Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

TL;DR

This paper develops an exact Gaussian basis method to improve the dephasing representation for computing time-resolved electronic spectra, demonstrating enhanced accuracy and efficiency in various quantum systems.

Contribution

The paper introduces an exact Gaussian basis method and derives a Gaussian dephasing representation, expanding the toolkit for accurate and efficient quantum spectral calculations.

Findings

Gaussian basis method improves spectral accuracy

Gaussian DR outperforms in chaotic systems

Methods validated on multiple quantum models

Abstract

We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. \v{S}ulc and J. Van\'i\v{c}ek, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These methods include the Gaussian DR, an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. The newly obtained methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0/S1 model, and quartic oscillator. Numerical results confirm that both the Gaussian basis method and the Gaussian DR increase the accuracy of the DR. Surprisingly, in chaotic systems the Gaussian DR can outperform the presumably more accurate Gaussian basis method, in which the two bases are evolved separately.