Transcript Time Dependent Schrodinger Equation

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
Equally spaced
lines
3.84235 cm-1
Rotation of a diatomic
molecule
r2
r1
m2
m1
R
Equivalent to
that of a
single
particle
The Rigid Rotor
(2J+1) fold
degeneracy!
J
EJ
3
10B
2
6B
1
2B
0
0
Electric field + diatomic
molecule
Selection Rules
Must have a
permanent
dipole
moment
Transition
Moment
Integral
Z -part
Final
state
=
Initial
state
X -part
Y -part
J
J
3
Blue –ALLOWED
Red – NOT
2
6B
1
2B
0
0
Equally
spaced lines!
J
EJ
3
10B
2
6B
1
2B
0
0
2B 4B 6B 8B
Intensities
10B
2B 4B 6B 8B
14B
12B
16B
Why does the
intensities increase
and then decrease?
Depends on initial
populations!
Population of levels
If B=2 cm-1 then
Isotope Effect
Non-Rigid Rotor
Polyatomics
Three moments of
Inertia!
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)
2. Non-Linear Molecules
a) Spherical Top
Examples: CH4, SF6 etc
Do not absorb
Microwave Radiation!
b) Symmetric Top
BCl3
CH3F
Prolate
CH3F
Oblate
BCl3
a) Asymmetric Top
No simple expression for
Allowed energy levels
Pulsed nozzle FTMW spectrometer
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!