Vibrational (Infrared) spectroscopy

Question 1

What does the absorption involve?

Answer 1

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

Question 2

What unit used on spectra?

Answer 2

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

Question 3

Vibration of a chemical bond?

Answer 3

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

Question 4

What is force constant?

Answer 4

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

Question 5

Typical molecular vibrational energies?

Answer 5

10-19 - 10-20 J, infrared frequencies

Question 6

Energy level of a harmonic oscillator?

Answer 6

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

Question 7

Gross selection rule in vibrational spectroscopy?

Answer 7

The dipole moment of a molecule must change during the vibration

Question 8

Specific selection rule in vibrational spectroscopy?

Answer 8

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

Question 9

Homonuclear diatomics?

Answer 9

Not IR active

Question 10

Heteronuclear diatomics?

Answer 10

IR active

Question 11

Polyatomics?

Answer 11

Some modes IR active some IR inactive

Question 12

How do we find the number of vibrational modes?

Answer 12

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

Question 13

Translational motion?

Answer 13

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

Question 14

Rotational motion?

Answer 14

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

Question 15

Vibrational motion?

Answer 15

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

Question 16

Vibrational spectroscopy for complex molecules?

Answer 16

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

Question 17

Effect of isotopic substitution?

Answer 17

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

Question 18

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

Answer 18

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

Question 19

The selection rule for anharmonic motion?

Answer 19

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

Question 20

Motion of a bond?

Answer 20

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

Question 21

More realistic motion of bond?

Answer 21

Anharmonic not harmonic as classically thought

Question 22

Anharmonic effect on the curve of energy levels?

Answer 22

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

Question 23

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

Answer 23

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

Question 24

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

Answer 24

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

Question 25

Equation for better description of energy levels?

Answer 25

Ev = (v + 1⁄2) hv – A (v + 1⁄2)2 hv

Question 26

Why So Many Peaks for Vibrational-Rotational Spectra?

Answer 26

Transitions occur simultaneously between vibrational and rotational levels

Question 27

What does IR detect?

Answer 27

Detects changes in the vibrational energy of molecules

Question 28

How can diatomic molecules be treated?

Answer 28

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

Question 29

What do triatomic molecules show?

Answer 29

Triatomic molecules show overtone and combination bands

Question 30

What do polyatomic molecules show?

Answer 30

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

Question 31

What do complex molecules show?

Answer 31

Complex molecules show characteristic frequencies for certain functional groups and a fingerprint region

Question 32

What do vibrational rotational spectra give?

Answer 32

Can give access to previously forbidden rotational signals, line-spacing in (high resolution) rotational fine structure allows calculation of the bond length

Question 33

How can a bond be treated like a spring of simple harmonic motion?

Answer 33

The greater the masses of the atoms the more slowly the spring vibrates, stiffness of the bond the bond is less easily deformed and vibrates more quickly, the bond vibrates because there is a restoring force when it is displaced from equilibrium position, as the bond is stretched the force pulls it back towards the equilibrium position as the bond is compressed the force pushes it back, the restoring force is proportional to the displacement the further the bond is stretched or compressed the large the force that restores it

Question 34

What does the penitential energy of the bond depend on?

Answer 34

The square of the extension x, at the extremes of the vibration when the bond is fully extended or compressed the kinetic energy is zero and all the energy of the spring is in the form of potential energy, as the spring passes through its equilibrium length the kinetic energy is at its maximum

Question 35

Constant k?

Answer 35

Force constant of the bond and is related to its stiffness as k increases the bond becomes stiffer the frequency of the vibration increases, as the reduced mass increases and the masses of the atoms become larger the frequency decreases

Question 36

Why is reduced mass used?

Answer 36

Since the frequency depends on the masses of both atoms, during bond vibration the heavy atom stays almost still while the light atom moves much larger distances

Question 37

Different isotopes?

Answer 37

Since the energy of a vibration depends on the masses of the atoms the energy will change if different isotopes are present in the molecules, the shift of the peak wavenumber due to isotopic substitution is largest for h and D but is significant for other elements and can be used to confirm the presence or otherwise of elements in a compound