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

Simon Elias Schrader¹, Håkon Emil Kristiansen¹, Thomas Bondo Pedersen¹

¹Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.

Journal of Chemical Theory and Computation

|August 21, 2025

Summary

Modeling strong-field processes like high-harmonic generation is challenging. Rothe's method with Gaussian basis sets offers an efficient solution for time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) calculations.

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Area of Science:

Computational physics
Quantum chemistry
Strong-field physics

Background:

Modeling time-dependent strong-field processes, such as high-harmonic generation, in many-body systems is computationally demanding.
Representing the electronic continuum accurately is a key challenge in these simulations.

Purpose of the Study:

To develop an efficient and accurate method for modeling time-dependent strong-field processes.
To reformulate time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations as an optimization problem.

Main Methods:

Application of Rothe's method to TDHF and TDDFT equations of motion for orbitals.
Utilizing thawed, complex-valued Gaussian basis sets for efficient propagation, eliminating the need for grids.
Investigating the use of a few flexible Gaussians to describe unbound dynamics.

Main Results:

Demonstrated efficient propagation of Gaussian basis sets for orbital-based TDHF and TDDFT approaches.
Showcased that qualitatively correct results for unbound dynamics can be achieved with minimal flexible Gaussians.
Achieved quantitative agreement with grid calculations using 30-100 Gaussians for intensities up to 4 × 10^14 W/cm^2 in 1D systems.

Conclusions:

Rothe's method combined with Gaussian basis sets provides an efficient alternative to grid-based methods for strong-field process modeling.
This approach simplifies the representation of the electronic continuum, enabling accurate simulations of high-harmonic generation.
The method shows promise for studying complex many-body systems under intense laser fields.