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Abstract We present a reproducible ab-initio method to produce benchmark tests between time-dependent Schrödinger equation (TDSE) in the single-active-electron approximation (SAE) and time-dependent density functional theory (TDDFT) in the highly nonlinear multiphoton and tunneling regime of strong-field physics. To this end we compare results for high-order harmonic generation from valence shells in atoms using the SAE-TDSE approach and TDDFT calculations. As key to the benchmark comparison we obtain an analytic form of SAE potentials based on density functional theory, which we applied for different atoms and ions. The ionization energies of atomic ground and excited states, as well as the energies of inner shells, for the SAE potentials agree well with experimental data. Using these potentials we find remarkable agreement between the results of the two independent numerical approaches (TDDFT and SAE-TDSE) for the high-order harmonic yields in helium, demonstrating the accuracy of the SAE potentials as well as the predictive power of SAE-TDSE and TDDFT calculations for the nonperturbative and highly nonlinear strong-field process of high harmonic generation in the ultraviolet and visible wavelength regime. Finally, as another application of the SAE potentials, high harmonic spectra from outer and inner valence shells are calculated and it is shown that unphysical artifacts in the SAE-spectra from the individual shells are removed once all the amplitudes are considered.
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This content will become publicly available on December 1, 2025
QMol-grid : A MATLAB package for quantum-mechanical simulations in atomic and molecular systems
The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems, currently implemented in one spatial dimension. It supports ground- and excited-state calculations for the Schrödinger equation, density-functional theory, and Hartree–Fock levels of theory as well as propagators for field-free and field-driven time-dependent Schrödinger equation (TDSE) and real-time time-dependent density-functional theory (TDDFT), using symplectic-split schemes. The package is written using MATLAB’s object-oriented features and handle classes. It is designed to facilitate access to the wave function(s) (TDSE) and the Kohn–Sham orbitals (TDDFT) within MATLAB’s environment.
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- Award ID(s):
- 2207656
- PAR ID:
- 10567438
- Publisher / Repository:
- SoftwareX
- Date Published:
- Journal Name:
- SoftwareX
- Volume:
- 28
- Issue:
- C
- ISSN:
- 2352-7110
- Page Range / eLocation ID:
- 101968
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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