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Updated: Sep 10, 2025

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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.