High-order geometric integrators for representation-free Ehrenfest dynamics

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.