On the numerical solution of the exact factorization equations

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 i...

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Bibliographic Details
Published in:The Journal of chemical physics 2019-04, Vol.150 (15), p.154112-154112
Main Authors: Gossel, Graeme H., Lacombe, Lionel, Maitra, Neepa T.
Format: Article
Language:English
Subjects:
Adiabatic flow
Factorization
Ion dynamics
Mathematical models
Numerical methods
Physics
Propagation
Schrodinger equation
Stability analysis
Time dependence
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Summary: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. Here, 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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.5090802