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High-order geometric integrators for representation-free Ehrenfest dynamics.

Seonghoon Choi1, Jiří Vaníček1

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New geometric integrators enhance Ehrenfest dynamics for molecular simulations. These methods preserve key properties like energy conservation and time-reversibility, offering efficient and accurate treatment of nonadiabatic effects.

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Area of Science:

  • * Quantum chemistry
  • * Computational physics
  • * Molecular dynamics

Background:

  • * Ehrenfest dynamics approximates ab initio mixed quantum-classical molecular dynamics.
  • * It treats electronically nonadiabatic effects but is an approximation to the Schrödinger equation.
  • * Standard Ehrenfest dynamics possesses symplectic, time-reversible, and energy-conserving properties.

Purpose of the Study:

  • * To develop efficient geometric integrators for representation-free Ehrenfest dynamics.
  • * To overcome challenges in coupling classical nuclear and quantum electronic motions.
  • * To achieve arbitrary even orders of accuracy in the time step.

Main Methods:

  • * Development of geometric integrators by symmetrically composing a second-order splitting method.
  • * Exact solution of kinetic and potential propagation steps.
  • * Implementation of representation-free dynamics, avoiding diabatic or adiabatic electronic state representations.

Main Results:

  • * The proposed numerical integrators are norm-conserving, symplectic, and time-reversible for any time step.
  • * Demonstrated exact preservation of geometric properties in simulations near conical intersections.
  • * Showed potential for higher efficiency compared to non-geometric integrators for accurate solutions.

Conclusions:

  • * Efficient geometric integrators for representation-free Ehrenfest dynamics have been successfully developed.
  • * These integrators maintain crucial physical properties regardless of the time step.
  • * They offer a promising and potentially more efficient approach for nonadiabatic molecular dynamics simulations.