# Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach

## TL;DR

This paper introduces a modification to the mapping approach in nonadiabatic dynamics that improves the accuracy of population relaxation predictions by treating the identity component of the population operator quantum mechanically.

## Contribution

The authors generalize a recent modification to quasiclassical methods, enhancing the accuracy of population dynamics in multi-state systems without altering existing equations.

## Key findings

- Significant improvement in population relaxation predictions for a seven-state model
- Enhanced accuracy of traditional mapping methods compared to exact quantum results
- Applicable to complex light-harvesting systems like Fenna-Matthews-Olson

## Abstract

The mapping approach addresses the mismatch between the continuous nuclear phase space and discrete electronic states by creating an extended, fully continuous phase space using a set of harmonic oscillators to encode the populations and coherences of the electronic states. Existing quasiclassical dynamics methods based on mapping, such as the linearised semiclassical initial value representation (LSC-IVR) and Poisson bracket mapping equation (PBME) approaches, have been shown to fail in predicting the correct relaxation of electronic-state populations following an initial excitation. Here we generalise our recently published modification to the standard quasiclassical approximation for simulating quantum correlation functions. We show that the electronic-state population operator in any system can be exactly rewritten as a sum of a traceless operator and the identity operator. We show that by treating the latter at a quantum level instead of using the mapping approach, the accuracy of traditional quasiclassical dynamics methods can be drastically improved, without changes to their underlying equations of motion. We demonstrate this approach for the seven-state Frenkel-Exciton model of the Fenna-Matthews-Olson light harvesting complex, showing that our modification significantly improves the accuracy of traditional mapping approaches when compared to numerically exact quantum results.