Runeson Johan E, Richardson Jeremy O
Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
J Chem Phys. 2020 Feb 28;152(8):084110. doi: 10.1063/1.5143412.
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. E. Runeson and J. O. Richardson, J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of N-level systems. This is done via a mapping to a classical phase space that preserves the SU(N)-symmetry of the original quantum problem. The theory reproduces the standard Meyer-Miller-Stock-Thoss Hamiltonian without invoking an extended phase space, and we thus avoid leakage from the physical subspace. In contrast to the standard derivation of this Hamiltonian, the generalized spin mapping leads to an N-dependent value of the zero-point energy parameter that is uniquely determined by the Casimir invariant of the N-level system. Based on this mapping, we derive a simple way to approximate correlation functions in complex nonadiabatic molecular systems via classical trajectories and present benchmark calculations on the seven-state Fenna-Matthews-Olson light-harvesting complex. The results are significantly more accurate than conventional Ehrenfest dynamics, at a comparable computational cost, and can compete in accuracy with other state-of-the-art mapping approaches.
我们最近基于二能级系统与自旋1/2粒子之间众所周知的量子等价性，推导出了一种用于处理经典环境中二能级系统非绝热动力学的自旋映射方法[J. E. 鲁内松和J. O. 理查森，《化学物理杂志》151, 044119 (2019)]。在本文中，我们将此方法推广以描述N能级系统的动力学。这是通过映射到一个保持原始量子问题SU(N)对称性的经典相空间来实现的。该理论无需引入扩展相空间就能重现标准的迈耶 - 米勒 - 斯托克 - 托斯哈密顿量，因此我们避免了从物理子空间的泄漏。与该哈密顿量的标准推导不同之处在于，广义自旋映射导致零点能量参数的值与N有关，该值由N能级系统的卡西米尔不变量唯一确定。基于此映射，我们通过经典轨迹推导出一种简单的方法来近似复杂非绝热分子系统中的关联函数，并给出了对七态费纳 - 马修斯 - 奥尔森光捕获复合物的基准计算结果。结果在可比的计算成本下比传统的埃伦费斯特动力学显著更准确，并且在精度上可以与其他最先进的映射方法相媲美。
