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What does the absorption involve?

Absorption of infrared energy involves the vibrations of chemical bonds, vibration means lots of things: stretch, bend etc


What unit used on spectra?

Typically uses wavenumber on the “energy” axis – 4000 cm -1 – 400 cm -1, corresponding to the change in energy 12 kJ mol-1


Vibration of a chemical bond?

Treat the chemical bond as a spring, If the spring is extended or compressed, there is a restoring force, F, Simple harmonic motion: Hookes Law, Force, F, is proportional to the extension, x F = -kx
Energy, E = 1⁄2 k x2
k is the force constant of the spring


What is force constant?

related to the stiffness of the spring (or strength of bond); how easy it is to set into motion


Typical molecular vibrational energies?

10-19 - 10-20 J, infrared frequencies


Energy level of a harmonic oscillator?

Energy levels are equally separated
All vibrational levels have degeneracy =1
The lowest energy possible, v=0, is NOT zero
This is called zero point energy


Gross selection rule in vibrational spectroscopy?

The dipole moment of a molecule must change during the vibration


Specific selection rule in vibrational spectroscopy?

Only transitions between adjacent energy levels can occur, delta v = ±1


Homonuclear diatomics?

Not IR active


Heteronuclear diatomics?

IR active



Some modes IR active some IR inactive


How do we find the number of vibrational modes?

We use a 3-D geometry to define molecules in space, the position of each atom in a molecule can be given in terms of three measurements,
1 atom = 3 degrees of freedom
2 atoms = 6 degrees of freedom
3 atoms = 9 degrees of freedom
N atoms = 3N degrees of freedom
A degree of freedom (DOF) is an independent mode of position or motion in a molecule


Translational motion?

Always 3 modes of translational motion (doesn’t matter how many atoms)


Rotational motion?

2 cases
Non linear, 3 axes = 3 DOF
Linear, 2 axes = 2 DOF
rotation about the x axes does not change positions of any atoms


Vibrational motion?

The other degrees of freedom (to make total up to 3N) are taken up by vibrational motion within molecules
Total Degrees of freedom = 3N for N atoms
Always 3 trans.+ either 2 or 3 rot = 5 or 6 (trans. + rot.)
Linear (3N – 5) vibrational modes
Non linear (3N – 6) vibrational modes
An independent mode of vibration (one that does not influence another mode) is called a normal mode


Vibrational spectroscopy for complex molecules?

As the number of atoms increase, the number of peaks increases rapidly, Usually not possible to assign all the peaks but can use the fingerprint region to identify characteristic frequencies


Effect of isotopic substitution?

As for rotational spectroscopy, E vibrational depends on reduced mass so will change if different isotopes are present, k depends on the electron distribution in the bond - adding neutrons to a nucleus has little effect on electron density, assume isotopic substitution does not change the force constant


How does changing from H to D affect the reduced mass?

The bond vibration of HCl gives an absorption at 2990 cm–1, replacing H by deuterium, D (2H), changes the reduced mass, this gives the D–Cl absorption at lower wavenumber, 2140 cm-1, Largest shifts occur for H → D but significant for other elements – can be used to confirm the presence or otherwise of elements in a compound


The selection rule for anharmonic motion?

The selection rule delta v = ± 1 strictly works only for harmonic motion, weak bands can be seen at 2hv0 3hv0 etc these are overtone bands


Motion of a bond?

The motion of a bond is not harmonic. At large displacements, atoms repel (at short distances) or bonds break (at long distances).
Anharmonicity effects --> separation between levels is not constant


More realistic motion of bond?

Anharmonic not harmonic as classically thought


Anharmonic effect on the curve of energy levels?

Energy – distance curve isn’t a true parabola - ”Morse” curve
If push the atoms together, repulsion increases - steeper slope
If we pull the atoms apart, the bond breaks - dissociation energy


What does solution of the Schrödinger equation for the Morse potential show for the selection rule?

The selection rule delta v = ± 1 is not strictly obeyed, overtones appear with delta v = ± 2 and delta v = ± 3


What does solution of the Schrödinger equation for the Morse potential show for the vibrational levels?

Vibrational levels are not equally spaced, separation gets smaller with increasing v and becomes = 0 at the limit


Equation for better description of energy levels?

Ev = (v + 1⁄2) hv – A (v + 1⁄2)2 hv


Why So Many Peaks for Vibrational-Rotational Spectra?

Transitions occur simultaneously between vibrational and rotational levels


What does IR detect?

Detects changes in the vibrational energy of molecules


How can diatomic molecules be treated?

Diatomic molecules can be treated as harmonic or (better) anharmonic oscillators which allows calculation of bond force constant and bond dissociation energy


What do triatomic molecules show?

Triatomic molecules show overtone and combination bands


What do polyatomic molecules show?

Polyatomic molecules with N atoms vibrate in 3N-5 (for linear) or 3N-6 (for non-linear) normal modes