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 γ∈(−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.

中文翻译：

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非绝热动力学Meyer-Miller映射模型中的负零点能量参数

著名的Meyer-Miller映射模型是生成基于轨迹的非绝热动力学方法的有用方法。通常假定零点能量（ZPE）参数为正。传统的Meyer-Miller映射哈密顿量对F电子状态系统所隐含的约束实际上需要γ∈（−1 / F，∞）表示每个电子自由度的ZPE参数。对于这样的参数，负值和正值都可能。我们首先建立了严格的公式，以在施加约束时在笛卡尔相空间中构建精确的映射模型。当通过线性化的半经典初始值表示来近似核动力学时，即使在极高的零温度条件下，负的ZPE参数也可以在描述凝聚相两态系统的典型自旋玻色子模型中的动力学行为时表现出相当好的性能。