On the numerical solution of the exact factorization equations

Gossel, Graeme H.; Lacombe, Lionel; Maitra, Neepa T.

doi:10.1063/1.5090802

Title: On the numerical solution of the exact factorization equations

Journal Article · Thu Apr 18 00:00:00 EDT 2019 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5090802· OSTI ID:1507622

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Hunter College, New York, NY (United States). Dept. of Physics and Astronomy
Hunter College, New York, NY (United States). Dept. of Physics and Astronomy; City Univ. of New York, NY (United States). Graduate Center. Physics Program. Chemistry Program

The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schrödinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic wavefunction. The potentials appearing in these equations have provided insight into non-adiabatic processes, and new practical non-adiabatic dynamics methods have been formulated starting from these equations. We provide a first demonstration of a self-consistent solution of the exact equations, with a preliminary analysis of their stability and convergence properties. The equations have an unprecedented mathematical form, involving a Hamiltonian outside the class of Hermitian Hamiltonians usually encountered in time-propagation, and so the usual numerical methods for time-dependent Schrödinger fail when applied in a straightforward way to the EF equations. We find an approach that enables stable propagation long enough to witness non-adiabatic behavior in a model system before non-trivial instabilities take over. Implications for the development and analysis of EF-based methods are discussed.

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Research Organization:: Hunter College, New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0015344

OSTI ID:: 1507622

Alternate ID(s):: OSTI ID: 1507620

Journal Information:: Journal of Chemical Physics, Vol. 150, Issue 15; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 16 works

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Exact Potential Energy Surface for Molecules in Cavities Lacombe, Lionel; Hoffmann, Norah M.; Maitra, Neepa T. Physical Review Letters, Vol. 123, Issue 8 https://doi.org/10.1103/physrevlett.123.083201	journal	August 2019
Beyond Born–Oppenheimer theory for spectroscopic and scattering processes Mukherjee, Bijit; Naskar, Koushik; Mukherjee, Soumya Taylor & Francis https://doi.org/10.6084/m9.figshare.9994787.v1	text	January 2019
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Beyond Born–Oppenheimer theory for spectroscopic and scattering processes Mukherjee, Bijit; Naskar, Koushik; Mukherjee, Soumya Taylor & Francis https://doi.org/10.6084/m9.figshare.9994787	text	January 2019
Exact Potential Energy Surface for Molecules in Cavities Lacombe, Lionel; Hoffmann, Norah M.; Maitra, Neepa T. arXiv https://doi.org/10.48550/arxiv.1906.02651	text	January 2019
Internal Conversion and Intersystem Crossing with the Exact Factorization Talotta, Francesco; Morisset, Sabine; Rougeau, Nathalie Journal of Chemical Theory and Computation, Vol. 16, Issue 8 https://doi.org/10.1021/acs.jctc.0c00493	journal	July 2020

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Title: On the numerical solution of the exact factorization equations

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