High-order geometric integrators for representation-free Ehrenfest dynamics
arXiv:2107.00607 · doi:10.1063/5.0061878
Abstract
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equation, Ehrenfest dynamics is symplectic, time-reversible, and conserves exactly the total molecular energy as well as the norm of the electronic wavefunction. Here, we surpass apparent complications due to the coupling of classical nuclear and quantum electronic motions and present efficient geometric integrators for "representation-free" Ehrenfest dynamics, which do not rely on a diabatic or adiabatic representation of electronic states and are of arbitrary even orders of accuracy in the time step. These numerical integrators, obtained by symmetrically composing the second-order splitting method and exactly solving the kinetic and potential propagation steps, are norm-conserving, symplectic, and time-reversible regardless of the time step used. Using a nonadiabatic simulation in the region of a conical intersection as an example, we demonstrate that these integrators preserve the geometric properties exactly and, if highly accurate solutions are desired, can be even more efficient than the most popular non-geometric integrators.
arXiv commentReplaced "Ehrenfest dynamics" with "representation-free Ehrenfest dynamics" in the title. Moved most of the supplementary material to the appendix of the main text. Added new references and a new Eq. (54)
References in corpus (21)
- Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
- A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics
- Mapping quantum-classical Liouville equation: projectors and trajectories
- Generalized spin mapping for quantum-classical dynamics
- Exact quantum statistics for electronically nonadiabatic systems using continuous path variables
- Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations
- An analysis of nonadiabatic ring-polymer molecular dynamics and its application to vibronic spectra
- Ab initio simulations of excited carrier dynamics in carbon nanotubes
- Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation
- Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects
- Deriving the exact nonadiabatic quantum propagator in the mapping variable representation
- Evaluation of the nondiabaticity of quantum molecular dynamics with the dephasing representation of quantum fidelity
- Symplectic Semiclassical Wave Packet Dynamics
- Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation
- Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
- Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
- Polaron formation: Ehrenfest dynamics vs. exact results
- Mixed quantum-classical dynamics using collective electronic variables: A better alternative to electronic friction theories
- Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation
- An Efficient Time-splitting Method for the Ehrenfest Dynamics
- A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid
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- NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase