for the chemical shifts is not maintained for the spin-spin coupling constants. For instance, the results for JPC obtained with Gaussian09 show a very good agreement with experiment along the series, while ADF2016 predicts values with relative errors three times larger. Also, JPH has a systematic relative error larger than 80 %, for all methods and both programs. The effect of the basis set employed is much more pronounced here than for chemical shiftsADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/ct900535d", "ISSN" : "1549-9618", "abstract" : "A benchmark study for relativistic density functional calculations of NMR spin\u2212spin coupling constants has been performed. The test set contained 47 complexes with heavy metal atoms (W, Pt, Hg, Tl, Pb) with a total of 88 coupling constants involving one or two heavy metal atoms. One-, two-, three-, and four-bond spin\u2212spin couplings have been computed at different levels of theory (nonhybrid vs hybrid DFT, scalar vs two-component relativistic). The computational model was based on geometries fully optimized at the BP/TZP scalar relativistic zeroth-order regular approximation (ZORA) and the conductor-like screening model (COSMO) to include solvent effects. The NMR computations also employed the continuum solvent model. Computations in the gas phase were performed in order to assess the importance of the solvation model. The relative median deviations between various computational models and experiment were found to range between 13% and 21%, with the highest-level computational model (hybrid density functio...", "author" : [ { "dropping-particle" : "", "family" : "Moncho", "given" : "Salvador", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Autschbach", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Journal of Chemical Theory and Computation", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2010", "1", "12" ] ] }, "page" : "223-234", "publisher" : " American Chemical Society", "title" : "Relativistic Zeroth-Order Regular Approximation Combined with Nonhybrid and Hybrid Density Functional Theory: Performance for NMR Indirect Nuclear Spin\u2212Spin Coupling in Heavy Metal Compounds", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[76]", "plainTextFormattedCitation" : "[76]", "previouslyFormattedCitation" : "[76]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[76]; there is a significant improvement when going to IGLOII in Gaussian09 and to jcpl in ADF2016. However, the effect of geometry (PBE vs PBE+D3) and the inclusion of relativistic corrections is not significant (see ADF2016 part of REF _Ref461443442 \h \* MERGEFORMAT Table 4). Table SI 7 in section 5.2 of the SI summarizes which functionals at which geometries provide the best and worst agreement for Gaussian09 results; we conclude that LC-ωPBE with solvent corrections is the best choice for describing spin-spin coupling constants.a)Gaussian09J HHJ PHJ PCExp (Hz)7.69.235.64135.87?x ? ± σ2.7 ± 0.43.8 ± 0.529.9 ± 3.113.3 ± 7.20.4 ± 0.31.3 ± 0.429.6 ± 2.711.6 ± 10.1δx (%)35.541.183.89.85.314.183.28.5b)ADF2016PBEPBE-D3Exp (Hz)ZORAZORA + SOCZORAZORA + SOCJ HH7.6?x / δx(%)1.6 / 21.5-1.6 / 21.71.6 / 20.70.4 / 4.70.3 / 3.80.4 / 4.80.3 / 3.99.2?x / δx(%)2.8 / 30.7-2.8 / 30.52.7 / 29.81.6 / 17.21.5 / 16.51.6 / 17.71.6 / 17.0J PH35.64?x / δx(%)28.5 / 80.0-26.5 / 74.326.6 / 74.731.7 / 88.931.7 / 89.030.0 / 84.330.1 / 84.7J PC135.87?x / δx(%)53.3 / 39.2-48.7 / 35.847.4 / 34.936.1 / 26.634.7 / 25.530.7 / 22.629.2 / 21.5Table SEQ Table \* ARABIC 4. Summary of calculated 1H NMR spin-spin coupling constants (Hz) for compound 12. ?x (Hz) and δx are the absolute and relative error, respectively. The relative error is calculated with respect to the averaged value of the absolute error (deviation). a) presents the values from Gaussian09. ? ± σ stand for the mean and standard deviation of the absolute errors. For each signal, the first row provides the results obtained with the pVDZ basis set, while the second row gives those from the IGLOII basis set. b) introduces the values from ADF2016 calculations at the PBE level (without and with dispersion corrections) and highlights the effect of explicitly including relativistic effects. For each signal, the first row presents the results obtained with the pVDZ basis set, while the second row gives the jcpl basis set pound 13Compound 13 displays a single 13C NMR experimental signal at 168.2 ppm vs TMS. The mean and standard deviation of the differences vs experiment of the calculated chemical shifts using the pVDZ basis set is -1.30 ± 2.61, which corresponds to a relative error of 1%. LC-ωPBE without considering the solvent yields the poorest result (-6.48 ppm) while TPSSh without solvent performs the best (-0.04 ppm). Following the trend observed for compounds 11 and 12, the IGLOII basis set performs more poorly for the 13C NMR signals, as the mean and standard deviation is 12.61 ± 3.12, which translates to an 8 % relative error. In this case, LC-ωPBE without inclusion of solvent again yields the least accurate results (-18.35 ppm), while TPPS with solvent is the closest to experiment (-9.12 ppm). Calculation of the chemicals shifts including relativistic effects via scalar ZORA or ZORA + SOC at the PBE optimized geometries are reported in REF _Ref482182976 \h \* MERGEFORMAT Table 5. As observed, the effect of both basis sets and spin orbit coupling appear to be negligible, since the relative errors vary between 7.0 and 7.6 %.Effect of exchange-correlation functional and inclusion of relativity.An interesting effect to evaluate over the three compounds studied is the role of the exchange-correlation functional, which has caused debate for 19F chemical shifts in UF6nCln compounds.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP001143A", "abstract" : "In this and a subsequent article, the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. In the given first paper, various issues are explored that are related to this goal. It is shown that both the relativistic DFT-ZORA (zeroth-order regular approximation, as developed for NMR properties by Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689) and the older quasi-relativistic (QR) DFT methods are applicable to these compounds. Another popular relativistic method, the use of relativistic effective core potentials (ECP) for the calculation of ligand NMR parameters, is tested as well. It is demonstrated that the ECP approach is beyond its limits for the very heavy actinide compounds. Comparing the ZORA and Pauli approaches, it is found that Pauli is more accurate for the 1H NMR in UF6-n(OCH3)n compounds whereas ZORA is m...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolff", "given" : "Stephen K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "J. Phys. Chem. A", "id" : "ITEM-1", "issue" : "35", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "8244\u20138255", "publisher" : "American Chemical Society", "title" : "NMR Shielding Calculations across the Periodic Table:\u2009 Diamagnetic Uranium Compounds. 1. Methods and Issues", "type" : "article-journal", "volume" : "104" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1016/j.chemphys.2004.10.041", "ISSN" : "03010104", "abstract" : "The 19F NMR nuclear shieldings of fluoride ligands in uranium complexes UFnCl6\u2212n (n=1\u20136) have been studied quantum chemically, using different exchange-correlation functionals and a relativistic small-core pseudopotential on uranium. In contrast to a recent study [G. Schreckenbach, S.W. Wolff, T. Ziegler, J. Phys. Chem. A 104 (2000) 8244] we find that pseudopotential methods are well suited for calculations of ligand chemical shifts in actinide compounds, provided that a sufficiently small core-size definition is used. With modern relativistic small-core pseudopotentials and gradient-corrected density functionals we obtain results of the same accuracy as were found with all-electron density functional ZORA or Pauli calculations. The unusually large dependence of the shifts on the exchange-correlation functional is discussed in the context of the description of \u03c3- and \u03c0-bonding, and also with respect to the accuracy of the optimized structures.", "author" : [ { "dropping-particle" : "", "family" : "Straka", "given" : "Michal", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaupp", "given" : "Martin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics", "id" : "ITEM-2", "issue" : "1", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "45-56", "title" : "Calculation of 19F NMR chemical shifts in uranium complexes using density functional theory and pseudopotentials", "type" : "article-journal", "volume" : "311" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1002/qua.20350", "ISSN" : "00207608", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-3", "issue" : "4", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "372-380", "publisher" : "Wiley Subscription Services, Inc., A Wiley Company", "title" : "Density functional calculations of ¹⁹ F and ²³⁵ U NMR chemical shifts in uranium (VI) chloride fluorides UF6\u2212 <i>n</i> Cl <i>n</i> : Influence of the relativistic approximation and role of the exchange-correlation functional", "type" : "article-journal", "volume" : "101" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[95,97,98]", "plainTextFormattedCitation" : "[95,97,98]", "previouslyFormattedCitation" : "[94,96,97]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[95,97,98] By looking at Tables SI 4, 6 and 7 in section 5 of the SI, one can draw some conclusions. For compound 11, for 1H chemical shifts hybrid functionals perform better for both basis sets investigated, while for 13C with IGLOII, GGA (PBE) is the most appropriate. For compound 12, for 1H chemical shifts, the best and worst performing functionals are hybrid and LC-ωPBE, respectively. For the 13C with the IGLOII basis set, there is a further dependency on which atoms are described. Thus, for the furthest located from the uranium centre (the tert-butyl ones), LC-ωPBE performs best whereas the GGA TPSS functional correctly predicts the chemical shifts of the closest carbon atom to uranium centre. For compound 13, the best option is TPSS and the worst LC-ωPBE. Finally, for the spin-spin coupling constants of compound 12, the best performing is the long-range corrected LC-ωPBE functional and the worst the hybrid PBE0. In model systems the clear separation seen between GGA, hybrid and long-range corrected functionals for the description of chemical shiftsADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP001143A", "abstract" : "In this and a subsequent article, the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. In the given first paper, various issues are explored that are related to this goal. It is shown that both the relativistic DFT-ZORA (zeroth-order regular approximation, as developed for NMR properties by Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689) and the older quasi-relativistic (QR) DFT methods are applicable to these compounds. Another popular relativistic method, the use of relativistic effective core potentials (ECP) for the calculation of ligand NMR parameters, is tested as well. It is demonstrated that the ECP approach is beyond its limits for the very heavy actinide compounds. Comparing the ZORA and Pauli approaches, it is found that Pauli is more accurate for the 1H NMR in UF6-n(OCH3)n compounds whereas ZORA is m...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolff", "given" : "Stephen K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "J. Phys. Chem. A", "id" : "ITEM-1", "issue" : "35", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "8244\u20138255", "publisher" : "American Chemical Society", "title" : "NMR Shielding Calculations across the Periodic Table:\u2009 Diamagnetic Uranium Compounds. 1. Methods and Issues", "type" : "article-journal", "volume" : "104" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1016/j.chemphys.2004.10.041", "ISSN" : "03010104", "abstract" : "The 19F NMR nuclear shieldings of fluoride ligands in uranium complexes UFnCl6\u2212n (n=1\u20136) have been studied quantum chemically, using different exchange-correlation functionals and a relativistic small-core pseudopotential on uranium. In contrast to a recent study [G. Schreckenbach, S.W. Wolff, T. Ziegler, J. Phys. Chem. A 104 (2000) 8244] we find that pseudopotential methods are well suited for calculations of ligand chemical shifts in actinide compounds, provided that a sufficiently small core-size definition is used. With modern relativistic small-core pseudopotentials and gradient-corrected density functionals we obtain results of the same accuracy as were found with all-electron density functional ZORA or Pauli calculations. The unusually large dependence of the shifts on the exchange-correlation functional is discussed in the context of the description of \u03c3- and \u03c0-bonding, and also with respect to the accuracy of the optimized structures.", "author" : [ { "dropping-particle" : "", "family" : "Straka", "given" : "Michal", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaupp", "given" : "Martin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics", "id" : "ITEM-2", "issue" : "1", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "45-56", "title" : "Calculation of 19F NMR chemical shifts in uranium complexes using density functional theory and pseudopotentials", "type" : "article-journal", "volume" : "311" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1002/qua.20350", "ISSN" : "00207608", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "International Journal of Quantum Chemistry", "id" : "ITEM-3", "issue" : "4", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "372-380", "publisher" : "Wiley Subscription Services, Inc., A Wiley Company", "title" : "Density functional calculations of ¹⁹ F and ²³⁵ U NMR chemical shifts in uranium (VI) chloride fluorides UF6\u2212 <i>n</i> Cl <i>n</i> : Influence of the relativistic approximation and role of the exchange-correlation functional", "type" : "article-journal", "volume" : "101" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[95,97,98]", "plainTextFormattedCitation" : "[95,97,98]", "previouslyFormattedCitation" : "[94,96,97]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[95,97,98] may arise due to the similar chemical environment of all centres. However, for the bigger, more realistic compounds investigated here, this appears to be not feasible.We now compare on a one-to-one basis the effect of using pseudopotentials or ZORA and ZORA+SOC to treat relativistic effects, together with the quality of the basis sets. REF _Ref482182976 \h \* MERGEFORMAT Table 5 presents the mean and standard deviation of the relative errors (in absolute values) associated with each 1H and 13C chemical shift for the three compounds 11 – 13. Those are calculated using the PBE functional, at the corresponding geometry, with Gaussian09 and ADF2016. REF _Ref482182976 \h \* MERGEFORMAT Table 5 is complementary to the more detailed Table SI 8 in section 5 of the SI. Supporting previous discussion, the experimental chemical 1H shifts of compound 11 show a more pronounced variation through the different methods, as compared to 13C. If one uses pseudopotentials for the uranium centre, the IGLOII basis set performs the best, whereas including relativistic effects through ZORA+SOC with the jcpl basis set results in a better agreement and a less dispersed set of data. Nevertheless, the overall agreement with the different experimental values is very good. Compound 12 shows a more pronounced variation for the 13C chemical shifts depending on the approach used, and a worse performance when the IGLOII basis set is employed. Interestingly, all investigated methods predict a chemical shift for the first 13C signal (7.09 ppm) that is persistently off the experimental value by more than 100%, except for ZORA+SOC with the jcpl basis set that shows a 35% relative error (see Table SI 8 in section 5 of the SI and Table 3). Interestingly, this carbon atom is the closest to the uranium centre (~2.9 ?) and sits between the two phosphorus atoms. This suggests that even if the rest of the chemical shifts are similarly reproduced by the different methods, only ZORA+SOC with jcpl ensures a good description of the chemical shifts of all atoms, no matter their surroundings. For compound 13 the agreement is independent on method and basis sets, at ~7% of relative error. Surprisingly, the smallest basis set performs noticeably better than larger counterparts. For all three compounds, including triple- and quadrupole-ζ polarized quality basis sets (cc-pVTZ and cc-pVQZ, respectively) does not introduce any further improvement. Gaussian09 a)ADF2016 b)? ± σ of |δx|ZORAZORA-SOCcc-pVDZIGLO-IIcc-pVTZcc-pVQZDZPjcplDZPjcpl111H 13.7 ± 13.55.4 ±2.66.1 ±2.06.0 ±4.214.3 ± 15.711.4 ±11.918.3 ±23.77.3 ±3.713C 3.0 ± 2.34.8 ±4.65.1 ±4.07.2 ±5.24.5 ±3.73.9 ± 1.83.4 ±3.95.3 ±2.6Total6.5 ± 8.45.0 ± 3.85.4 ± 3.36.8 ± 4.57.8 ± 9.16.4 ± 6.78.4 ± 13.56.0 ± 2.8121H 10.0 ± 6.88.4 ± 9.09.9 ± 10.410.5 ± 10.88.7 ± 8.19.0 ± 7.99.8 ± 8.09.5 ± 8.013C 15.0 ± 35.721.7 ± 43.419.8 ± 35.423.7 ± 38.317.5 ± 46.714.1 ± 28.213.1 ± 28.38.2 ± 9.0Total13.1 ± 28.116.6 ± 34.616.0 ± 28.518.7 ± 31.114.1 ± 36.812.1 ± 22.511.8 ± 22.58.7 ± 8.51313C 0.26.67.68.87.37.67.07.4Table SEQ Table \* ARABIC 5. Average and standard deviation (? ± σ) of the relative errors (δx, in absolute value) calculated for 1H and 13C chemical shifts with PBE functional, for compounds 11 – 13. a) presents the data calculated for different basis sets within Gaussian09. b) presents the results obtained when relativistic effects are included either scalar ZORA or spin-orbit ZORA, with DZP and jcpl basis sets.To sum up, there is no clear recommendation as to which DFTbased approach provides consistently better results for 1H and 13C chemical shifts, and spin-spin couplings. However, there are some conclusions that hold for the three compounds investigated. First, the geometry used does not introduce large deviations for the 1H and 13C chemical shifts, for both Gaussian09 and ADF2016. This is expected since the different functionals predict very similar geometries, but it contrasts with early results on the dependence on geometries.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP001143A", "abstract" : "In this and a subsequent article, the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. In the given first paper, various issues are explored that are related to this goal. It is shown that both the relativistic DFT-ZORA (zeroth-order regular approximation, as developed for NMR properties by Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689) and the older quasi-relativistic (QR) DFT methods are applicable to these compounds. Another popular relativistic method, the use of relativistic effective core potentials (ECP) for the calculation of ligand NMR parameters, is tested as well. It is demonstrated that the ECP approach is beyond its limits for the very heavy actinide compounds. Comparing the ZORA and Pauli approaches, it is found that Pauli is more accurate for the 1H NMR in UF6-n(OCH3)n compounds whereas ZORA is m...", "author" : [ { "dropping-particle" : "", "family" : "Schreckenbach", "given" : "Georg", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wolff", "given" : "Stephen K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ziegler", "given" : "Tom", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "J. Phys. Chem. A", "id" : "ITEM-1", "issue" : "35", "issued" : { "date-parts" : [ [ "2000" ] ] }, "page" : "8244\u20138255", "publisher" : "American Chemical Society", "title" : "NMR Shielding Calculations across the Periodic Table:\u2009 Diamagnetic Uranium Compounds. 1. Methods and Issues", "type" : "article-journal", "volume" : "104" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[95]", "plainTextFormattedCitation" : "[95]", "previouslyFormattedCitation" : "[94]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[95] Compound 12 has the largest deviations from experiment, but even so the disagreement rarely exceeds 15%. The relative errors calculated for compounds 11 and 13 are persistently small. For 1H chemical shifts calculated with Gaussian09, the IGLOII basis set provides better results than pVDZ while the opposite holds for 13C shifts. Triple- and quadrupole-ζ polarized quality basis sets perform substantially worse than IGLOII for either case, at least for the PBE functional. The effect of including relativistic effects via scalar ZORA or ZORA + SOC in ADF2016 results in a smaller standard deviation of the relative errors for the latter; however, this effect is not large vs Gaussian09. The use of a relativistic pseudopotential for describing the inner electrons of uranium performs as well as a description of relativistic effects via scalar ZORA or ZORA + SOC plus all electron basis sets for chemical shifts. Therefore, the comparative ease of use and speed of SCF convergence using the pseudopotential approach with Gaussian09 makes this the best approach for calculating chemical shifts in these types of closed shell compounds. However, it is found that the correct description of 13C NMR chemical shifts of carbon atoms close to the uranium centre requires the use of ZORA+SOC with the jcpl basis set. Our range of relative errors for 13C chemical shifts agrees with the PBE results from similar studies, where the role of exchange-correlation is investigated.