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

7.1 Foundations of transition state theory 153
∆ ‡ : Born-Oppenheimer potential energy barrier (7.30)
∆ 0 : zero-point corrected threshold energy for the reaction (7.31)
: Arrhenius activation energy (7.32)
∆ 0 is given with respect to the zero-point energies of the reactants and the TS,
= 1 2
X
(7.33)
7.1.4 Tolman’s interpretation of the Arrhenius activation energy
I We now understand the difference between E and ∆E 0 :
2 ln ( )
=
Ã
= 2
ln
‡ µ
exp
= ∆ 0 + + 2 ln ‡
−
| {z }
=h reacting moleculesi
− ∆ 0
(7.34)
! (7.35)
µ
2 ln
+ 2 ln
(7.36)
| {z }
=h all molecules i
• ∆ 0 is difference of the zero-point levels of the reactants and the TS,
• the term is the mean translational energy in the RC (from the factor),
• the 2 ln terms are the internal (vibration-rotation) energies of the TS and
the reactants, respectively. y
I Tolman’s interpretation of E (see Fig. 7.4):
= h reacting molecules i − h all molecules i (7.37)