8-1
Vibrational and Rotational Spectroscopy of
Diatomic Molecules
Study of interaction with electromagnetic radiation>
Can study
-Vibrational frequencies
Bond lengths
Structures (bonding)
Reactivity
Fundamental Equation of Spectroscopy
Recall Electromagnetic spectrum
Type of spectroscopy divided roughly by wavelengths used.

8-2
Energy can transfer to “molecule” shown if electric field and dipole oscillation are in phase with same frequency.
Classical “molecule” can absorb any amount of energy. Has a continuous absorbance spectrum.
Quantum molecule has discrete levels and therefore a discrete absorbance spectrum.
Basic concepts in spectroscopy
• Wavenumber, often used for transition, especially for IR. (cm -1 )
• Selection rules restrict possible transitions. (not all transitions are possible)

8-3
• Molecule must have permanent or dynamic dipole to couple to EM field in dipole description.
• Dynamic dipole – changing magnetic moment due to vibration
• Raman spectroscopy can be used if no permanent or dynamic dipole (e.g. homonuclear diatomics)
3 possible processes from interaction with light:
1. absorption
2. spontaneous emission
3. stimulated emission
Spontaneous emission – random event, light is incoherent (random phase and direction, e.g. light bulb)
Stimulate emission – coherent source (e.g. laser) all photons have same phase and direction

8-4
Vibrational spectroscopy
Usually only ground state vibrational level, n =0, state occupied.
Selection rules -
 n = n final
– n initial
= +1
Generally see only n = 0 → n = 1 transition.
Can see overtones with sensitive instrumentation.
These transitions are weak but possible for real molecules (anharmonic oscillators)
Anharmonicity modeled with the Morse potential
V ( R )

D e
[ 1
 e
 
( R

R e
)
]
2
- More realistic potential
- Allows dissociation
- Allows
 n=±2, ±3(very weak).

E between adjacent levels not the all same.
D
0
- bond energy from lowest level
D e
- dissociation from bottom of potential
Note: Just skim selections rules in section 8.4

8-5
Adsorption of IR light excites normal modes, not individual bonds.
Neither mode is simple O-H bond stretch because all three atoms coupled through bonds.
Characteristic group frequencies
IR absorption spectroscopy
Recall the Beer-Lambert law
A=
 cl

8-6
Experimental setup and spectra
Number of peaks < expected. Count degrees of freedom.
CH
4
3n-6 = 9 Only see 2 major peaks.
2 sets of 3-fold degeneracy, 3 modes are IR inactive for symmetry reasons.
CO 3n-5 = 1 See 2 peaks, not just 1.
Peaks are broadened due to rotational changes on top of vibrational changes.

8-7
Rotational spectroscopy
Permanent dipole needed to couple molecular rotations to EM field.
Pure rotational spectra are obtained in microwave spectroscopy.
Energy levels are given by
Where . B is the rotational constant
and has units of cm -1 .
The selection rule for rotational transitions is

J= ±1

8-8
So for

J = +1
And for

J = -1
Notice spacing varies in units of
Spectral peaks are therefore equally spaced by
Unlike vibrational spectroscopy, energy difference between adjacent energy levels not the same.

8-9
Since spacing of rotational levels is small compared to vibrational levels, IR radiation can be used to obtain combined vibrational-rotational spectra.
Because rotational levels more closely spaced than vibrational levels, vibrational excitation will also lead to rotational excitation.
Peak frequencies (equally
spaced!) determined by
energy level spacing.
Peak intensities determined
by number of molecules of
originating level.

8-10
Spacing between rotational levels << k
B
T so many rotational levels may be populated at ambient temperatures.
The population ratio of molecules in state J relative to the ground state J = 0 is:
The population of levels is rather sensitive to temp.
High resolution spectrum for CO.