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/C6CP06129J", "ISSN" : "1463-9076", "abstract" : "Previous relativistic quantum-chemical predictions of unusually large 1H and 13C NMR chemical shifts for ligand atoms directly bonded to a diamagnetic uranium(VI) center (P. Hrob\u00e1rik, V. Hrob\u00e1rikov\u00e1, A. H. Greif and M. Kaupp, Angew. Chem., Int. Ed., 2012, 51, 10884) have been revisited by two- and four-component relativistic density functional methods. In particular, the effect of the exchange\u2013correlation response kernel, which had been missing in the previously used two-component version of the Amsterdam Density Functional program, has been examined. Kernel contributions are large for cases with large spin\u2013orbit (SO) contributions to the NMR shifts and may amount to up to \u223c30% of the total shifts, which means more than a 50 ppm difference for the metal-bonded carbon shifts in some extreme cases. Previous calculations with a PBE-40HF functional had provided overall reasonable predictions, due to cancellation of errors between the missing kernel contributions and the enhanced exact-exchange (EXX) admixture of 40%. In the presence of an exchange\u2013correlation kernel, functionals with lower EXX admixtures give already good agreement with experiments, and the PBE0 functional provides reasonable predictive quality. Most importantly, the revised approach still predicts unprecedented giant 1H NMR shifts between +30 ppm and more than +200 ppm for uranium(VI) hydride species. We also predict uranium-bonded 13C NMR shifts for some synthetically known organometallic U(VI) complexes, for which no corresponding signals have been detected to date. In several cases, the experimental lack of these signals may be attributed to unexpected spectral regions in which some of the 13C NMR shifts can appear, sometimes beyond the usual measurement area. An extremely large uranium-bonded 13C shift above 550 ppm, near the upper end of the diamagnetic 13C shift range, is predicted for a known pincer carbene complex. Bonding analyses allow in particular the magnitude of the SO shifts, and of their dependence on the functional, on the ligand position in the complex, and on the overall electronic structure to be better appreciated, and improved confidence ranges for predicted shifts have been obtained.", "author" : [ { "dropping-particle" : "", "family" : "Greif", "given" : "Anja H.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hrob\u00e1rik", "given" : "Peter", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Autschbach", "given" : "Jochen", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kaupp", "given" : "Martin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Phys. Chem. Chem. Phys.", "id" : "ITEM-1", "issue" : "44", "issued" : { "date-parts" : [ [ "2016" ] ] }, "page" : "30462-30474", "publisher" : "The Royal Society of Chemistry", "title" : "Giant spin\u2013orbit effects on 1 H and 13 C NMR shifts for uranium( vi ) complexes revisited: role of the exchange\u2013correlation response kernel, bonding analyses, and new predictions", "type" : "article-journal", "volume" : "18" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[101]", "plainTextFormattedCitation" : "[101]", "previouslyFormattedCitation" : "[100]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[101] For spin-spin couplings, LC-ωPBE with solvent corrections at the geometry optimized with LC-ωPBE appears the best choice. However, due to the difficulty of obtaining converged structures, the most appropriate approach would be to use the LC-ωPBE functional at the PBE-D3 optimized geometries. UV-vis spectraThe UV-vis spectra of compounds 10, 11 and 13 – 15 were simulated using time-dependent DFT (TDDFT) within the Gaussian09 and ADF2016 programs, using the same functionals and basis sets discussed in section 3 and used for the previously presented results. The geometries are those from our previous optimisations, unless otherwise indicated. We have also included solvent effects in Gaussian09 for each geometry through single point calculations with the PCM. Additionally, the CAMB3LYP functionalADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1016/j.cplett.2004.06.011", "ISSN" : "00092614", "abstract" : "A new hybrid exchange\u2013correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree\u2013Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the standard error function with parameter 0.33.", "author" : [ { "dropping-particle" : "", "family" : "Yanai", "given" : "Takeshi", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tew", "given" : "David P", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Handy", "given" : "Nicholas C", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics Letters", "id" : "ITEM-1", "issue" : "1", "issued" : { "date-parts" : [ [ "2004" ] ] }, "page" : "51-57", "title" : "A new hybrid exchange\u2013correlation functional using the Coulomb-attenuating method (CAM-B3LYP)", "type" : "article-journal", "volume" : "393" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[59]", "plainTextFormattedCitation" : "[59]", "previouslyFormattedCitation" : "[59]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[59] was employed at the PBE optimized geometries, as it is a widely used functional for studying optical properties, and has previously been recommended.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/c0cp02534h", "abstract" : "The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO22+, NUO+ and NUN molecules. Different exchange\u2013correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gomes", "given" : "Andr\u00e9 Severo Pereira", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ekstr\u00f6m", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Chemistry Chemical Physics", "id" : "ITEM-1", "issue" : "13", "issued" : { "date-parts" : [ [ "2011" ] ] }, "page" : "6249", "publisher" : "The Royal Society of Chemistry", "title" : "Electronic spectroscopy of UO22+, NUO+ and NUN: an evaluation of time-dependent density functional theory for actinides", "type" : "article-journal", "volume" : "13" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/jp3011266", "ISSN" : "1089-5639", "abstract" : "Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange\u2013correlation functional for the [UO2Cl4]2\u2013 system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approxi...", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bast", "given" : "Radovan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ruud", "given" : "Kenneth", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "27", "issued" : { "date-parts" : [ [ "2012", "7", "12" ] ] }, "page" : "7397-7404", "publisher" : "American Chemical Society", "title" : "Charge-Transfer Excitations in Uranyl Tetrachloride ([UO ₂ Cl ₄ ] ^2\u2013 ): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?", "type" : "article-journal", "volume" : "116" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1063/1.4812360", "ISSN" : "00219606", "abstract" : "We present an EOMCCSD (equation of motion coupled cluster with singles and doubles) study of excited states of the small [UO2]2+ and [UO2]+ model systems as well as the larger U VI O2(saldien) complex. In addition, the triples contribution within the EOMCCSDT and CR-EOMCCSD(T) (completely renormalized EOMCCSD with non-iterative triples) approaches for the [UO2]2+ and [UO2]+ systems as well as the active-space variant of the CR-EOMCCSD(T) method\u2014CR-EOMCCSd(t)\u2014for the U VI O2(saldien) molecule are investigated. The coupled cluster data were employed as benchmark to choose the \u201cbest\u201d appropriate exchange\u2013correlation functional for subsequent time-dependent density functional (TD-DFT) studies on the transition energies for closed-shell species. Furthermore, the influence of the saldien ligands on the electronic structure and excitation energies of the [UO2]+ molecule is discussed. The electronic excitations as well as their oscillator dipole strengths modeled with TD-DFT approach using the CAM-B3LYP exchange\u2013correlation functional for the [U V O2(saldien)]\u2212 with explicit inclusion of two dimethyl sulfoxide molecules are in good agreement with the experimental data of Takao et al. [Inorg. Chem.49, 2349 (Year: 2010)10.1021/ic902225f].", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Govind", "given" : "Niranjan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kowalski", "given" : "Karol", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jong", "given" : "Wibe A.", "non-dropping-particle" : "de", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-3", "issue" : "3", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "034301", "publisher" : "AIP Publishing", "title" : "Reliable modeling of the electronic spectra of realistic uranium complexes", "type" : "article-journal", "volume" : "139" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1063/1.2814157", "ISSN" : "00219606", "abstract" : "In order to assess the accuracy of wave-function and density functional theory(DFT) based methods for excited states of the uranyl(VI) U O 2 2 + molecule excitation energies and geometries of states originating from excitation from the \u03c3 u , \u03c3 g , \u03c0 u , and \u03c0 g orbitals to the nonbonding 5 f \u03b4 and 5 f \u03d5 have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCF\u2215CASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFT\u2215MRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFT\u2215MRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied \u03c3 u orbital are symmetric while that arising from excitations out of the \u03c0 u orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.", "author" : [ { "dropping-particle" : "", "family" : "Re\u0301al", "given" : "Florent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vallet", "given" : "Vale\u0301rie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Marian", "given" : "Christel", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wahlgren", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-4", "issue" : "21", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "214302", "publisher" : "AIP Publishing", "title" : "Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: A comparison between wave-function theory and density functional theory", "type" : "article-journal", "volume" : "127" }, "uris" : [ "" ] }, { "id" : "ITEM-5", "itemData" : { "DOI" : "10.1039/c3cp52090k", "abstract" : "In this work we explore the use of frozen density embedding [Gomes et al., Phys. Chem. Chem. Phys., 2008, 10, 5353] as a way to construct models of increasing sophistication for describing the low-lying electronic absorption spectra of UO22+ in the Cs2UO2Cl4 crystal. We find that a relatively simple embedding model, in which all but the UO22+ unit are represented by an embedding potential, can already describe the main spectral features and the main environment effects can be attributed to the four chloride ions situated at the UO22+ equatorial plane. Contributions from species further away, albeit small, are found to be important for reaching a close agreement with experimentally observed quantities such as the excited states' relative positions. These findings suggest that such an embedding approach is a viable alternative to supermolecular calculations employing larger models of actinyl species in condensed phase. Nevertheless, we observe a slight red shift of the excitation energies calculated with our models compared to experimental results, and attribute this discrepancy to inaccuracies in the underlying structural parameters.", "author" : [ { "dropping-particle" : "", "family" : "Gomes", "given" : "Andr\u00e9 Severo Pereira", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jacob", "given" : "Christoph R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "R\u00e9al", "given" : "Florent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vallet", "given" : "Val\u00e9rie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Chemistry Chemical Physics", "id" : "ITEM-5", "issue" : "36", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "15153", "publisher" : "The Royal Society of Chemistry", "title" : "Towards systematically improvable models for actinides in condensed phase: the electronic spectrum of uranyl in Cs2UO2Cl4 as a test case", "type" : "article-journal", "volume" : "15" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[102\u2013106]", "plainTextFormattedCitation" : "[102\u2013106]", "previouslyFormattedCitation" : "[101\u2013105]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[102–106] Therefore, per functional per compound there are four different UV-vis spectra. The agreement with experiment has been quantified by calculating the relative error (in %) in the energy position of the experimental maximum absorbance peak with respect to the transition with the largest oscillator strength for each functional.In general, similar conclusions hold for each of the closed-shell compounds 10, 11 and 13 – 15, so we will discuss in detail only the results for compound 14, as a representative example. Computed data for the other compounds can be found in section 6 of the SI, and the experimental UV-vis spectrum of compound 10 is given in section 7 of the SI. REF _Ref465681025 \h \* MERGEFORMAT Figure 6 compares the experimental UV-vis spectrum of compound 14 with those simulated by TDDFT. An overlapped graphical representation of all spectra obtained can be found in Figure SI 28 in section 6 of the SI. The geometries used are from the same functional as for the TDDFT calculations, except for CAMB3LYP results which are obtained at the PBE optimized geometry. For each subplot, the experimental absorbance is compared with the absorbance calculated with the excitation energies and oscillator strengths predicted by a particular functional, with and without solvent.There are two main conclusions that one can derive from REF _Ref465681025 \h \* MERGEFORMAT Figure 6, and from the rest of compounds presented in section 6 of the SI. Firstly, using the optimised geometry with or without dispersion corrections does not modify the curves and the inclusion of the solvent only modifies the peaks height. Secondly, and more importantly, pure exchange functionals consistently provide more accurate results (14 % of averaged relative errors for PBE) while long-range corrected functionals are off by 40 – 50 %. Hybrid functionals lie within these two extremes. This seemingly better performance of the pure exchange functionals stems from their predicting transitions in the lower energy regions, whereas long-range corrected functionals largely overestimate these energies. This is summarized in REF _Ref469409797 \h \* MERGEFORMAT Table 6 where the relative errors of all the investigated compounds are presented. Hyphen-containing rows of compounds 10, 11, 13 – 15 denote that the calculation did not converge properly and stopped due to “Excessive mixing of frozen core and valence orbitals.” Interestingly, these results appear to be in sharp contrast to the recommendations made for other U(VI) molecules,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/c0cp02534h", "abstract" : "The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO22+, NUO+ and NUN molecules. Different exchange\u2013correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Gomes", "given" : "Andr\u00e9 Severo Pereira", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ekstr\u00f6m", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Chemistry Chemical Physics", "id" : "ITEM-1", "issue" : "13", "issued" : { "date-parts" : [ [ "2011" ] ] }, "page" : "6249", "publisher" : "The Royal Society of Chemistry", "title" : "Electronic spectroscopy of UO22+, NUO+ and NUN: an evaluation of time-dependent density functional theory for actinides", "type" : "article-journal", "volume" : "13" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/jp3011266", "ISSN" : "1089-5639", "abstract" : "Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange\u2013correlation functional for the [UO2Cl4]2\u2013 system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approxi...", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bast", "given" : "Radovan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ruud", "given" : "Kenneth", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "27", "issued" : { "date-parts" : [ [ "2012", "7", "12" ] ] }, "page" : "7397-7404", "publisher" : "American Chemical Society", "title" : "Charge-Transfer Excitations in Uranyl Tetrachloride ([UO ₂ Cl ₄ ] ^2\u2013 ): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?", "type" : "article-journal", "volume" : "116" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1063/1.4812360", "ISSN" : "00219606", "abstract" : "We present an EOMCCSD (equation of motion coupled cluster with singles and doubles) study of excited states of the small [UO2]2+ and [UO2]+ model systems as well as the larger U VI O2(saldien) complex. In addition, the triples contribution within the EOMCCSDT and CR-EOMCCSD(T) (completely renormalized EOMCCSD with non-iterative triples) approaches for the [UO2]2+ and [UO2]+ systems as well as the active-space variant of the CR-EOMCCSD(T) method\u2014CR-EOMCCSd(t)\u2014for the U VI O2(saldien) molecule are investigated. The coupled cluster data were employed as benchmark to choose the \u201cbest\u201d appropriate exchange\u2013correlation functional for subsequent time-dependent density functional (TD-DFT) studies on the transition energies for closed-shell species. Furthermore, the influence of the saldien ligands on the electronic structure and excitation energies of the [UO2]+ molecule is discussed. The electronic excitations as well as their oscillator dipole strengths modeled with TD-DFT approach using the CAM-B3LYP exchange\u2013correlation functional for the [U V O2(saldien)]\u2212 with explicit inclusion of two dimethyl sulfoxide molecules are in good agreement with the experimental data of Takao et al. [Inorg. Chem.49, 2349 (Year: 2010)10.1021/ic902225f].", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Govind", "given" : "Niranjan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Kowalski", "given" : "Karol", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jong", "given" : "Wibe A.", "non-dropping-particle" : "de", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-3", "issue" : "3", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "034301", "publisher" : "AIP Publishing", "title" : "Reliable modeling of the electronic spectra of realistic uranium complexes", "type" : "article-journal", "volume" : "139" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1063/1.2814157", "ISSN" : "00219606", "abstract" : "In order to assess the accuracy of wave-function and density functional theory(DFT) based methods for excited states of the uranyl(VI) U O 2 2 + molecule excitation energies and geometries of states originating from excitation from the \u03c3 u , \u03c3 g , \u03c0 u , and \u03c0 g orbitals to the nonbonding 5 f \u03b4 and 5 f \u03d5 have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCF\u2215CASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFT\u2215MRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFT\u2215MRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied \u03c3 u orbital are symmetric while that arising from excitations out of the \u03c0 u orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.", "author" : [ { "dropping-particle" : "", "family" : "Re\u0301al", "given" : "Florent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vallet", "given" : "Vale\u0301rie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Marian", "given" : "Christel", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wahlgren", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-4", "issue" : "21", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "214302", "publisher" : "AIP Publishing", "title" : "Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: A comparison between wave-function theory and density functional theory", "type" : "article-journal", "volume" : "127" }, "uris" : [ "" ] }, { "id" : "ITEM-5", "itemData" : { "DOI" : "10.1039/c3cp52090k", "abstract" : "In this work we explore the use of frozen density embedding [Gomes et al., Phys. Chem. Chem. Phys., 2008, 10, 5353] as a way to construct models of increasing sophistication for describing the low-lying electronic absorption spectra of UO22+ in the Cs2UO2Cl4 crystal. We find that a relatively simple embedding model, in which all but the UO22+ unit are represented by an embedding potential, can already describe the main spectral features and the main environment effects can be attributed to the four chloride ions situated at the UO22+ equatorial plane. Contributions from species further away, albeit small, are found to be important for reaching a close agreement with experimentally observed quantities such as the excited states' relative positions. These findings suggest that such an embedding approach is a viable alternative to supermolecular calculations employing larger models of actinyl species in condensed phase. Nevertheless, we observe a slight red shift of the excitation energies calculated with our models compared to experimental results, and attribute this discrepancy to inaccuracies in the underlying structural parameters.", "author" : [ { "dropping-particle" : "", "family" : "Gomes", "given" : "Andr\u00e9 Severo Pereira", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jacob", "given" : "Christoph R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "R\u00e9al", "given" : "Florent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vallet", "given" : "Val\u00e9rie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Chemistry Chemical Physics", "id" : "ITEM-5", "issue" : "36", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "15153", "publisher" : "The Royal Society of Chemistry", "title" : "Towards systematically improvable models for actinides in condensed phase: the electronic spectrum of uranyl in Cs2UO2Cl4 as a test case", "type" : "article-journal", "volume" : "15" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[102\u2013106]", "plainTextFormattedCitation" : "[102\u2013106]", "previouslyFormattedCitation" : "[101\u2013105]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[102–106] for which CAMB3LYP functional is favoured.Figure SEQ Figure \* ARABIC 6. Predicted UV-vis spectra for compound 14 using Gaussian09. The left y-axis in each subplot presents the calculated absorbance whereas the right y-axis refers to the predicted oscillator strength, denoted here by vertical lines; x-axis shows the wavelength values in nm. A half-field value of 0.4 eV has been used. The experimental absorbance is shown as black vertical lines, to which an arbitrary shift factor of 4000 has been applied to facilitate comparison between computed and measured data. The list of relative errors for each functional in the same order as the subplots is [(9,18,14,15),(40,40,41,37),(22,22,19,20),(32,30),(32,32,34,29),(49,52,50,50),(39,39,40,41)].In order to explore these discrepancies further, we performed TD-DFT calculations on [UO2Cl4]2-, using pure-exchange (PBE, TPSS) and long-range corrected (LC-ωPBE, CAMB3LYP) functionals. [UO2Cl4]2- features the UO22+ unit at the heart of all of our other target systems, and has been previously studied both experimentally and computationally. The geometry we employ has D4h point group symmetry with U-O and U-Cl distances of 1.783 ? and 2.712 ?, respectively; these are the same as those reported by Pierloot et al. in their CASPT2ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.2121608", "ISSN" : "00219606", "abstract" : "A theoretical study is presented of the electronic spectra of the U O 2 2 + and U O 2 Cl 4 2 \u2212 ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-\u00c5. Malmqvist et al., Chem. Phys. Lett.357, 230 (2002); B. O. Roos and P.-\u00c5. Malmqvist, Phys. Chem. Chem. Phys.6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs 2 U O 2 Cl 4 crystals from Denning [Struct. Bonding (Berlin)79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A.105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.", "author" : [ { "dropping-particle" : "", "family" : "Pierloot", "given" : "Kristine", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Besien", "given" : "Els", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "20", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "204309", "publisher" : "AIP Publishing", "title" : "Electronic structure and spectrum of UO[sub 2][sup 2+] and UO[sub 2]Cl[sub 4][sup 2\u2212]", "type" : "article-journal", "volume" : "123" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[107]", "plainTextFormattedCitation" : "[107]", "previouslyFormattedCitation" : "[106]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[107] calculations, for which results match experiment.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1007/BFb0036502", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "R. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Complexes, Clusters and Crystal Chemistry", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1992" ] ] }, "page" : "215-276", "publisher" : "Springer-Verlag", "title" : "Electronic structure and bonding in actinyl ions", "type" : "chapter" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1016/0009-2614(91)87123-S", "ISSN" : "00092614", "abstract" : "The polarised excited-state optical absorption spectrum of a single crystal of Cs2UO2Cl4 at 77 K is reported. The intense absorption band near 580 nm is polarised parallel to the U\ue5f8O axis. This observation is used to locate the highest-filled gerade orbital and to establish the role of the 6d orbitals in the formation of the uranyl ion.", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "R.G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Morrison", "given" : "I.D.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chemical Physics Letters", "id" : "ITEM-2", "issue" : "1", "issued" : { "date-parts" : [ [ "1991" ] ] }, "page" : "101-104", "publisher" : "North-Holland", "title" : "The electronic structure of actinyl ions: the excited-state absorption spectrum of Cs2UO2Cl4", "type" : "article-journal", "volume" : "180" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1021/ic00258a018", "ISSN" : "0020-1669", "author" : [ { "dropping-particle" : "", "family" : "Barker", "given" : "Trevor J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Denning", "given" : "Robert G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Thorne", "given" : "Jonathan R. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-3", "issue" : "11", "issued" : { "date-parts" : [ [ "1987", "6" ] ] }, "page" : "1721-1732", "publisher" : "American Chemical Society", "title" : "Applications of two-photon spectroscopy to inorganic compounds. 1. Spectrum and electronic structure of dicesium tetrachlorodioxouranate", "type" : "article-journal", "volume" : "26" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1021/IC001027M", "abstract" : "The optical absorption, emission, FT Raman, one-photon excitation, two-photon excitation, and luminescence lifetime measurements are reported for UO2Cl42- in 40:60 AlCl3\u2212EMIC (where EMIC \u2261 1-ethyl-3-methylimidazolium chloride), a room-temperature ionic liquid. Comparison of the spectra with previous results from single crystals containing UO2Cl42- allowed the characterization of four ground-state vibrational frequencies, two excited-state vibrational frequencies, and the location of eight electronic excited-state energy levels. The vibrational frequencies and electronic energy levels are found to be consistent with the UO2Cl42- ion. Comparison of the one-photon and two-photon excitation spectra, and the relative intensities of the transitions in the emission spectrum indicate that the center of symmetry is perturbed by an interaction with the solvent.", "author" : [ { "dropping-particle" : "", "family" : "Todd A. Hopkins", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "John M. Berg", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "David A. Costa", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wayne H. Smith", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dewey", "given" : "Harry J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-4", "issue" : "8", "issued" : { "date-parts" : [ [ "2001" ] ] }, "page" : "1820-1825", "publisher" : "American Chemical Society", "title" : "Spectroscopy of UO2Cl42- in Basic Aluminum Chloride\u22121-Ethyl-3-methylimidazolium Chloride", "type" : "article-journal", "volume" : "40" }, "uris" : [ "" ] }, { "id" : "ITEM-5", "itemData" : { "DOI" : "10.1063/1.1510445", "ISSN" : "0021-9606", "abstract" : "Polarized oxygen K\u03b1 x-ray absorption and emission spectra, near 530 eV, of a single crystal of Cs2UO2Cl4 are reported. With the aid of density functional theory calculations and the absorption data, the relative energies of the empty molecular orbitals having primarily uranium 5f and 6d character are assigned. The emission spectra give access to the energy of excitations to these orbitals from the various filled valence-shell orbitals. These energies support the conclusion from the optical spectra that valence excitations from the \u03c3u occupied valence orbitals occur at substantially lower energies than those from the \u03c3g, \u03c0g, and \u03c0u orbitals. This latter group of molecular orbitals have much larger oxygen-2p character. The participation of the pseudocore 6p shell in the covalent bonding is established directly by the presence of a charge-transfer transition in emission. With the aid of previous work on the polarized uranium L1- and L3-edge absorption spectra, the order of the empty metal-centered antibondin...", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "R. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Green", "given" : "J. C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hutchings", "given" : "T. E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dallera", "given" : "C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tagliaferri", "given" : "A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Giarda", "given" : "K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Brookes", "given" : "N. