Time-Dependent Gaussian Basis Sets for Many-Body Systems Using Rothe's Method: A Mean-Field Study

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 reformulate 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 × 10¹⁴ W/cm² for the one-dimensional molecular systems considered in this work.