# Spin-mapping approach for nonadiabatic molecular dynamics

## TL;DR

This paper introduces a spin-mapping approach for nonadiabatic molecular dynamics that improves accuracy over traditional methods by using a quantum-mechanically exact spin representation, avoiding extra projection operators, and showing significant performance gains.

## Contribution

The authors develop a spin-based mapping method for nonadiabatic dynamics that enhances accuracy and simplifies implementation compared to existing MMST-based approaches.

## Key findings

- Significant improvement over Ehrenfest dynamics.
- Better results than linearized semiclassical MMST mapping.
- No additional computational complexity required.

## Abstract

We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1/2 coherent state, we construct a classical phase space of a spin vector constrained to a spherical surface with a radius consistent with the quantum magnitude of the spin. In contrast with the singly-excited harmonic oscillator basis used in Meyer-Miller-Stock-Thoss (MMST) mapping, the theory requires no additional projection operators onto the space of physical states. When treated under a quasiclassical approximation, we show that the resulting dynamics is equivalent to that generated by the MMST Hamiltonian. What differs is the value of the zero-point energy parameter as well as the initial distribution and the measurement operators. For various spin-boson models the results of our method are seen to be a significant improvement compared to both standard Ehrenfest dynamics and linearized semiclassical MMST mapping, without adding any computational complexity.