Vibronic spectra at nonzero temperatures from Herman-Kluk coherence thermofield dynamics

TL;DR

This paper introduces a semiclassical Herman--Kluk approach combined with coherence thermofield dynamics to accurately compute vibrationally resolved electronic spectra at nonzero temperatures, especially in highly anharmonic systems.

Contribution

It derives a Herman--Kluk representation for the thermofield wavepacket autocorrelation function and demonstrates its effectiveness over existing methods in capturing hot bands in spectra.

Findings

Herman--Kluk thermofield dynamics accurately reproduces spectra in highly anharmonic Morse potentials.

Thawed Gaussian thermofield dynamics fails to capture hot bands at high anharmonicity.

The method is validated against numerically exact calculations across different temperatures.

Abstract

We combine the semiclassical Herman--Kluk approximation with the coherence thermofield dynamics in order to evaluate vibrationally resolved electronic spectra at nonzero temperatures. In coherence thermofield dynamics, the dipole time correlation function is rewritten exactly as a wavepacket autocorrelation function, and the corresponding wavepacket is a solution to a zero-temperature time-dependent Schr\"odinger equation on an augmented configuration space of doubled dimension. We derive the Herman--Kluk representation for the thermofield wavepacket autocorrelation function and demonstrate how it can be computed from individual trajectories. To analyze this method, we compare spectra of Morse potentials of increasing anharmonicity evaluated at various temperatures with a numerically exact approach, with the Herman--Kluk coherence thermofield dynamics, and with the single-trajectory thawed Gaussian coherence thermofield dynamics. At low anharmonicity, both approximate methods yield accurate spectra. However, in a Morse potential with higher anharmonicity, the thawed Gaussian thermofield dynamics, based on the local harmonic approximation, fails to capture emerging hot bands, whereas the Herman--Kluk thermofield approach successfully reproduces them.