Vibrational Spectroscopy

Question 1

How many degrees of freedom does an isolated atom have?

Answer 1

3

Question 2

What are the three different types of motion for a diatomic molecule?

Answer 2

• Translation (In-phase displacement with not change in internuclear separation)
• Rotation (Change in orientation but no change in internuclear separation or centre of mass)
• Vibration (No change in centre of mass or orientation but a change in internuclear separation)

Question 3

What is the equation for determining the number of modes of vibration for a LINEAR molecule?

Answer 3

3N - 5
Where N = number of molecules

Question 4

What is the equation for determining the number of modes of vibration for a NON-LINEAR molecules?

Answer 4

3N - 6
Where N = number of molecules

Question 5

What is a normal mode of vibration for a molecule?

Answer 5

The natural vibrations of a molecule:

Question 6

What are the 3 things that happen to all nuclei during a normal mode?

Answer 6

• They undergo simple harmonic motion
• Have the same frequency of oscillation
• Move in phase (but with different amplitudes)

Question 7

What is Hooke’s law in context of a simple harmonic oscillator?

Answer 7

F = - kx
Where: F is the restoring force
k is stiffness of the bond (force constant)
x is the displacement from equilibrium (= bond length - equilibrium bond length)

Question 8

For an anharmonic oscillator, as k tends to 0 what happens to r?

Answer 8

r becomes larger and larger

Question 9

For a harmonic oscillator where are nuclei post likely to be found and why?

Answer 9

At the end of the vibration as they travel more slowly

Question 10

Are bending frequencies higher or lower than stretching frequencies?

Answer 10

Lower frequency

Question 11

Does infrared spectroscopy produce a scattering or absorption spectrum?

Answer 11

Absorption

Question 12

What is transmittance and how is it defined in an equation?

Answer 12

Transmittance is the fraction of incident light that successfully “passes” through a substance. Therefore:
T = I/Io
I = transmitted light
I = incident light

Question 13

How does an IR spectrometer work?

Answer 13

Photons in a substance absorb incident polychromatic light when the energy of the incident photo exactly matches ΔE for excitation from v=0 to v=1. The transmitted light is then recorded to form an IR spectrum.

Question 14

What are the two selection rules for harmonic oscillators for IR?

Answer 14

1) A transition is allowed only if the dipole moment changes with displacement
2) Transitions can only occur between adjacent levels

Question 15

How do the selection rules between harmonic and anharmonic oscillators differ for IR?

Answer 15

In harmonic oscillators transitions can only occur between adjacent levels whereas in anharmonic oscillators transitions can occur to many levels (know as overtones)

Question 16

How does the energy, frequency and wavelength change from the fundamental absorption to the first overtone?

Answer 16

The first overtone is twice the energy, twice the frequency and half the wavelength

Question 17

Explain where would a v=1 to v=2 hotband appear compared to v=0 to v=1

Answer 17

The v=1 to v=2 band would appear slightly to the left of the v=0 to v=1 band as in an anharmonic oscillator the energy levels become closer together as they increase, meaning that they are closer in energy to each other so the overtone band would be of a lower energy

Question 18

Why are the called hot bands?

Answer 18

As temperature increases the intensity of a hotband increases

Question 19

Does the requirement for a changing dipole mean that only polar molecules display an infrared spectrum?

Answer 19

NO - asymmetric stretches or bendings induces a dipole

Question 20

What did Raman discover?

Answer 20

That monochromatic scattered light produces both unaltered incident light and light of a lower frequency - light is scatted both elastically (Reyleigh) and inelastically (Stokes and Anti-Stokes)

Question 21

What happens during Stokes scattering?

Answer 21

Inelastic scattering - photon loses energy by supplying energy to a molecule

Question 22

What is polarisability?

Answer 22

A measure of the extent to which electrons in an atom or molecule can be displace relative to the nuclei by an electric field

Question 23

What is the selection rule for Raman emission?

Answer 23

The molecular polarisability must change during the molecular vibration

Question 24

What is a Fermi resonance?

Answer 24

Two Raman peaks can appear due to fundamental band and the overtone band are at the same wavenumber.

Question 25

What is the procedure for using symmetry to determine vibrational activity? (5 steps)

Answer 25

1) Identify point group
2) Place 3 Cartesian displacement vectors onto each of the N atoms
3) Use the invariance principle to identify the symmetry species of the reducible representations spanned by all 3N displacements
4) Use the reduction formula to reduce the symmetry into irreducible representations
5) Discard translations and rotations