# Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics

## TL;DR

This paper introduces an efficient method for constructing generalized master equation memory kernels for multi-state quantum systems using quantum-classical dynamics, enabling accurate long-time dynamics with reduced computational effort.

## Contribution

The authors develop an algorithm to accelerate the quantum-classical GQME approach by selectively sampling key kernel matrix elements, improving efficiency for multi-state systems.

## Key findings

- The memory kernel decays within ~65 fs, capturing dynamics over tens of picoseconds.
- The method accurately reproduces dynamics of FMO and LHCII complexes.
- Quadratic scaling of trajectory number with system size improves computational feasibility.

## Abstract

Methods derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the non-perturbative combination of the GQME with quantum-classical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantum-classical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. Here we show that, while the non-Markovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantum-classical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantum-classical GQME by providing a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MF-GQME) to models of the Fenna-Matthews-Olson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that MF-GQME is able to accurately capture all the relevant dynamical time-scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time-scale, the steady state-type trapping on the picosecond time-scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays after only $\sim$65 fs.