1. Spectroscopy Microwave (Rotational) Infrared (Vibrational)
Raman (Rotational & Vibrational)
Texts
“Physical Chemistry”, 6th edition, Atkins
“Fundamentals of Molecular Spectroscopy”, 4th edition, Banwell & McCash

2. Introduction-General Principles
Spectra - transitions between energy states
Molecule, Ef - Ei = hu photon
Transition probability
selection rules
Populations (Boltzmann distribution)
number of molecules in level j at equilibrium

3. Typical energies

4. Fate of molecule? Non-radiative transition: M* + M ® M + M + heat
Spontaneous emission: M* ® M + hn (very fast for large DE)
Stimulated emission (opposite to stimulated absorption)
These factors contribute to linewidth & to lifetime of excited state.

5. MCWE or Rotational Spectroscopy Classification of molecules
Based on moments of inertia, I=mr2
IA ¹ IB ¹ IC very complex eg H2O
IA = IB = IC no MCWE spectrum eg CH4
IA ¹ IB = IC complicated eg NH3
IA = 0, IB = IC linear molecules eg NaCl

6. Microwave spectrometer
MCWE 3 to 60 GHz X-band at 8 to 12 GHz; mm
Path-length 2 m; pressure 10-5 bar; Ts up to 800K; vapour-phase
Very high-resolution eg 12C16O absorption at 115, MHz
Stark electric field: each line splits into (J+1) components

7. Rotating diatomic molecule
Degeneracy of Jth level is (2J+1)
Selection rules for absorption are:
DJ = +1
The molecule must have a non-zero dipole moment, p ¹ 0. So N2 etc do not absorb microwave radiation.
Compounds must be in the vapour-phase
But it is easy to work at temperatures up to 800K since cell is made of brass with mica windows. Even solid NaCl has sufficient vapour pressure to give a good spectrum.

8. Rotational energy levels
For DJ=1
DE = 2 ( J+1) h2/8p2I
0®1 DE = 2 h2/8p2I
1®2 DE = 4 h2/8p2I
2®3 DE = 6 h2/8p2I
etc., etc., etc.
Constant difference of:
DE = 2 h2/8p2I

9. Populations of rotational levels

10. Example
Pure MCWE absorptions at , and GHz on flowing dibromine gas over hot copper metal at 1100K.
What transitions do these frequencies represent?
Note: = and
also = 6.028
So, constant diff. of GHz or 6.028´109 s-1.
DE = 2 h2/8p2I = h (6.028´109 s-1)
So ¸ = ie J=13 ® J=14
& ¸ = 15 ie J=14 ® J=15
& ¸ = 16 ie J=15 ® J=16

11. Moment of inertia, I Þ (J s)/(s-1) = J s2 = kg m2 s-2 s2 = kg m2
DE = 2 h2/8p2I = hv = h(6.028´109 s-1)
I = 2 h/(8p ´109 )
I = 2 (6.626´10-34)/(8p ´109 )
I = 2.784´10-45
Units?
Þ (J s)/(s-1) = J s2 = kg m2 s-2 s2 = kg m2
But I = mr2
m = (0.063´0.079)/( )NA = 5.82´10-26 kg
Þ r = Ö(I/m) = 218.6´10-12 m = pm

12. Emission spectroscopy?
Radio-telescopes pick up radiation from interstellar space. High resolution means that species can be identified unambiguously.
Owens Valley Radio Observatory 10.4 m telescope
Orion A molecular cloud »300K, »10-7 cm-3
517 lines from 25 species
CN, SiO, SO2, H2CO, OCS, CH3OH, etc
13CO (220,399 MHz) and 12CO (230,538 MHz)

13. IR / Vibrational spectroscopy
Ev = (v + 1/2) (h/2p) (k/m)1/2
v = 0, 1, 2, 3, …
Selection rules:
Dv = 1 & p must change during vibration
Let we = wavenumber of transition then “energy”:
ev = (v + 1/2) we
Untrue for real molecules since parabolic potential does not allow for bond breaking.
ev = (v + 1/2) we - (v + 1/2)2 we xe
where xe is the anharmonicity constant

14. Differences?
Energy levels unequally spaced, converging at high energy. The amount of distortion increases with increasing energy.
All transitions are no longer the same
Dv > 1 are allowed
fundamental 0®1
overtone 0®2
hot band 1®2

15. Example
HCl has a fundamental band at 2,885.9 cm-1, and an overtone at 5,668.1cm-1.
Calculate we and the anharmonicity constant xe.
ev = (v + 1/2) we - (v + 1/2)2 we xe
e2 = (2 + 1/2) we - (2 + 1/2)2 we xe
e1 = (1 + 1/2) we - (1 + 1/2)2 we xe
e0 = (0 + 1/2) we - (0 + 1/2)2 we xe
e2 - e0 = 2we - 6we xe= 5,668.1
e1 - e0 = we - 2we xe= 2,885.9
\ we = 2,989.6 cm-1 we xe = 51.9 cm-1 xe =

16. High resolution infrared
Ev = (v + 1/2) (h/2p) (k/m)1/2
ev = (v + 1/2) we
EJ = J(J+1) (h2/8I)
eJ = J(J + 1) Bv
Vibrational + rotational energy changes
e(v,J) = (v + 1/2) we + J(J + 1) Bv
Selection rule: Dv=+1, DJ=±1
Rotational energy change must accompany a vibrational energy change.

17. Vibrational + rotational changes in the IR

18. Hi-resolution spectrum of HCl
Above the “gap”; DJ = +1
Below the “gap”: DJ = –1
Intensities mirror populations of starting levels

19. Example: HBr Lines at … 2590.95, 2575.19, 2542.25, 2525.09, ... cm-1
Difference is roughly 15 except between 2nd & 3rd where it is double this. Hence, missing transition lies around 2560 cm-1.
So 2575 is (v=0,J=0) ® (v=1,J=1) & 2590 is (v=0,J=1) ® (v=1,J=2)
So 2542 is (v=0,J=1) ® (v=1,J=0) & 2525 is (v=0,J=2) ® (v=1,J=1)
( ) = 6B0 B0=8.35 cm-1
( ) = 6B1 B1=8.12 cm-1
Missing transition at B0 = cm-1

20. Raman spectroscopy
Different principles. Based on scattering of (usually) visible monochromatic light by molecules of a gas, liquid or solid
Two kinds of scattering encountered:
Rayleigh (1 in every 10,000) same frequency
Raman (1 in every 10,000,000) different frequencies

21. Raman Light source? Laser He-Ne 633 nm or Argon ion 488, 515 nm
Monochromatic, Highly directional, Intense
He-Ne 633 nm or Argon ion 488, 515 nm
Cells? Glass or quartz; so aqueous solutions OK
Form of emission spectroscopy
Spectrum highly symmetrical eg for liquid CCl4 there are peaks at ±218, ±314 and ±459 cm-1 shifted from the original incident radiation at 633 nm (15,800 cm-1).
The lower wavenumber side or Stokes radiation tends to be more intense (and therefore more useful) than the higher wavenumber or anti-Stokes radiation.

23. Why? Rayleigh scattering: no change in wavenumber of light
Raman scattering: either greater than original or less than original by a constant amount determined by molecular energy levels & independent of incident light frequency

24. Raman selection rules Vibrational energy levels
Dv = ± 1
Polarisability must change during particular vibration
Rotational energy levels
DJ = ± 2
Non-isotropic polarisability (ie molecule must not be spherically symmetric like CH4, SF6, etc.)
Combined

25. Vibrational Raman Symmetric stretching vibration of CO2
Polarisability changes
therefore Raman band at 1,340 cm-1
Dipole moment does not
no absorption at 1,340 cm-1 in IR

26. Vibrational Raman Asymmetric stretching vibration of CO2
Polarisability does not change during vibration
No Raman band near 2,350 cm-1
Dipole moment does change
CO2 absorbs at 2,349 cm-1 in the IR

27. Pure Rotational Raman Polarisability is not isotropic
CO2 rotation is Raman active
some 20 absorption lines are visible on either side of the Rayleigh scattering peak with a maximum intensity for the J=7 to J=9 transition.
The DJ = +2 and DJ = -2 are nearly equal in intensity
Very near high intensity peak of exciting radiation; needs good quality spectrometers

28. Rotational Raman

29. Raman vs IR
CHCl3
Which?
Very similar
Diffs.?