A random matrix/transition state theory for the probability distribution of state‐specific unimolecular decay rates: Generalization to include total angular momentum conservation and other dynamical symmetries

1993 ◽  
Vol 99 (2) ◽  
pp. 950-962 ◽  
Author(s):  
Rigoberto Hernandez ◽  
William H. Miller ◽  
C. Bradley Moore ◽  
William F. Polik
Keyword(s):  
Angular Momentum ◽  
Probability Distribution ◽  
Transition State ◽  
Random Matrix ◽  
Total Angular Momentum ◽  
Transition State Theory ◽  
Momentum Conservation ◽  
State Theory ◽  
Decay Rates ◽  
Dynamical Symmetries

Microscopic Interpretation of Arrhenius Parameters

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Activation Energy ◽  
Transition State ◽  
Transition State Theory ◽  
Average Energy ◽  
Zero Point ◽  
State Theory ◽  
Exponential Factor ◽  
Quantum Tunnelling ◽  
Microscopic Interpretation ◽  
The Difference

This chapter reviews the microscopic interpretation of the pre-exponential factor and the activation energy in rate constant expressions of the Arrhenius form. The pre-exponential factor of apparent unimolecular reactions is, roughly, expected to be of the order of a vibrational frequency, whereas the pre-exponential factor of bimolecular reactions, roughly, is related to the number of collisions per unit time and per unit volume. The activation energy of an elementary reaction can be interpreted as the average energy of the molecules that react minus the average energy of the reactants. Specializing to conventional transition-state theory, the activation energy is related to the classical barrier height of the potential energy surface plus the difference in zero-point energies and average internal energies between the activated complex and the reactants. When quantum tunnelling is included in transition-state theory, the activation energy is reduced, compared to the interpretation given in conventional transition-state theory.

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