CH447 CLASS 13 - KAIST



CH437 CLASS 13

INFRARED SPECTROSCOPY 1

Synopsis. Principles: molecular vibrations and coupled oscillators, fundamental and other vibrations, selection rule, dispersive and FT IR instruments.

The Infrared Absorption Process: Bond Vibrations

The infrared part of the electromagnetic spectrum lies between ca. 12,500 cm-1 (800 nm) and 100 cm-1 (10,000 nm), but only the section between 4000 cm-1 and 400 cm-1 is used routinely by organic chemists, because this section reveals the most information regarding the structure of organic compounds.

The bonds in molecules are constantly vibrating, that is to say, stretching or bending (deforming), so that when a bond in a molecule absorbs a quantum of infrared radiation (whose frequency corresponds to the vibrational frequency of the bond) that bond vibrates with greater amplitude. This corresponds to a vibrational transition and only occurs if the vibrational motion causes a change in dipole moment of the bond, as in non-symmetric bonds. This is because the changing electric dipole needs to interact with the sinusoidally changing electromagnetic field of the incident infrared photon in order for a vibrational transition to occur.

Such a vibration is said to be infrared active. Other vibrations, characteristic of symmetric bonds (e.g. H-H, Cl-Cl, O=O and N(N) are infrared inactive and do not absorb IR radiation. Pseudosymmetric bonds, such as R1R2C=CR3R4 and R1C(CR2 may have low intensity absorptions.

In any group of three or more atoms, at least two of which are identical, there are two modes of stretching: asymmetric and symmetric. Similarly there are asymmetric and symmetric modes of in plane bending and out of plane bending. These are illustrated for the methylene group, below.

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Asymmetric and symmetric stretches for other groups are shown on the next page. Note that asymmetric stretching vibrations occur at higher frequencies (higher energies and higher reciprocal wavelengths) than symmetric ones and that stretching occurs at higher frequencies than bending.

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Fundamental Vibrations, Overtones, Combination Bands, Difference Bands and Fermi Resonance

All the above vibrations are fundamental vibrations: they arise from excitation from the ground state to the lowest energy excited state. However in real IR spectra, there are bands (= ”peaks”), usually of low intensity, that arise from non-fundamental vibrations: overtones, combination, difference and Fermi resonance. Overtones result from excitation from the ground state to higher energy states, which correspond to (approximate) integral multiples of the fundamental frequency: in the IR spectrum, it will be possible to observe weak overtone bands at, say, 2850 and 1900 cm-1 of a fundamental band at 950 cm-1. The overtone frequencies are in actuality not quite exact integral multiples because most polyatomic molecules behave as anharmonic oscillators, which have a non-uniform spacing of energy levels, given by

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The discrepancy between overtone wavenumber calculations based upon anharmonic and harmonic oscillators for the fundamental C-H stretching vibration of chloroform (at 3019 cm-1) is demonstrated below.

|Transition, n = 0 to n =|Observed wavenumber /cm-1|Anharmonic oscillator |Harmonic oscillator |Relative absorbance |

| | |calculation*/cm-1 |calculation#/cm-1 |(1 cm cell) |

|1 |3019 |3019 |3019 |1 |

|2 |5912 |5912 |6038 |0.088 |

|3 |8677 |8679 |9057 |3.2 x 10-3 |

|4 |11318 |11320 |12076 |1.2 x 10-4 |

*(( = 3145n – 63(n2 + n) # (( = 3019n

The potential energy versus bond length diagrams are compared for harmonic and anharmonic oscillators below: the integers correspond to the quantum numbers (n) of the vibrational energy levels.

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Combination and Difference Bands

A non-linear molecule with x atoms can be considered as 3x – 6 separate oscillators. For a harmonic oscillator, the vibrational energy is given by

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Each of the oscillators has its own quantum number n and its own frequency (: for a truly harmonic system, only one vibration may be excited at one time and its quantum number may change by only one. However, real molecules behave like anharmonic oscillators and this anharmonicity causes weak combination and difference bands. A combination band appears near the frequency of the sum of two (and sometimes three) fundamental bands. This results from a transition from the ground state to a new combination level (one that is not involved in fundamental transitions). This combination level involves two different normal coordinates with nonzero quantum numbers, which means that, in this type of transition, one photon excites two different vibrations simultaneously by increasing two vibrational quantum numbers, each by one in this case. The energy of such a photon corresponds to a frequency approximately equal to the sum of the two photon frequencies that are needed to excite the two vibrations separately. Such transitions are allowed for anharmonic oscillators, but like overtones, are weak.

A difference band arises from transition from an excited level of one vibration (usually of low frequency) to an excited level of another higher frequency vibration. This transition uses existing energy levels (no new ones are involved) and since its intensity depends upon the population of the initial excited state, it will be lower for higher frequencies and lower temperatures. This temperature dependence is not observed for combination bands. Provided anharmonicity is present, the transition is allowed, but the intensity is low. The wavenumber of a difference band is exactly equal to the wavenumber difference of the two fundamentals, regardless of anharmonicity. For example, in the IR spectrum of CO2, the bending vibration fundamental at 667cm-1 has weak bands on either side at 721 and 618 cm-1. These are difference bands involving the 667 cm-1 band and bands at 1388 and 1285 cm-1.

Fermi Resonance

As we have already seen, if anharmonicity is present in a molecule, new bands involving overtone and combination transitions can appear in the IR spectrum but normally these are weak. Sometimes, the frequency of an overtone or combination band happens to have nearly the same frequency as another fundamental vibration. In such cases, two strong bands are often observed where only one strong band for the fundamental was expected. These are observed at higher and lower frequencies than the expected unperturbed frequency of the fundamental, or overtone. This phenomenon is known as Fermi resonance. Both bands involve the fundamental and the overtone, the apparent higher intensity of the overtone arises from the fact that the fundamental is involved with both bands. A common situation is where the n = 1 level of one vibration has an energy close to that of the n = 2 level of a different vibration. Quantum mechanical interaction of these levels occurs because of the anharmonic terms in the potential energy expression: these terms cause a significant perturbation when the energy difference between the two unperturbed levels is small. A well-known example of Fermi resonance is seen in the IR spectra of aldehydes, as described below.

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The carbonyl CH stretching in aldehydes is seen as a doublet if the CH deformation mode occurs at a wavenumber close to half that of the stretching mode: this is the clearest manifestation of Fermi resonance and is seen for many aldehydes, such as benzaldehyde above.

Bond Properties and Absorption Trends

The attention is turned back to fundamental vibrations, particularly stretches, in order to consider how bond strength and the masses of bonded atoms influence the IR absorption frequency. For simplicity, diatomic molecules acting as harmonic oscillators will be used for discussion here and will be likened to two vibrating masses (m1 and m2) connected by a spring. As for any harmonic oscillator, when a bond vibrates, its energy is continually and periodically changing between kinetic and potential energy. The total energy is proportional to the frequency of vibration:

Eosc ( h(osc

For a harmonic operator, Eosc is determined by the force constant (K) of the spring and the masses of the connected atoms. In mechanical systems (springs), K describes stiffness or resistance to stretching; in molecules, K is a measure of bond strength. The natural frequency of vibration is given by

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There are several things to note from this equation:

1. Stronger bonds have higher force constants and vibrate at higher frequencies than weak bonds.

2. Multiple bonds have higher force constants: K(triple bond) ~ 3K(single bond) and K(double bond) ~ 2K(single bond),

for bonds between the same atoms.

3. K for stretching vibrations > K for deformations.

4. K depends upon the electronic hybridization of the bonded atom: K increases with increase in % s-character.

5. K is reduced by resonance (delocalization) effects.

6. Bonds between atoms of higher masses (with larger reduced mass, () vibrate at lower frequencies than bonds between lighter atoms.

These points are illustrated by the following examples.

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Equation (1) reduces to the following if c is taken as 3.0 x 1010 cm/sec, the masses are expressed as amu (= mass in g/NA) and K is in dynes/cm:

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By assuming that K for single, double and triple bonds is 5, 10 and 15 x 105 dynes/cm, respectively, it is possible to estimate approximate band positions for different bonds. For example, using equation (2) gives 1682 cm-1, 3032 cm-1 and 2228 cm-1 for the C=C, C-H and C-D bonds, respectively, in good agreement with experiment (1650 cm-1, 3000 cm-1 and 2206 cm-1, respectively).

The Infrared Spectrometer

There are two types of infrared spectrometers (or more precisely, spectrophotometers) in use today: dispersive and Fourier transform (FT) instruments. The two kinds of spectrometers give nearly identical spectra for the same compound, but dispersive instruments are cheaper and slower, whereas FT machines are more expensive, but much faster and generally more versatile. The diagram overleaf schematically illustrates the components of a dispersive instrument. This is a typical double beam instrument: the sample is placed in one beam, whilst the other beam is used as a reference. The beams are passed alternately through the beam chopper (a rotating sector) onto a slowly rotating diffraction grating, which varies the wavelength of IR radiation that reaches the detector (a thermocouple). The part of the instrument that contains the beam chopper, grating, and associated mirrors and slits is known as the monochromator. The detector senses the ratio between intensities of the reference and sample beams for each wavelength, so that it can determine which wavelengths have been absorbed by the sample and which are unaffected.

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The FT instrument is rather more complex in that it uses an interferometer rather than a monochromator and it also requires a computer to convert the interference patterns, by Fourier transform, into conventional frequency (or wavelength) spectra. The interferometer consists of a beam splitter and two mirrors, one fixed and the other moveable (see (a) overleaf). The beam splitter transmits half the radiation and reflects the other half when incident radiation strikes it at a 45o angle (see (b) overleaf). The transmitted and reflected beams from the beam splitter strike the two mirrors that are oriented perpendicular to each beam, and are reflected back to the beam splitter. When only one mirror is in place (see (c) overleaf), the beam reflected from the mirror returns to the beam splitter, which sends half the radiation to the detector and half back to the source. If both mirrors are in place (see (d) – (f) overleaf), interference occurs at the beam splitter where there is overlap of the radiation from the two mirrors. When the two mirrors are equidistant from the beam splitter (the “retardation” is zero), for all wavelengths, constructive interference occurs for the beam passing to the detector, whereas destructive interference occurs to the beam going back to the detector (see (d) below). When the retardation is (/2 (see (e) below), when the moving mirror has moved (/4 away from the equidistant position, destructive interference occurs to the beam going to the detector. Conversely, when the retardation is ( (corresponding to the position of the moving mirror at (/2 – see (f) below), constructive interference occurs to the beam passing to the detector. The detector thus senses a cosine variation of intensity that depends on the retardation and a plot of such a response versus retardation is known as an interferogram (see (g) below.

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In practice, the interferogram of the polychromatic source can be considered as the sum of all the cosine waves from each wavelength and they are each detected simultaneously. This interferogram, saved in the computer memory is converted to a conventional spectrum by Fourier transform. Because several “scans” can be performed, the signal-to-noise ratio is superior to that of a dispersive instrument.

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