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On the numerical solution of the exact factorization equations.

Graeme H Gossel1, Lionel Lacombe1, Neepa T Maitra1

  • 1Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA.

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This study demonstrates a self-consistent solution for exact factorization (EF) equations in electron-ion dynamics. A novel numerical approach enables stable propagation, revealing non-adiabatic behavior in model systems.

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Area of Science:

  • Quantum chemistry
  • Theoretical chemistry
  • Computational physics

Background:

  • The exact factorization (EF) approach simplifies the time-dependent molecular Schrödinger equation into coupled electron and nuclear wavefunctions.
  • This method offers insights into non-adiabatic processes and has inspired new dynamics methods.

Purpose of the Study:

  • To demonstrate the first self-consistent solution of the exact factorization equations.
  • To analyze the stability and convergence properties of this novel numerical approach.

Main Methods:

  • Development of a numerical method to solve the coupled electron-nuclear Schrödinger equations within the EF framework.
  • Addressing the challenges posed by the non-Hermitian nature of the EF Hamiltonian, which deviates from standard time-propagation techniques.

Main Results:

  • A stable propagation method was achieved for the EF equations, allowing observation of non-adiabatic dynamics.
  • Preliminary analysis of stability and convergence properties was performed, highlighting limitations due to instabilities.

Conclusions:

  • The study presents a viable, albeit preliminary, method for solving exact factorization equations.
  • Findings pave the way for further development and analysis of EF-based methods for quantum dynamics.