Time correlation function and path integral analysis of quantum rate constants

1989 ◽  
Vol 93 (19) ◽  
pp. 7009-7015 ◽  
Author(s):  
Gregory A. Voth ◽  
David Chandler ◽  
William H. Miller
Keyword(s):  
Correlation Function ◽  
Path Integral ◽  
Rate Constants ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Integral Analysis

scholarly journals Path-integral approximations to quantum dynamics

2021 ◽  
Vol 94 (7) ◽  
Author(s):  
Stuart C. Althorpe
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Imaginary Time ◽  
Integral Methods ◽  
Ring Polymer ◽  
Recent Extension

Abstract Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

Two-body dynamics in fluids as probed by interaction-induced light scattering

1981 ◽  
Vol 59 (10) ◽  
pp. 1504-1509 ◽  
Author(s):  
U. Balucani ◽  
R. Vallauri
Keyword(s):  
Correlation Function ◽  
Light Scattering ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Simulation Experiments ◽  
Particle Pairs ◽  
Body Dynamics ◽  
Atomic Fluids ◽  
Relative Dynamics

The relative dynamics of particle pairs in fluids is investigated both theoretically and by simulation experiments. The physical implications of this analysis are important in all interaction-induced phenomena and illustrated in the case of the pair time correlation function relevant to collision-induced light scattering in atomic fluids.

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