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

8.4 The specific unimolecular reaction rate constants () 198
b) Density of states:
() = ( + () ) −1
( − 1)! Q
=1
(8.106)
c) Specific rate constant:
³
() = 1 − 0 + ‡ ( − 0 ) ‡ ´−1
() +
()( − 1)! Q −
−1
=1 ‡
(4) For energies sufficiently above 0 , we can use the expressions
and
to obtain
y
‡ ( − 0 )=
() = ‡ ( − 0 )
()
() =
() =
=
³
− 0 + ‡ ´−1
( − 1)! Q −1
=1 ‡
( + ) −1
( − 1)! Q
=1
³
‡ (0) ‡ ´−1
()( − 1)! Q −1
=1 ‡
(8.107)
(8.108)
(8.109)
³
Q
=1 − 0 + ‡ ´−1
Q −1
=1 ‡
( + ) −1 (8.110)
Q
=1
Q −1
=1 ‡
The resemblence to the Kassel formula is obvious.
Ã
− 0 + ‡
+
! −1
(8.111)
8.4.3 The SACM and VRRKM model
More advanced models allow for the tightening of the TS with increasing (variational
RRKM theory = VRRKM theory) or even for individual adiabatic channel potential
curves (statistical adiabatic channel model = SACM). The latter model has to be used
for reactions with loose transition states.