# Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations

## TL;DR

This paper introduces a hybrid quantum master equation framework to simulate conical intersection dynamics in condensed phases, capturing nonadiabatic effects and bath interactions with improved accuracy.

## Contribution

It develops a novel approach combining wavepacket dynamics and quantum master equations with frozen modes to model complex conical intersection processes.

## Key findings

- Quantum yield increases with reorganization energy in Markovian baths.
- Quantum yield decreases with reorganization energy in non-Markovian baths.
- The method accurately reproduces exact results for pyrazine and rhodopsin models.

## Abstract

We present a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation, and treated as sources of static disorder. In this way, we adopt the recently developed frozen-mode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic timescale of the bath, in a two-mode model of photoisomerization. We find that the yield is monotonically increasing with reorganization energy for a Markovian bath, but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase.