CHEMISTRY 51



Introduction to Molecular Modeling

OBJECTIVES

The following exercises have been designed to give you an introduction to a very powerful molecular modeling package known as Spartan ’08. This program is user-friendly and will allow the non-experts to calculate reliable values of molecular properties such as geometries and energies. For those of you who are continuing onto Organic Chemistry next year, you will explore more advanced techniques using this same package that is used to obtain the molecular pictures you observe in your textbook. After the demonstration, given in the computational laboratory (Room 113), you should be able to:

a) Open/Close Spartan and create simple molecules and ions and save files in your

space.

b) Manipulate molecules using the select, rotate, translate and scale options.

c) Click on MODEL to represent molecules in

i) Ball and Wire

ii) Tube

iii) Ball and Spoke

iv) Space Filling (this will give you an indication of the size of the molecule)

v) Label the atoms in the molecule or ion.

vi) Remove/Add the hydrogen atoms if the molecule contains them.

d) Using the GEOMETRY menu, determine the distance between atoms or the bond length, measure angles between 3 atoms as well as measure the dihedral angle or angle between two intercepting planes in a molecule.

e) Using the PROPERTIES menu, determine the Energy, Dipole Moment, Atomic Charges and Vibrational Modes of the species in question.

f) Using the GRAPHICAL SURFACES, obtain a Density Surface with Potential as Property, as well as the LUMO and HOMO surfaces of the species.

g) Using the SETUP menu, select CALCULATIONS to set up simple ab initio calculations to obtain properties such as Energy. The method we will use is the HARTREE-FOCK approximation. Sometimes the energy is given in a.u. or kcal/mol or kJ/mol. The conversion factor is:

1au= 627.5 kcal/mol=2625 kJ/mol

h) Learn how to delete dangling bonds and how to build molecules using Expert Mode. You will need this for the exercise you will do.

i) When your species is an ion, select in the Setup menu and Calculations submenu, the proper “Total Charge” as Anion or Cation.

You also have the choice of Dianion or Dication.

BACKGROUND

In lecture you were introduced to the Schrödinger wave equation:

[pic]

where the wave function ( is a function of the coordinates (x,y, and z) of the electron’s position in three dimensional space and where [pic] (the Hamiltonian) represents a set of mathematical instructions called an operator. This operator acts to give back the wave function multiplied by the constant E, which represents the total energy of the atom (the sum of the potential energy due to the attraction between the proton and the electron and the kinetic energy of the moving electron). The Schrödinger equation has been solved exactly for the hydrogen atom (a system that has one electron), where its solutions are actually quite familiar to chemist as s-, p-, and d- atomic orbitals. Although the Schrödinger equation may easily be written down for many-electron atoms and for molecules, it cannot be solved. Approximations must be made. Among them we have the following three:

a) Separation of nuclear electron motions (the “Born-Oppenheimer approximation”).

b) Separation of electron motions (the “Hartree-Fock approximation”).

c) Representation of the individual molecular orbitals in terms of linear combination of atom-centered basis functions or “atomic orbitals” (the “LCAO” approximation”).

In the calculations we will do today, we will use a basis set called 3-21G, which is among the simplest ab initio models used. This is successful in providing equilibrium (and transition state) geometries, as well as energetics of reaction which do not involve bond formation and bond breaking. Gaussian is the leading program for serious quantum chemistry but it is particularly difficult to use. Instead we will use Spartan’06. The College has a site license for Spartan that supports up to 15 simultaneous users.

Specifics of Today’s Computational Lab.

We will not demonstrate every aspect of the program but just the basic ones that will allow you to get important information. If you wish to familiarize yourself with the program, consult the tutorial, Spartan ’08 Tutorial and User’s Guide available through the Help function of the program. Spartan is relatively easy to use and you will be able to fly solo after the lab session. After today’s demo and discussion, do the exercises at the end of this document. It is due next week. When you arrive in lab (Seaver North 113 for this exercise), select a computer and log on. Create a folder in your own space and label it “SPARTAN_CHEM._1B_yourlastname”. You will save all the examples we do today there for your future reference. Click on “start” then choose “programs” and then “Spartan 08”. Again, we encourage you to save all the work in your own space in the folder you created since the disk on a public computer is cleaned up when the user logs off. You are probably familiar with this routine from your use of Excel.

MODELING EXPERIMENTS

Let’s start with a simple molecule to get you familiar with the basics, namely CH4.

STEP ONE: Start the program.

Go to

You should get the following screen:

[pic]

STEP TWO:

Click on File and select New and you will get some buttons active on the top and a Model Kit on the right as follows:

[pic]

STEP THREE:

a) Let’s build methane. Click on C and then click in the area and you will be placing a C atom with 4 dangling bonds.

b) If you then click on V you will see then that the program automatically places 4

hydrogen atoms, one attached to each of the dangling bonds. Now you have an initial geometry of this molecule.

The instructor will demonstrate how to

a) Click on each of the atoms and look at the lower right corner of the screen. It tells you the name of the element as well as the label given to that atom.

b) Let’s learn how to manipulate the molecule. Use the following table to learn how to rotate, translate and scale the molecule in the screen:

|Using the Mouse |

|The following functions are associated with the two-button mouse. |

|[pic] |

|keyboard |left buttona |right buttona |

|[pic] |

|- |picking, X/Y rotate |X/Y translate |

|Shift |range picking, Z rotate |scalingb |

|Control |multiple picking, global X/Y rotateb |global X/Y translate |

|Control + Shift |global Z rotatec |scalingb |

|Alt |group picking, bond rotation |bond stretching |

|Control ("Build" mode) |fragment X/Y rotate |fragment X/Y translate |

|Control + Shift ("Build" mode) |fragment Z rotate |scalingb |

|[pic] |

|a) Left and right buttons together with no modifier keys are used for defining a section box. |

|b) Scaling is always applied to all open molecules and fragments. |

|c) Global rotations can be either molecule or screen centered. This is controlled by Global Rotate in the Preferences dialog |

|(Options menu). |

c) Let’s represent the molecule in different formats by using the Model feature:

i) Wire, ii) Ball and Wire, iii) Tube, and iv) Space Filling

d) Learn how to place and remove labels as well as add or remove the hydrogens of

molecules that contain them.

STEP FOUR:

Before we measure the bond lengths and angles let’s minimize the structure by clicking [pic] on the energy minimization button.

Use the Geometry menu to

a) Measure Distance b) Measure Angle c) Measure Dihedral Angle

1) Water

a) Build the molecule of water.

b) Measure angle and bond length after minimizing the structure.

c) Let’s do a calculation and obtain vibrational modes, total energy, charges and other

properties, but before you do that, save this molecule in your folder

“SPARTAN_CHEM._1B_yourlastname”. You could save this Spartan File

as “water”.

d) Click on Setup and choose Calculations. A menu will appear where you tell the program what kind of calculation you want to do. We will calculate the Equilibrium Geometry at Ground state with Hartree-Fock 3-21G in vacuum. We will start from the Initial geometry, subject to Symmetry. Since water is a neutral molecule, the Total charge should be Neutral and Multiplicity “Singlet” (paired electrons). You will compute infrared, “IR”, spectra, “Thermodynamics”, “Vibrational Modes” and “Atomic Charges”. After you make these selections it should look like this:

[pic]

Click on Submit

Since you had already saved this file as “water”, it will give you a message that the job has started. Click on the “OK” button.

When the calculation has finished another message will appear letting you know that the job has been completed. Click on the “OK” in that message. If you don’t receive this message soon, click on Options and then select Monitor to get the status of your calculation.

Let’s explore the results of this calculation by clicking on Display. You have several options: Output, Properties, Surfaces, Spectra, Spreadsheet, Plots, etc... If you click on Output you will get a page that contains all the results of the calculations done. If you click on Properties you get a summary of the molecular properties of water in this case:

[pic]

Now, while you have this window opened, click on the box next to Display Dipole Vector under Dipole Moment: 2.39 debye and see the molecule on the screen. The arrow points to the most electronegative atom, which in this case is oxygen. Also click on one of the atoms of the water molecule and you will get the following menu that gives you the charges.

[pic]

If you click on the oxygen atom, for example, you will get the Mass Number as well as the Charges of it.

To get back to the previous window, click again on oxygen to “deselect” it.

2) How do the different modes of vibration look like in water?

Click on Display and select Spectra. Because we told the program to calculate these at the beginning of the calculation they should be displayed like this:

Now play with these three vibrational modes and see what happens. Click on the first yellow box, namely the water vibration of frequency 1798.86 cm-1 and notice how this vibration is animated on the screen. Try the other two.

To stop the animation click on the box again to deselect it. You may display the spectra for the molecule by clicking on Draw Calculated in the lower right hand corner of the Spectra box. If you would like to remove a spectrum after it has been displayed in the background, select Delete Calculated. If you used the view button (V) to add the hydrogen atoms, they will be removed from the atom, but the calculations do not need to be run again. Simply click on the view button again.

3) Is water bent or linear? How can you prove it?

[pic]

When you write the Lewis structure of water, you do not know what the geometry is. Is it linear or bent? You know by now it is bent, but how can you prove it by doing a calculation? Well, do the same type of calculation and see what kind of vibrations you get and total energy and see which one is more stable.

In order to build linear water you will have to use the Inorganic Model Kit. In that kit, select oxygen and below choose the button that has a central atom with two linear bonds, as well as single bonds. See figure on the left. Once you have selected an oxygen with linear bonds, click on the green screen and it will give you the linear form of water. Run the same type of calculations as you did for bent water and look at the vibrational modes. You will find that two of these vibrations are imaginary values. This is an indication that this molecule is unstable or does not exist.

4) Ammonia.

Measure the bond lengths, angles and dihedral angles. Do the bond angles agree with what is predicted from VSEPR theory?

Now let’s generate the different types of SURFACES you can get. For this case of Ammonia, Go to Setup and then choose Surfaces. Click on the “Add” button and choose the following four surfaces with the corresponding properties for each one as in the figure.

SURFACE PROPERTIES

a) density NONE

b) HOMO NONE

c) density potential

d) LUMO NONE

[pic]

Then go to Setup and choose Submit. You will get a message indicating that the generation of the surfaces has started. Click on the “OK” button. After a while you will get a message indicating that the calculations are done. Click on the “OK” button. Go to the Display and select Surfaces. You should get the following description but now with yellow boxes before the name of the surfaces. Click on one of the yellow boxes at a time to explore the corresponding surface. If you click on more than one at a time you will get an overlap of the selected surfaces.

[pic]

An electron density surface is a surface with the property that the electrons in the molecule will be found on or inside the surface a certain fraction of the time. This fraction is given by one minus the isovalue parameter. Hence with the default isovalue = 0.002, the electrons will be found on or inside the surface with 99.8% probability. Explore the surfaces for the HOMO (highest occupied molecular orbital) and notice the surface with the red color (negative sign) and the surface with the blue color (positive sign). Do the same for the LUMO.

Also notice that once you show a surface, you can go to the lower right corner and select the style this surface is drawn: dots, mesh, solid or transparent. Experiment with the different options in order to see how they influence the surface’s appearance.

NAME ___________________________Lab Section_____________ Date:__________

EXERCISE:

PROBLEM 1: Exploring Electronegativity and Dipole Moments

We have discussed the different types of bonding, molecular dipoles and dipole moments in class. Most real chemical bonds are neither fully ionic nor fully covalent but possess a mixture of ionic and covalent character. Bonds in which there is a partial charge transfer are considered to be polar covalent. Molecular dipoles are the result of this uneven charge distribution. Dipole moments are a measure of this separation of charge. As you know the presence or absence of a dipole influences, to some degree, chemical reactivity. Let’s examine the following three compounds: LiH, HF and H2. In each case, we need to build a model and evaluate the molecule’s electron density. Based on what you know about electronegativity, do you think that they will have dipole moments and if so, where will the excess charge be on each?

First draw each molecule’s Lewis structure, and then build the model using Spartan. You will run the same calculations as before. The potential density surface will be useful in visualizing the results, so be sure to select this Surfaces option. After the calculations are complete, display the properties and record the following values in your lab notebook: dipole moment, bond length and energy.

If you click on the check box next to the dipole moment, Spartan will draw an arrow through the molecule pointing towards the more electronegative atom. (You may need to change the model type to a ball and wire to see the actual arrow in these linear compounds). Do the results agree with your thoughts?

|Molecule |Dipole Moment (debyes) |Dipole Direction |Energy (a.u.) |Charge on Hydrogen|Bond Length (angstroms) |

| | | | |Atom | |

| | | | | | |

| | | | | | |

| | | | | | |

After you have run the calculations for all three molecules, review the data. Which molecule has the largest dipole moment? Is this what you expected? Please explain.

PROBLEM 2: Carbon Monoxide and Cyanide as Ligands. (The following problem was obtained from Professor Steinmetz).

Most people know that cyanide (CN-) and carbon monoxide (CO) are potent poisons but are probably unaware of the chemical basis for this property. They are strong ligands and bind to transition metal species such as iron(II). One important issue to address is the orientation of the ligand when it forms a coordinate covalent bond. Is it M-CX or M-XC where X is N or O? The preference for one orientation or isomer will be explored in this exercise. To answer the question, we should display the molecular orbital with the highest energy, the so-called Highest Occupied Molecular Orbital or HOMO for short. Electron deficient species interact with the electrons in this orbital the most and hence of all the molecular orbitals in the molecule, the HOMO is most indicative of the species chemistry. Fukui shared the Nobel Prize with Hoffman and Woodward for developing the study of these “frontier” orbitals. Similarly, in examining the chemistry in which a reagent donates charge to a molecule under study, the most instructive orbital for this chemistry, i.e. the relevant frontier orbital, is the Lowest Unoccupied Molecular Orbital or LUMO.

As before, complete the following steps:

a) Draw the structure of your compound. Use a triple bond between the two atoms in the ligand. In the case of cyanide delete the dangling bond or a hydrogen atom will be appended when you leave the molecular editor.

b) As before, set up an energy calculation. Use Hartree-Fock and a 3-21G basis set. Be sure to provide the charge if your ligand is an ion. Submit the job as before.

c) When the calculation is completed, draw the HOMO. This is accessed via Setup and Surfaces. You used this utility before to draw the electron density and potential surfaces. This same approach is used in this case but HOMO is selected as the surface.

Examine the HOMO with the atoms labeled. Copy and paste a copy of the HOMO diagram for both molecules and explain which end of the ligand will be the preferential site of attack.

Preferential site of attack:____________ Preferential site of attack:____________

-----------------------

Start

Programs

Carbon Monoxide Ligand HOMO:

Cyanide Ligand HOMO:

Spartan ’09 V1.0.0

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