Zero-Cost Corrections to Influence Functional Coefficients from Bath Response Functions

TL;DR

This paper introduces a Kubo-based correction method for influence functional coefficients that enhances accuracy at lower temperatures without additional computational cost, using correlation functions from classical and quantum dynamics.

Contribution

It provides a novel, zero-cost correction to influence functional coefficients derived from classical trajectory data, extending applicability to lower temperatures.

Findings

Correction improves accuracy at lower temperatures.

Method is compatible with ring-polymer and centroid molecular dynamics.

Zero-cost correction enhances influence functional calculations.

Abstract

Recent work has shown that it is possible to circumvent the calculation of the spectral density and directly calculate the coefficients of the discretized influence functionals using data from classical trajectory simulations. However, the accuracy of this procedure depends on the validity of the high temperature approximation. In this work, an alternative derivation based on the Kubo formalism is provided. This enables the calculation of additional correction terms that increases the range of applicability of the procedure to lower temperatures. Because it is based on the Kubo-transformed correlation function, this approach enables the direct use of correlation functions obtained from methods like ring-polymer molecular dynamics and centroid molecular dynamics in determining the influence functional coefficients for subsequent system-solvent simulations. The accuracy of the original procedure and the corrected procedure is investigated across a range of parameters. It is interesting that the correction term comes at zero additional cost. Furthermore, it is possible to improve upon the correction using zero-cost physical intuition and heuristics making the method even more accurate.