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Basis Functions for Time-Dependent Kohn-Sham Inversion

  • Paul M. Zimmerman
  • Joshua Kammeraad
  • Duy-Khoi Dang
  • Harish S. Bhat
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Abstract

Floquet theory provides insight into the inversion of time-dependent Kohn-Sham density functional theory. Specifically, mathematical derivations show that the fundamental frequencies of a time-dependent wavefunction solution are the leading-order harmonics for the TD-KS state. Numerical tests of the resulting ansatz in 1D and 3D for atomic and molecular cases demonstrate its utility. In particular, low L2 errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.

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Cite

BibTeXRIS
BibTeX
@misc{zimmerman2026basis,
  title = {{Basis Functions for Time-Dependent Kohn-Sham Inversion}},
  author = {Paul M. Zimmerman and Joshua Kammeraad and Duy-Khoi Dang and Harish S. Bhat},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34164},
  eprint = {2609.34164},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34164},
}
RIS
TY  - UNPB
TI  - Basis Functions for Time-Dependent Kohn-Sham Inversion
AU  - Paul M. Zimmerman
AU  - Joshua Kammeraad
AU  - Duy-Khoi Dang
AU  - Harish S. Bhat
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.34164
UR  - https://arxiv.org/abs/2609.34164
AB  - Floquet theory provides insight into the inversion of time-dependent Kohn-Sham density functional theory. Specifically, mathematical derivations show that the fundamental frequencies of a time-dependent wavefunction solution are the leading-order harmonics for the TD-KS state. Numerical tests of the resulting ansatz in 1D and 3D for atomic and molecular cases demonstrate its utility. In particular, low L_2 errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.
ER  -