Path-Integral Isomorphic Hamiltonian for Including Nuclear Quantum Effects in Non-adiabatic Dynamics

TL;DR

This paper introduces a path-integral isomorphic Hamiltonian that accurately incorporates nuclear quantum effects into non-adiabatic dynamics simulations, compatible with existing mixed quantum-classical methods.

Contribution

A novel isomorphic Hamiltonian framework that enables efficient inclusion of nuclear quantum effects in non-adiabatic simulations, compatible with surface hopping and Ehrenfest dynamics.

Findings

Improved accuracy in deep-tunneling regimes.

Successful modeling of multi-level systems.

Enhanced simulation of non-adiabatic processes.

Abstract

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced, such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.