scholarly journals Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

2017 ◽  
Vol 146 (15) ◽  
pp. 154505 ◽  
Author(s):  
Sheida Ahmadi ◽  
Richard K. Bowles
Keyword(s):  
Transition State ◽  
Transition State Theory ◽  
State Theory ◽  
Small System ◽  
One Dimensional

Quantum mechanical tunnelling in the processes D + H2 → DH + H and CH4 + H → CH3 + H2. Eckart's tunnelling corrections for rate constants given by ab initio calculations

1979 ◽  
Vol 44 (12) ◽  
pp. 3452-3457 ◽  
Author(s):  
Petr Čársky
Keyword(s):  
Transition State ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Rate Constants ◽  
Transition State Theory ◽  
State Theory ◽  
Quantum Mechanical ◽  
Rate Data ◽  
Dimensional Approach ◽  
One Dimensional

Results of the best reported ab initio calculations are used to evaluate the rate constants of the title processes by means of the transition state theory. The computed rate constants are corrected for the quantum mechanical tunnelling by the Eckart's one-dimensional approach and comparison is made with experimental rate data

scholarly journals Transition state theory approach to polymer escape from a one dimensional potential well

2015 ◽  
Vol 142 (22) ◽  
pp. 224906 ◽  
Author(s):  
Harri Mökkönen ◽  
Timo Ikonen ◽  
Tapio Ala-Nissila ◽  
Hannes Jónsson
Keyword(s):  
Transition State ◽  
Transition State Theory ◽  
State Theory ◽  
Theory Approach ◽  
Potential Well ◽  
One Dimensional

scholarly journals Application of one-dimensional semiclassical transition state theory to the CH 3 OH + H ⇌ CH 2 OH/CH 3 O + H 2 reactions

2018 ◽  
Vol 376 (2115) ◽  
pp. 20170147 ◽  
Author(s):  
Xiao Shan ◽  
David C. Clary
Keyword(s):  
Transition State ◽  
Rate Constants ◽  
Transition State Theory ◽  
Single Point ◽  
Computational Cost ◽  
State Theory ◽  
Reverse Direction ◽  
Point Energy ◽  
One Dimensional ◽  
Theory Calculation

The rate constants of the two branches of H-abstractions from CH 3 OH by the H-atom and the corresponding reactions in the reverse direction are calculated using the one-dimensional semiclassical transition state theory (1D SCTST). In this method, only the reaction mode vibration of the transition state (TS) is treated anharmonically, while the remaining internal degrees of freedom are treated as they would have been in a standard TS theory calculation. A total of eight ab initio single-point energy calculations are performed in addition to the computational cost of a standard TS theory calculation. This allows a second-order Richardson extrapolation method to be employed to improve the numerical estimation of the third- and fourth-order derivatives, which in turn are used in the calculation of the anharmonic constant. Hindered-rotor (HR) vibrations are identified in the equilibrium states of CH 3 OH and CH 2 OH, and the TSs of the reactions. The partition function of the HRs are calculated using both a simple harmonic oscillator model and a more sophisticated one-dimensional torsional eigenvalue summation (1D TES) method. The 1D TES method can be easily adapted in 1D SCTST computation. The resulting 1D SCTST with 1D TES rate constants show good agreement to previous theoretical and experimental works. The effects of the HR on rate constants for different reactions are also investigated. This article is part of the theme issue ‘Modern theoretical chemistry’.

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.

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.

Quasiclassical Trajectory and Transition State Theory Studies of the N(4S) + H2↔ NH(X3Σ-) + H Reaction

2002 ◽  
Vol 106 (16) ◽  
pp. 4125-4136 ◽  
Author(s):  
Ronald Z. Pascual ◽  
George C. Schatz ◽  
Gÿorgÿ Lendvay ◽  
Diego Troya
Keyword(s):  
Transition State ◽  
Transition State Theory ◽  
State Theory
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