The Flux-Flux Correlation Function for Anharmonic Barriers

TL;DR

This paper introduces an analytical method using classical and quantum normal forms to compute flux-flux correlation functions for anharmonic barriers, simplifying quantum calculations to an effective one-dimensional problem.

Contribution

It presents a novel analytical approach to calculate classical and quantum flux-flux correlation functions for anharmonic barriers using normal form techniques.

Findings

Derived an analytical expression for quantum microcanonical flux-flux correlation function.

Reduced quantum flux-flux calculations to an effective one-dimensional problem.

Analyzed short-time and harmonic limits of the correlation functions.

Abstract

The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits.