Negative Zero-Point-Energy Parameter in the Meyer-Miller Mapping Model for Nonadiabatic Dynamics

TL;DR

This paper revisits the Meyer-Miller mapping model for nonadiabatic dynamics, revealing that the zero-point-energy parameter can be negative without loss of accuracy, which broadens the model's applicability.

Contribution

It establishes a rigorous formulation for exact mapping models with a negative ZPE parameter, challenging the conventional assumption of positivity.

Findings

Negative ZPE parameters can produce accurate dynamics in spin-boson models.

The model remains effective even at zero temperature.

The formulation allows for more flexible mapping Hamiltonians.

Abstract

The celebrated Meyer-Miller mapping model has been a useful approach for generating practical trajectory-based nonadiabatic dynamics methods. It is generally assumed that the zero-point-energy (ZPE) parameter is positive. The constraint implied in the conventional Meyer-Miller mapping Hamiltonian for an F-electronic-state system actually requires that parameter \gamma is larger than -1/F for the ZPE parameter for each electronic degree of freedom. Both negative and positive values are possible for such a parameter. We first establish a rigorous formulation to construct exact mapping models in the Cartesian phase space when the constraint is applied. When nuclear dynamics is approximated by the linearized semiclassical initial value representation, a negative ZPE parameter could lead to reasonably good performance in describing dynamic behaviors in typical spin-boson models for condensed-phase two-state systems, even at challenging zero temperature.