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PreprintCC BYChemRxiv

Energy conserving variational dynamics with Gaussian wavepackets in the nonadiabatic regime

  • Michael Anim Safo
  • Giacomo Botti
  • Sophya Garashchuk
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Abstract

We present a theoretical framework for a “trajectory”-driven nonadiabatic dynamics, that generalizes the variational Gaussian wavepacket approach to dynamics on multiple diabatic states. By applying the time-dependent variational principle to a single Gaussian wavepacket per state, we obtain a set of coupled equations for the Gaussian center and width parameters that include terms arising from the coupling potential. We investigate the role of these terms as they change the Gaussian time-evolution, and of the initial conditions on the wavefunction for several standard benchmarks of nonadiabatic dynamics, including a three-state and a two-dimensional model. The state populations obtained with the fully variational Gaussian dynamics is found in close agreement with exact quantum results. Finally, we demonstrate that the use of Gaussian wavefunction in nonadiabatic dynamics preserves the symplecticity of the variational space, which ensures the energy conservation and minimization of error when solving the time-dependent Schrödinger equation.

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Cite

BibTeXRIS
BibTeX
@misc{safo2026energy,
  title = {{Energy conserving variational dynamics with Gaussian wavepackets in the nonadiabatic regime}},
  author = {Michael Anim Safo and Giacomo Botti and Sophya Garashchuk},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010925/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010925/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Energy conserving variational dynamics with Gaussian wavepackets in the nonadiabatic regime
AU  - Michael Anim Safo
AU  - Giacomo Botti
AU  - Sophya Garashchuk
PY  - 2026
DA  - 2026/10/23
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010925/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010925/v1
AB  - We present a theoretical framework for a “trajectory”-driven nonadiabatic dynamics, that generalizes the variational Gaussian wavepacket approach to dynamics on multiple diabatic states. By applying the time-dependent variational principle to a single Gaussian wavepacket per state, we obtain a set of coupled equations for the Gaussian center and width parameters that include terms arising from the coupling potential. We investigate the role of these terms as they change the Gaussian time-evolution, and of the initial conditions on the wavefunction for several standard benchmarks of nonadiabatic dynamics, including a three-state and a two-dimensional model. The state populations obtained with the fully variational Gaussian dynamics is found in close agreement with exact quantum results. Finally, we demonstrate that the use of Gaussian wavefunction in nonadiabatic dynamics preserves the symplecticity of the variational space, which ensures the energy conservation and minimization of error when solving the time-dependent Schrödinger equation.
ER  -