Accurate Non-adiabatic Quantum Dynamics from Pseudospectral Sampling of Time-dependent Gaussian Basis Sets

TL;DR

This paper introduces a pseudospectral Gaussian basis method for non-adiabatic quantum dynamics that reduces computational scaling and accurately models population transfer and coherence in molecular systems.

Contribution

It presents a novel pseudospectral sampling technique that improves efficiency and accuracy in simulating non-adiabatic quantum dynamics with Gaussian basis functions.

Findings

Accurately models nonadiabatic population transfer.

Reduces potential energy evaluation complexity from O(N^2) to O(N).

Achieves quantitative agreement with exact calculations.

Abstract

Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required. In this paper, we employ pseudospectral sampling of time-dependent Gaussian basis functions for the simulation of non-adiabatic dynamics. Unlike other methods, the pseudospectral Gaussian molecular dynamics tests the Schr\"{o}dinger equation with $N$ Dirac delta functions located at the centers of the Gaussian functions reducing the scaling of potential energy evaluations from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. By projecting the Gaussian basis onto discrete points in space, the method is capable of efficiently and quantitatively describing nonadiabatic population transfer and intra-surface quantum coherence. We investigate three model systems; the photodissociation of three coupled Morse oscillators, the bound state dynamics of two coupled Morse oscillators, and a two-dimensional model for collinear triatomic vibrational dynamics. In all cases, the pseudospectral Gaussian method is in quantitative agreement with numerically exact calculations. The results are promising for nonadiabatic molecular dynamics in molecular systems where strongly correlated ground or excited states require expensive electronic structure calculations.