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Braicovich", "given" : "L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-5", "issue" : "17", "issued" : { "date-parts" : [ [ "2002", "11" ] ] }, "page" : "8008-8020", "publisher" : "American Institute of PhysicsAIP", "title" : "Covalency in the uranyl ion: A polarized x-ray spectroscopic study", "type" : "article-journal", "volume" : "117" }, "uris" : [ "" ] }, { "id" : "ITEM-6", "itemData" : { "DOI" : "10.1021/JP071061N", "abstract" : "This Feature Article seeks to present the current state of knowledge, both experimental and theoretical, of the electronic structure and bonding in actinyl ions and related species, such as the isoelectronic imido compounds as well as in linear triatomic actinide molecules of the type X\u2212An\u2212Y.", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "Robert G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-6", "issue" : "20", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "4125\u20134143", "publisher" : "American Chemical Society", "title" : "Electronic Structure and Bonding in Actinyl Ions and their Analogs", "type" : "article-journal", "volume" : "111" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[108\u2013113]", "plainTextFormattedCitation" : "[108\u2013113]", "previouslyFormattedCitation" : "[107\u2013112]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[108–113] The experimental values that we use as a reference are in Table 2 of reference ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/IC001027M", "abstract" : "The optical absorption, emission, FT Raman, one-photon excitation, two-photon excitation, and luminescence lifetime measurements are reported for UO2Cl42- in 40:60 AlCl3\u2212EMIC (where EMIC \u2261 1-ethyl-3-methylimidazolium chloride), a room-temperature ionic liquid. Comparison of the spectra with previous results from single crystals containing UO2Cl42- allowed the characterization of four ground-state vibrational frequencies, two excited-state vibrational frequencies, and the location of eight electronic excited-state energy levels. The vibrational frequencies and electronic energy levels are found to be consistent with the UO2Cl42- ion. Comparison of the one-photon and two-photon excitation spectra, and the relative intensities of the transitions in the emission spectrum indicate that the center of symmetry is perturbed by an interaction with the solvent.", "author" : [ { "dropping-particle" : "", "family" : "Todd A. Hopkins", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "John M. Berg", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "David A. Costa", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wayne H. Smith", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dewey", "given" : "Harry J.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Inorganic Chemistry", "id" : "ITEM-1", "issue" : "8", "issued" : { "date-parts" : [ [ "2001" ] ] }, "page" : "1820-1825", "publisher" : "American Chemical Society", "title" : "Spectroscopy of UO2Cl42- in Basic Aluminum Chloride\u22121-Ethyl-3-methylimidazolium Chloride", "type" : "article-journal", "volume" : "40" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[111]", "plainTextFormattedCitation" : "[111]", "previouslyFormattedCitation" : "[110]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[111].Prior to commenting on our results, it is instructive to highlight some wellunderstood features of the [UO2Cl4]2- electronic spectrum. It is experimentally knownADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1007/BFb0036502", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "R. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Complexes, Clusters and Crystal Chemistry", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1992" ] ] }, "page" : "215-276", "publisher" : "Springer-Verlag", "title" : "Electronic structure and bonding in actinyl ions", "type" : "chapter" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/JP071061N", "abstract" : "This Feature Article seeks to present the current state of knowledge, both experimental and theoretical, of the electronic structure and bonding in actinyl ions and related species, such as the isoelectronic imido compounds as well as in linear triatomic actinide molecules of the type X\u2212An\u2212Y.", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "Robert G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "20", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "4125\u20134143", "publisher" : "American Chemical Society", "title" : "Electronic Structure and Bonding in Actinyl Ions and their Analogs", "type" : "article-journal", "volume" : "111" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[108,113]", "plainTextFormattedCitation" : "[108,113]", "previouslyFormattedCitation" : "[107,112]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[108,113] and theoretically supportedADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.2121608", "ISSN" : "00219606", "abstract" : "A theoretical study is presented of the electronic spectra of the U O 2 2 + and U O 2 Cl 4 2 \u2212 ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-\u00c5. Malmqvist et al., Chem. Phys. Lett.357, 230 (2002); B. O. Roos and P.-\u00c5. Malmqvist, Phys. Chem. Chem. Phys.6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs 2 U O 2 Cl 4 crystals from Denning [Struct. Bonding (Berlin)79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A.105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.", "author" : [ { "dropping-particle" : "", "family" : "Pierloot", "given" : "Kristine", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Besien", "given" : "Els", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "20", "issued" : { "date-parts" : [ [ "2005" ] ] }, "page" : "204309", "publisher" : "AIP Publishing", "title" : "Electronic structure and spectrum of UO[sub 2][sup 2+] and UO[sub 2]Cl[sub 4][sup 2\u2212]", "type" : "article-journal", "volume" : "123" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1063/1.2735297", "ISSN" : "00219606", "abstract" : "The electronic spectra of U O 2 2 + and [ U O 2 Cl 4 ] 2 \u2212 are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding \u03c3 u + orbital into the nonbonding \u03b4 u or \u03d5 u orbitals for U O 2 2 + and the corresponding excitations for [ U O 2 Cl 4 ] 2 \u2212 are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U\u2013O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.", "author" : [ { "dropping-particle" : "", "family" : "Pierloot", "given" : "Kristine", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Besien", "given" : "Els", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lenthe", "given" : "Erik", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "Evert Jan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-2", "issue" : "19", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "194311", "publisher" : "AIP Publishing", "title" : "Electronic spectrum of UO[sub 2][sup 2+] and [UO[sub 2]Cl[sub 4]][sup 2\u2212] calculated with time-dependent density functional theory", "type" : "article-journal", "volume" : "126" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[107,114]", "plainTextFormattedCitation" : "[107,114]", "previouslyFormattedCitation" : "[106,113]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[107,114] that the lowest energy excitations (below ~30000 cm-1 = 333 nm) are effectively confined to the orbitals of the uranyl unit, originating from the σu HOMO. The more energetic region (~33000 cm-1 = 303 nm) is assigned to chloride-to-uranyl charge transfers, on the basis of CASSCF dataADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/JP003032H", "abstract" : "The electronic energy levels of the uranyl ion (UO22+) and the neptunyl ion (NpO22+) in the crystalline environment of Cs2UO2Cl4 are studied theoretically and compared with the spectroscopic work of Denning and co-workers. A layered-cluster computational method is used. The valence electrons of the actinyl ion and the nearest-neighbor chloride ions are treated explicitly, the closest cesium ions are replaced by all-electron core potentials, and all ions further away are replaced by point charges. The cluster is approximately spherical overall and contains 1873 ions. For the electrons treated explicitly, we use relativistic quantum chemical theory, including relativistic effective core potentials, corresponding spin\u2212orbit operators, and spin\u2212orbit, graphical unitary group configuration interaction. The effects of the crystalline environment on bond distances, vibrational frequencies, excitation energies, energy splittings, and wave function character are examined. Shifts are generally more accurate than ab...", "author" : [ { "dropping-particle" : "", "family" : "Spiridoula Matsika", "given" : "", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Pitzer", "given" : "Russell M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "3", "issued" : { "date-parts" : [ [ "2001" ] ] }, "page" : "637-645", "publisher" : "American Chemical Society", "title" : "Actinyl Ions in Cs2UO2Cl4", "type" : "article-journal", "volume" : "105" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[115]", "plainTextFormattedCitation" : "[115]", "previouslyFormattedCitation" : "[114]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[115] in a crystalline environment and gas-phase CASPT2ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp911271q", "ISSN" : "1089-5639", "abstract" : "The electronic spectra of uranyl(VI) coordinated with four equatorial halide ligands, [UO2X4]2\u2212 (X = F, Cl, Br, and I), have been calculated at the all-electron level using the multiconfigurational CASPT2 method, with spin\u2212orbit coupling included through the variational-perturbational method. The halide-to-uranyl charge-transfer states were taken into account in the calculation by including ligand orbitals in the active space. In order to do that, it is assumed that the charge transfer takes place from only one of the four ligands. Two models, which in principle can describe this, were investigated: the first one makes use of a localizing technique and the second one replaces three ligands by ab initio model potentials (AIMPs). The basis set dependence was investigated by using two different basis sets for the halides, of triple-\u03b6 and quadruple-\u03b6 quality. The localization procedure turned out to be strongly basis set dependent, and the most stable results were obtained with ab initio model potentials. The...", "author" : [ { "dropping-particle" : "", "family" : "Ruipe\u0301rez", "given" : "Fernando", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wahlgren", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "10", "issued" : { "date-parts" : [ [ "2010", "3", "18" ] ] }, "page" : "3615-3621", "publisher" : " American Chemical Society", "title" : "Charge Transfer in Uranyl(VI) Halides [UO ₂ X ₄ ] ^2\u2212 (X = F, Cl, Br, and I). A Quantum Chemical Study of the Absorption Spectra", "type" : "article-journal", "volume" : "114" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[116]", "plainTextFormattedCitation" : "[116]", "previouslyFormattedCitation" : "[115]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[116] calculations. This agrees with what has been observed for uranyl(VI) aquo ions showing ligand-to-metal charge transfer (LMCT) at around 272 – 219 nm.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1039/C4SC02022G", "ISSN" : "2041-6520", "author" : [ { "dropping-particle" : "", "family" : "Drobot", "given" : "Bj\u00f6rn", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Steudtner", "given" : "Robin", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Raff", "given" : "Johannes", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Geipel", "given" : "Gerhard", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Brendler", "given" : "Vinzenz", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tsushima", "given" : "Satoru", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Chem. Sci.", "id" : "ITEM-1", "issue" : "2", "issued" : { "date-parts" : [ [ "2015" ] ] }, "page" : "964-972", "publisher" : "Royal Society of Chemistry", "title" : "Combining luminescence spectroscopy, parallel factor analysis and quantum chemistry to reveal metal speciation \u2013 a case study of uranyl(VI) hydrolysis", "type" : "article-journal", "volume" : "6" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[117]", "plainTextFormattedCitation" : "[117]", "previouslyFormattedCitation" : "[116]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[117] However, no clear experimental information on these LMCT transitions in [UO2Cl4]2- is available. The comparison between our calculated and the experimental UV-vis spectrum for [UO2Cl4]2- can be found in Figure SI 31 in section 6 of the SI, and reveals the same behaviour as for compounds 10, 11 and 13 – 15 (see last row of REF _Ref469409797 \h \* MERGEFORMAT Table 6). REF _Ref469909821 \h \* MERGEFORMAT Figure 7a summarizes the [UO2Cl4]2- results, highlighting the energy range spanned by the orbitals that participate in electronic transitions with an oscillator strength larger than 0.01. It is clear that:for both pure-exchange and long-range corrected functionals, the predicted excitation spectra are governed largely by transitions originating from orbitals centred on the chlorine atoms, as noted previously from DFT calculations.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1063/1.2735297", "ISSN" : "00219606", "abstract" : "The electronic spectra of U O 2 2 + and [ U O 2 Cl 4 ] 2 \u2212 are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding \u03c3 u + orbital into the nonbonding \u03b4 u or \u03d5 u orbitals for U O 2 2 + and the corresponding excitations for [ U O 2 Cl 4 ] 2 \u2212 are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U\u2013O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.", "author" : [ { "dropping-particle" : "", "family" : "Pierloot", "given" : "Kristine", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Besien", "given" : "Els", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Lenthe", "given" : "Erik", "non-dropping-particle" : "van", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Baerends", "given" : "Evert Jan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-1", "issue" : "19", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "194311", "publisher" : "AIP Publishing", "title" : "Electronic spectrum of UO[sub 2][sup 2+] and [UO[sub 2]Cl[sub 4]][sup 2\u2212] calculated with time-dependent density functional theory", "type" : "article-journal", "volume" : "126" }, "uris" : [ "" ] }, { "id" : "ITEM-2", "itemData" : { "DOI" : "10.1021/JP071061N", "abstract" : "This Feature Article seeks to present the current state of knowledge, both experimental and theoretical, of the electronic structure and bonding in actinyl ions and related species, such as the isoelectronic imido compounds as well as in linear triatomic actinide molecules of the type X\u2212An\u2212Y.", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "Robert G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-2", "issue" : "20", "issued" : { "date-parts" : [ [ "2007" ] ] }, "page" : "4125\u20134143", "publisher" : "American Chemical Society", "title" : "Electronic Structure and Bonding in Actinyl Ions and their Analogs", "type" : "article-journal", "volume" : "111" }, "uris" : [ "" ] }, { "id" : "ITEM-3", "itemData" : { "DOI" : "10.1063/1.1510445", "ISSN" : "0021-9606", "abstract" : "Polarized oxygen K\u03b1 x-ray absorption and emission spectra, near 530 eV, of a single crystal of Cs2UO2Cl4 are reported. With the aid of density functional theory calculations and the absorption data, the relative energies of the empty molecular orbitals having primarily uranium 5f and 6d character are assigned. The emission spectra give access to the energy of excitations to these orbitals from the various filled valence-shell orbitals. These energies support the conclusion from the optical spectra that valence excitations from the \u03c3u occupied valence orbitals occur at substantially lower energies than those from the \u03c3g, \u03c0g, and \u03c0u orbitals. This latter group of molecular orbitals have much larger oxygen-2p character. The participation of the pseudocore 6p shell in the covalent bonding is established directly by the presence of a charge-transfer transition in emission. With the aid of previous work on the polarized uranium L1- and L3-edge absorption spectra, the order of the empty metal-centered antibondin...", "author" : [ { "dropping-particle" : "", "family" : "Denning", "given" : "R. G.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Green", "given" : "J. C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Hutchings", "given" : "T. E.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Dallera", "given" : "C.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Tagliaferri", "given" : "A.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Giarda", "given" : "K.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Brookes", "given" : "N. B.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Braicovich", "given" : "L.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Chemical Physics", "id" : "ITEM-3", "issue" : "17", "issued" : { "date-parts" : [ [ "2002", "11" ] ] }, "page" : "8008-8020", "publisher" : "American Institute of PhysicsAIP", "title" : "Covalency in the uranyl ion: A polarized x-ray spectroscopic study", "type" : "article-journal", "volume" : "117" }, "uris" : [ "" ] }, { "id" : "ITEM-4", "itemData" : { "DOI" : "10.1039/c3cp52090k", "abstract" : "In this work we explore the use of frozen density embedding [Gomes et al., Phys. Chem. Chem. Phys., 2008, 10, 5353] as a way to construct models of increasing sophistication for describing the low-lying electronic absorption spectra of UO22+ in the Cs2UO2Cl4 crystal. We find that a relatively simple embedding model, in which all but the UO22+ unit are represented by an embedding potential, can already describe the main spectral features and the main environment effects can be attributed to the four chloride ions situated at the UO22+ equatorial plane. Contributions from species further away, albeit small, are found to be important for reaching a close agreement with experimentally observed quantities such as the excited states' relative positions. These findings suggest that such an embedding approach is a viable alternative to supermolecular calculations employing larger models of actinyl species in condensed phase. Nevertheless, we observe a slight red shift of the excitation energies calculated with our models compared to experimental results, and attribute this discrepancy to inaccuracies in the underlying structural parameters.", "author" : [ { "dropping-particle" : "", "family" : "Gomes", "given" : "Andr\u00e9 Severo Pereira", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Jacob", "given" : "Christoph R.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "R\u00e9al", "given" : "Florent", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Vallet", "given" : "Val\u00e9rie", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Physical Chemistry Chemical Physics", "id" : "ITEM-4", "issue" : "36", "issued" : { "date-parts" : [ [ "2013" ] ] }, "page" : "15153", "publisher" : "The Royal Society of Chemistry", "title" : "Towards systematically improvable models for actinides in condensed phase: the electronic spectrum of uranyl in Cs2UO2Cl4 as a test case", "type" : "article-journal", "volume" : "15" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[106,112\u2013114]", "plainTextFormattedCitation" : "[106,112\u2013114]", "previouslyFormattedCitation" : "[105,111\u2013113]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[106,112–114]the long-range corrected functionals yield a spectrum with a single dominant absorption at ~40485 cm-1 = 247 nm and ~35714 cm-1 = 280 nm, giving an error relative to experiment of 50 and 43% for LCωPBE and CAMB3LYP, respectively. These excitations are dominated by chloride-to-uranyl charge transfers, but also feature the πg orbitals of the uranyl unit.pure exchange functionals yield two features involving chloride-to-uranyl orbitals only: a main one centred at ~23255 cm-1 = 430 nm and ~24096 cm-1 = 415 nm for PBE and TPSS, respectively (relative errors to experiment of 13 and 16%), and a second transition occurring at more-or-less the same energy as those for long-range corrected functionals, matching the chloride-to-uranyl charge transfers predicted by CASPT2 results.ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp911271q", "ISSN" : "1089-5639", "abstract" : "The electronic spectra of uranyl(VI) coordinated with four equatorial halide ligands, [UO2X4]2\u2212 (X = F, Cl, Br, and I), have been calculated at the all-electron level using the multiconfigurational CASPT2 method, with spin\u2212orbit coupling included through the variational-perturbational method. The halide-to-uranyl charge-transfer states were taken into account in the calculation by including ligand orbitals in the active space. In order to do that, it is assumed that the charge transfer takes place from only one of the four ligands. Two models, which in principle can describe this, were investigated: the first one makes use of a localizing technique and the second one replaces three ligands by ab initio model potentials (AIMPs). The basis set dependence was investigated by using two different basis sets for the halides, of triple-\u03b6 and quadruple-\u03b6 quality. The localization procedure turned out to be strongly basis set dependent, and the most stable results were obtained with ab initio model potentials. The...", "author" : [ { "dropping-particle" : "", "family" : "Ruipe\u0301rez", "given" : "Fernando", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Wahlgren", "given" : "Ulf", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "10", "issued" : { "date-parts" : [ [ "2010", "3", "18" ] ] }, "page" : "3615-3621", "publisher" : " American Chemical Society", "title" : "Charge Transfer in Uranyl(VI) Halides [UO ₂ X ₄ ] ^2\u2212 (X = F, Cl, Br, and I). A Quantum Chemical Study of the Absorption Spectra", "type" : "article-journal", "volume" : "114" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[116]", "plainTextFormattedCitation" : "[116]", "previouslyFormattedCitation" : "[115]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[116]the orbitals implicated by the pure exchange functionals span a much narrower energy range than the long-range corrected functionals, the latter predicting the πg orbitals of the uranyl to be ~11 eV lower in energy than the empty f-orbitals. This explains why the excitations predicted by long-range corrected functionals are much more energetic than the pure functionals (see Figure SI 31 in section 6 of SI).Note that we also performed analogous studies on [UO2Cl4]2- at the various different reported geometries,ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "DOI" : "10.1021/jp3011266", "ISSN" : "1089-5639", "abstract" : "Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange\u2013correlation functional for the [UO2Cl4]2\u2013 system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approxi...", "author" : [ { "dropping-particle" : "", "family" : "Tecmer", "given" : "Pawe\u0142", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Bast", "given" : "Radovan", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Ruud", "given" : "Kenneth", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" }, { "dropping-particle" : "", "family" : "Visscher", "given" : "Lucas", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "The Journal of Physical Chemistry A", "id" : "ITEM-1", "issue" : "27", "issued" : { "date-parts" : [ [ "2012", "7", "12" ] ] }, "page" : "7397-7404", "publisher" : "American Chemical Society", "title" : "Charge-Transfer Excitations in Uranyl Tetrachloride ([UO ₂ Cl ₄ ] ^2\u2013 ): How Reliable are Electronic Spectra from Relativistic Time-Dependent Density Functional Theory?", "type" : "article-journal", "volume" : "116" }, "uris" : [ "" ] } ], "mendeley" : { "formattedCitation" : "[103]", "plainTextFormattedCitation" : "[103]", "previouslyFormattedCitation" : "[102]" }, "properties" : { "noteIndex" : 0 }, "schema" : "" }[103] and found similar results to those summarised above.In order to examine the potential role of diffuse functions, we repeated our study of [UO2Cl4]2- using the aug-cc-pVDZ basis sets for oxygen and chlorine, retaining the same uranium ECP and basis. The results are almost identical to those obtained without diffuse functions. Thus, PBE with (and without) diffuse functions predicts two main electronic excitations at 434 and 305 nm (430 and 301 nm) with the largest oscillator strengths. On the other hand CAMB3LYP predicts a single electronic excitation at 291 nm (281 nm).We now turn our attention to our target compounds. The above observations (i)(iv) are equally applicable to compound 14, as shown in REF _Ref469909821 \h \* MERGEFORMAT Figure 7 b), as well as the rest of U(VI) molecules investigated (see Figure SI 32 for an explicit comparison with compound 10). An additional feature present in compound 14 is that the spectra predicted by LC-ωPBE and CAMB3LYP also contain contributions from excitations to virtual orbitals located entirely on the ligands; this is not found using the pure-exchange functionals. As in the case of uranyl, we investigate the effect of diffuse functions for compound 14 and find essentially the same conclusions, except for an electronic excitation at 252 nm for which the use of diffuse functions reduces its oscillator strength by one order of magnitude.We therefore conclude that all the forms of TDDFT we have explored perform poorly. While the longrange corrected functionals do at least capture some of the anticipated uranyl character of the transitions, they predict the wrong orbital to be involved (?g as opposed to ?u) and predict the energy of the transition very poorly. By contrast, the pure functionals give much better agreement with experiment in terms of energies, but the character of the predicted transitions is incorrect. We therefore do not recommend any form of TDDFT for the simulation of uranyl (VI) electronic absorption spectra. Finally, we briefly discuss the results obtained when all-electron basis sets and scalar relativistic effects are included via the ZORA Hamiltonian. As in REF _Ref469409797 \h \* MERGEFORMAT Table 6, Table SI 8 presents the relative error between the energy position of the experimental maximum absorbance and the largest calculated oscillator strength, using the PBE functional. These results indicate that, for these compounds, including scalar relativistic corrections not only does not improve the results obtained with respect to pseudopotentials but in some cases leads to poorer agreement with experimental energies.Relative error (%)Pure exchangeHybridLong-range correctedPBETPSSPBE0TPSShB3LYPLC-ωPBECAMB3LYPcompound10-4-1231017393211--4----131115362628--1492240323249391512-42252851-[UO2Cl4]2-13165043Table SEQ Table \* ARABIC 6. Summary of relative errors in % for the UV-vis spectra of all closed-shell compounds, as predicted by the employed functionals using a pseudopotential in Gaussian09. Note that these results are obtained at the geometries consistent with the TDDFT method, except for compound 10 and [UO2Cl4]2- for which we used the experimental structures.Figure SEQ Figure \* ARABIC 7. Energies and associated orbitals involved in key transitions (oscillator strengths > 0.01) as predicted by the pure exchange PBE and long-range corrected CAMB3LYP functionals. a) [UO2Cl4]2- and b) compound 14 (hydrogen atoms have been omitted for clarity). The energy of the π-type uranyl orbitals has been set to zero as reference for both cases. Vertical dashed lines separate occupied and virtual orbitals. Red bars indicate the energetic range involved in the orbitals taking part in the most relevant excitations.ConclusionsIn this contribution, we have performed a detailed investigation of the performance of a range of DFT methodologies for the description of the ground and excited state properties of a series of representative uranium-based molecules, comparing our results with experimental data throughout. The molecules investigated cover a wide variety of oxidation states and ligand types, ensuring the generality of the conclusions, the principal ones of which are:The most robust approach to obtain accurate geometries is to employ the PBE functional with dispersion corrections.The principal factor guiding the choice of functional for calculating IR spectra is the functional which consistently predicts the most accurate molecular structures, i.e. PBE. By contrast, there is no clear recommendation as to which functional to use when seeking accurate Raman spectra, although PBE also generally performs a little better than the other functionals tested.For NMR parameters of closed shell U(VI) species, no DFT based approach provides consistently reliable results for 1H and 13C chemical shifts and spinspin couplings, although we can make some general observations: i) Among the investigated approaches, the disagreement with experiment of the averaged 1H and 13C chemical shifts rarely exceeds 15% for the three compounds ii) the geometry employed has relatively little effect on the 1H and 13C chemical shifts iii) The NMR-specific IGLOII and jcpl basis sets provide the best results overall; increasing the quality of the basis set to include triple- and quadrupole-ζ polarization does not bring any improvement iv) for the 13C chemical shifts, PBE0 and TPSS often perform worse than other functionals v) for spin-spin couplings, LC-ωPBE with solvent corrections at the geometry optimized with LC-ωPBE works best (albeit based on a small data set) vi) the inclusion of relativistic effects via scalar ZORA + SOC results in a less dispersed set of results for 13C NMR signals vs scalar ZORA vii) ZORA + SOC with jcpl basis sets is required for a balanced description of the chemical shifts of all NMR active atoms in the molecule.No form of TDDFT performs acceptably in predicting both the character and energies of the electronic excitations of uranyl (VI) compounds.The use of a pseudopotential on the uranium centres provides equal, if not better, agreement with experiment vs all-electron basis set calculations, for all properties investigated.We are now extending our study to the calculation of the electronic excitation energies and magnetic properties of both our closed and openshell targets using wavefunction-based approaches, and these results will be reported in a forthcoming paper.Acknowledgements.We thank the STFC for funding (DR and FO) and the University of Manchester’s Computational Shared Facility for computational resources. We also thank Henry Storms La Pierre for ideas, help and advice with the synthesis of compounds 9, 10 and 17 and Karsten Meyer for providing a studentship placement for SR. We are grateful to the EPSRC for funding a Career Acceleration Fellowship (LSN) and a studentship (SR) (grant number EP/G004846/1). We also thank the Leverhulme Trust for additional postdoctoral funding (FO) (RL-2012-072) and a research Leadership award (LSN). This work was also part funded by the EPSRC (grant number EP/K039547/1)ReferencesADDIN Mendeley Bibliography CSL_BIBLIOGRAPHY [1]M. Reiher, A. Wolf, Relativistic quantum chemistry: the fundamental theory of molecular science, Wiley-VCH, 2009.[2]M. Dolg, Computational methods in lanthanide and actinide chemistry, Wiley-VCH, 2015.[3]N. Kaltsoyannis, Recent developments in computational actinide chemistry, Chem. Soc. Rev. 32 (2003) 9–16.[4]D. Wang, W.F. van Gunsteren, Z. Chai, Recent advances in computational actinoid chemistry, Chem. Soc. 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