Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
Acc Chem Res. 2021 Dec 7;54(23):4215-4228. doi: 10.1021/acs.accounts.1c00511. Epub 2021 Nov 10.
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent in the molecular structure or induced by the (intense) external field. The curse of dimensionality indicates the intractable exponential scaling of calculation effort with system size and restricts the implementation of "numerically exact" approaches for realistic large systems. The phase space formulation of quantum mechanics offers an important theoretical framework for constructing practical approximate trajectory-based methods for quantum dynamics. This Account reviews our recent progress in phase space mapping theory: a unified framework for constructing the mapping Hamiltonian on phase space for coupled -state systems where the renowned Meyer-Miller Hamiltonian model is a special case, a general phase space formulation of quantum mechanics for nonadiabatic systems where the electronic degrees of freedom are mapped onto constraint space and the nuclear degrees of freedom are mapped onto infinite space, and an isomorphism between the mapping phase space approach for nonadiabatic systems and that for nonequilibrium electron transport processes. While the zero-point-energy parameter is conventionally assumed to be positive, we show that the constraint implied in the conventional Meyer-Miller mapping Hamiltonian requires that such a parameter can be negative as well and lies in (-1/, +∞) for each electronic degree of freedom. More importantly, the zero-point-energy parameter should be interpreted as a special case of a commutator matrix in the comprehensive phase space mapping Hamiltonian for nonadiabatic systems. From the rigorous formulation of mapping phase space, we propose approximate but practical trajectory-based nonadiabatic dynamics methods. The applications to both gas phase and condensed phase problems include the spin-boson model for condensed phase dissipative two-state systems, the three-state photodissociation models, the seven-site model of the Fenna-Matthews-Olson monomer in photosynthesis of green sulfur bacteria, the strongly coupled molecular/atomic matter-optical cavity systems designed for controlling and manipulating chemical dynamical processes, and the Landauer model for a quantum dot state coupled with two electrodes. In these applications the overall performance of our phase space mapping dynamics approach is superior to two prevailing trajectory-based methods, Ehrenfest dynamics and fewest switches surface hopping.
非绝热动力学过程是非化学、材料、生物和环境分子系统中最重要的量子力学现象之一，其中不同电子态之间的耦合要么存在于分子结构中，要么由（强）外场诱导。维数诅咒表明计算工作量与系统尺寸呈难以处理的指数级增长，限制了“数值精确”方法在实际大系统中的实施。量子力学的相空间表述为构建实用的基于近似轨迹的量子动力学方法提供了一个重要的理论框架。本综述回顾了我们在相空间映射理论方面的最新进展：一种统一的框架，用于构建耦合态系统的相空间映射哈密顿量，其中著名的 Meyer-Miller 哈密顿量模型是一个特例；一种非绝热系统的通用相空间表述，其中电子自由度被映射到约束空间，核自由度被映射到无限空间；以及非绝热系统的映射相空间方法与非平衡电子输运过程的映射相空间方法之间的同构。虽然传统上假设零点能参数为正，但我们表明，传统 Meyer-Miller 映射哈密顿量所隐含的约束要求该参数也可以为负，并且对于每个电子自由度，该参数位于（-1/，+∞）之间。更重要的是，零点能参数应被解释为非绝热系统综合相空间映射哈密顿量中对易子矩阵的特例。从映射相空间的严格表述出发，我们提出了一种近似但实用的基于轨迹的非绝热动力学方法。这些方法在气相和凝聚相问题中的应用包括凝聚相耗散二能级系统的自旋-玻色子模型、三能级光解模型、光合作用绿硫细菌中 Fenna-Matthews-Olson 单体的七个位点模型、用于控制和操纵化学动力学过程的强耦合分子/原子物质光学腔系统以及与两个电极耦合的量子点状态的 Landauer 模型。在这些应用中，我们的相空间映射动力学方法的整体性能优于两种流行的基于轨迹的方法， Ehrenfest 动力学和最少切换表面跳跃。
