DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
DFT Reactivity Descriptors and Catalysis - Vrije Universiteit Brussel
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• Rate Constant Evaluation<br />
• Transition State Theory<br />
k<br />
r<br />
k T<br />
h<br />
Q<br />
Q<br />
‡<br />
B<br />
= ⋅ ⋅<br />
∏<br />
i<br />
i<br />
e<br />
−E<br />
/ bar<br />
RT<br />
• Q ‡ ,Q i …: partition functions in rigid rotor, harmonic oscillator approximation<br />
• E bar : activation barrier<br />
Example: one step reaction, A <strong>and</strong> B reacting simultaneously with an acidic<br />
zeolite HZ: reaction rate per acid proton<br />
‡<br />
( Q Q Q<br />
)<br />
k T<br />
k ( )<br />
−<br />
r<br />
= N<br />
AvV × ⋅e<br />
h Q Q Q Q Q Q Q Q Q<br />
2 B<br />
v r t TS<br />
−<br />
E /<br />
RT<br />
( ) ( ) ( )<br />
v r t A v r t B v r t HZ<br />
bar<br />
Arrhenius type analysis<br />
E A , A, ∆S Act<br />
• Tested via H/D Exchange reaction of methane: 3T cluster model<br />
fair agreement between theoretical <strong>and</strong> experimental activation energy<br />
A.M. Vos, F.De Proft, R.A.Schoonheydt, P. Geerlings, Chem.Comm., 1108 (2001)<br />
Pag.<br />
30-9-2008 25
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