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Microwave Spectroscopy

Equally spaced lines. 3.84235 cm -1. Microwave Spectroscopy. Wave length ~ 1 cm to 100 m 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. r 1. r 2. R.

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Microwave Spectroscopy

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  1. Equally spaced lines 3.84235 cm-1 Microwave Spectroscopy Wave length ~ 1 cm to 100 mm Wave number ~ 1 to 100 cm-1. Frequency ~ 3 x 1010 to 3 x 1012 Hz Energy ~ 10 to 1000 Joules/mole Spectrum of CO

  2. r1 r2 R Rotation of a diatomic molecule m2 m1

  3. Equivalent to that of a single particle

  4. The Rigid Rotor

  5. (2J+1) fold degeneracy! 3 2 1 0 J EJ 10B 6B 2B 0

  6. Electric field + diatomic molecule

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

  8. X -part Y -part

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

  10. Equally spaced lines! J EJ 3 10B 2 6B 1 2B 0 0 2B 4B 6B 8B

  11. 10B 14B 12B 16B 2B 4B 6B 8B Why does the intensities increase and then decrease? Depends on initial populations! Intensities

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

  13. Isotope Effect

  14. Non-Rigid Rotor

  15. Three moments of Inertia! Polyatomics 1. Linear Molecules –similar to diatomics 16O12C32S - B = 6,081.48 MHz 16O12C33S - B = 6,005.05 MHz 16O12C34S - B = 5,932.83 MHz (from: Graybeal)

  16. 2. Non-Linear Molecules

  17. Do not absorb Microwave Radiation! a) Spherical Top Examples: CH4, SF6 etc

  18. CH3F BCl3 b) Symmetric Top

  19. CH3F Prolate

  20. BCl3 Oblate

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

  22. Pulsed nozzle FTMW spectrometer

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

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