Time-dependent Gaussian basis sets for many-body systems using Rothe's method: A mean-field study

TL;DR

This paper introduces a method using Rothe's approach with Gaussian basis sets to efficiently model time-dependent strong-field processes in many-body systems, avoiding grid reliance and achieving accurate results with few basis functions.

Contribution

It demonstrates the effective use of thawed, complex-valued Gaussian basis sets with Rothe's method for time-dependent Hartree-Fock and DFT, enabling efficient and accurate simulations of unbound electron dynamics.

Findings

Gaussian basis sets can reproduce grid calculations quantitatively.

Few Gaussians suffice for qualitative results in unbound dynamics.

Method is effective for high-intensity laser-matter interactions.

Abstract

A challenge in modeling time-dependent strong-field processes such as high-harmonic generation for many-body systems, is how to effectively represent the electronic continuum. We apply Rothe's method to the time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) equations of motion for the orbitals, which reformulates them as an optimization problem. We show that thawed, complex-valued Gaussian basis sets can be propagated efficiently for these orbital-based approaches, removing the need for grids. In particular, we illustrate that qualitatively correct results can often be obtained by using just a few fully flexible Gaussians that describe the unbound dynamics for both TDHF and TDDFT. Grid calculations can be reproduced quantitatively using $30$--$100$ Gaussians for intensities up to $4\times10^{14}$ W/cm$^2$ for the one-dimensional molecular systems considered in this work.