THEORETICAL STUDIES OF ANHARMONIC EFFECT IN THE RICE–RAMSPERGER–KASSEL–MARCUS THEORY

2008 ◽  
Vol 22 (31) ◽  
pp. 3043-3052 ◽  
Author(s):  
L. YAO ◽  
Y. L. LIU ◽  
S. H. LIN
Keyword(s):  
Theoretical Approach ◽  
Transition State Theory ◽  
State Theory ◽  
Model Systems ◽  
Partition Functions ◽  
Morse Oscillator ◽  
Anharmonic Effect ◽  
Oscillator Potential ◽  
Inverse Laplace Transformation ◽  
Activated Complex

The purpose of this paper is to propose a theoretical approach, which can evaluate anharmonic effects on the rate constants within the transition state theory. In treating unimolecular reactions under collision-free conditions by using the RRKM theory, we make use of the inverse Laplace transformation of the partition functions to obtain both the total number of states for the activated complex and density of states for the reactant with the Morse oscillator potential. To demonstrate the applications of our theoretical approach, we choose some model systems and a real reaction as examples.

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

Static Solvent Effects, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Rate Constant ◽  
Solvent Effects ◽  
Transition State Theory ◽  
Equilibrium Structure ◽  
State Theory ◽  
Potential Of Mean Force ◽  
Distribution Functions ◽  
Average Force ◽  
Activated Complex

This chapter discusses static solvent effects on the rate constant for chemical reactions in solution. It starts with a brief discussion of the thermodynamic formulation of transition-state theory. The static equilibrium structure of the solvent will modify the potential energy surface for the chemical reaction. This effect is analyzed within the framework of transition-state theory. The rate constant is expressed in terms of the potential of mean force at the activated complex. Various definitions of this potential and their relations to n-particle- and pair-distribution functions are considered. The potential of mean force may, for example, be defined such that the gradient of the potential gives the average force on an atom in the activated complex, Boltzmann averaged over all configurations of the solvent. It concludes with a discussion of a relation between the rate constants in the gas phase and in solution.

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