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arXiv · 2506.10701

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

Simon Elias Schrader·Håkon Emil Kristiansen·Thomas Bondo Pedersen·Simen Kvaal
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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.

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Simon Elias Schrader, Håkon Emil Kristiansen, Thomas Bondo Pedersen, Simen Kvaal. 2025-08-11. Time-dependent Gaussian basis sets for many-body systems using Rothe's method: A mean-field study. https://doi.org/10.1021/acs.jctc.5c00970

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