Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra

TL;DR

This paper introduces a mean-field Matsubara dynamics approach that accurately reproduces rovibrational spectra of molecules across a range of temperatures, highlighting the role of path curvature effects and comparing with centroid molecular dynamics.

Contribution

The authors derive a mean-field version of Matsubara dynamics that reduces phase problems, enabling numerical tests and revealing its accuracy in simulating rovibrational spectra.

Findings

Matsubara dynamics converges to quantum results with minor discrepancies.

Non-centroid fluctuations are crucial below 250 K for accurate spectra.

Transition from shallow to deep curvature regimes affects path instantons in dynamics.

Abstract

It was shown recently that smooth and continuous "Matsubara" phase-space loops follow a quantum-Boltzmann-conserving classical dynamics when decoupled from non-smooth distributions, which was suggested as the reason that many dynamical observables appear to involve a mixture of classical dynamics and quantum Boltzmann statistics. Here we derive a mean-field version of this "Matsubara dynamics" which sufficiently mitigates its serious phase problem to permit numerical tests on a two-dimensional "champagne-bottle" model of a rotating OH bond. The Matsubara-dynamics rovibrational spectra are found to converge toward close agreement with the exact quantum results at all temperatures tested (200-800 K), the only significant discrepancies being a temperature-independent 22 cm$^{-1}$ blue-shift in the position of the vibrational peak and a slight broadening in its line shape. These results are compared with centroid molecular dynamics (CMD) to assess the importance of non-centroid fluctuations. Above 250 K, only the lowest-frequency non-centroid modes are needed to correct small CMD red-shifts in the vibrational peak; below 250 K, more non-centroid modes are needed to correct large CMD red-shifts and broadening. The transition between these "shallow curvature" and "deep curvature" regimes happens when imaginary-time Feynman paths become able to lower their actions by cutting through the curved potential surface, giving rise to artificial instantons in CMD.