2. Microwave Spectroscopy Wave length ~ 1 cm to 100  m Wave number ~ 1 to 100 cm -1. Frequency ~ 3 x 10 10 to 3 x 10 12 Hz Energy ~ 10 to 1000 Joules/mole Spectrum of CO 3.84235 cm -1 Equally spaced lines

3. Rotation of a diatomic molecule R r1r1 r2r2 m2m2 m1m1

4. Equivalent to that of a single particle

5. The Rigid Rotor

6. (2J+1) fold degeneracy! 2 1 0 10B 6B 2B 0 3 JEJEJ

8. Electric field + diatomic molecule

10. Must have a permanent dipole moment Selection Rules Z -part Initial state Final state Transition Moment = Integral

11. X -part Y -part

12. J 3 2 1 0 J 6B 2B 0 Blue –ALLOWED Red – NOT

13. J 3 2 1 0 10B 6B 2B 0 EJEJ 4B6B8B Equally spaced lines!

14. Intensities 2B4B6B8B 10B 12B 14B 16B Why does the intensities increase and then decrease? Depends on initial populations!

15. Population of levels If B=2 cm -1 then

16. Isotope Effect

17. Non-Rigid Rotor

18. Polyatomics 1. Linear Molecules – similar to diatomics Three moments of Inertia! 16 O 12 C 32 S - B = 6,081.48 MHz 16 O 12 C 33 S - B = 6,005.05 MHz 16 O 12 C 34 S - B = 5,932.83 MHz (from: Graybeal)

19. 2. Non-Linear Molecules

20. a) Spherical Top Examples: CH 4, SF 6 etc Do not absorb Microwave Radiation!

21. b) Symmetric Top BCl 3 CH 3 F

22. Prolate CH 3 F

23. Oblate BCl 3

24. a) Asymmetric Top No simple expression for Allowed energy levels

25. Pulsed nozzle FTMW spectrometer

26. Benzene dimer, c.m-c.m distance 4.96Å Distance very close to what is found in crystal! Arunan and Gutowsky J. Chem. Phys. 98, 4294 (1993)