Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

TL;DR

This paper develops an exact path integral method using continuous variables for calculating equilibrium and real-time properties of electronically nonadiabatic systems, leveraging the Stock-Thoss mapping.

Contribution

It introduces a novel, exact path integral representation with proper electronic subspace constraints for nonadiabatic systems, enabling accurate equilibrium and dynamical simulations.

Findings

The PI-ST method is exact for equilibrium properties.

It effectively initializes semiclassical trajectories for real-time correlation functions.

Numerical tests on model systems validate the approach.

Abstract

We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly constrains the electronic Cartesian coordinates to the physical subspace of the mapping. We numerically demonstrate that the resulting PI-ST representation is exact for the calculation of equilibrium properties of systems with coupled electronic and nuclear degrees of freedom. We further show that the PI-ST formulation provides a natural means to initialize semiclassical trajectories for the calculation of real-time thermal correlation functions, which is numerically demonstrated in applications to a series of nonadiabatic model systems.