Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.4 Advanced collision theory 136
• Radial velocity component:
y
• Kinetic energy:
• Angular velocity:
=
cos = =
=
1
2 2 +
| {z }
translation via LC
1
2 2
| {z }
= 1 2 2 2 (rotation)
(5.200)
(5.201)
(5.202)
=
=
=
=
=
2 (5.203)
• Kinetic energy:
= 1 2 ( ) 2 + 1 2 ( ) 2 (5.204)
= 1 2 · 2 + 1 2
2 2 2 (5.205)
= 1 2 · 2 + 1 2 2
2 (5.206)
= 1 2 · 2 + 1 2 2 2
2 2 (5.207)
• Orbital angular momentum: is the orbital angular momentum
= 2
= = (5.208)
y
= 1 2 · 2 +
2
2 2 (5.209)
From quantum mechanics, 2 = ~ 2 ( +1)with as orbital angular momentum
quantum number. y
= 1 2 · 2 + ~2 ( +1)
2 2 (5.210)
= 1 2 · 2 + 2 ( +1) (5.211)
where 2 = ~2
is formally an -dependent rotational constant.
22 • Centrifugal barrier: The centrifugal kinetic energy term ~2 ( +1)
acts as a
2 2
centrifugal barrier
centrifugal = 1 2 2
= ~2 ( +1)
(5.212)
2 2 2