Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801, USA.
J Chem Phys. 2012 Dec 14;137(22):22A553. doi: 10.1063/1.4767980.
We present a quantum-classical methodology for propagating the density matrix of a system coupled to a polyatomic (large molecular or solvent) environment. The system is treated via a full path integral, while the dynamics of the environment is approximated in terms of classical trajectories. We obtain quantum-classical path integral (QCPI) expressions in which the trajectories can undergo transitions to other quantum states at regular time intervals, but the cumulative probability of these transitions is governed by the local strength of the state-to-state coupling as well as the magnitude of the solvent reorganization energy. If quantum effects in the coordinates of the environment are relatively weak, an inexpensive random hop approximation leads to accurate descriptions of the dynamics. We describe a systematic iterative scheme for including quantum mechanical corrections for the solvent by gradually accounting for nonlocal "quantum memory" effects. As the length of the included memory approaches the decoherence time of the environment, the iterative QCPI procedure converges to the full QCPI result. The methodology is illustrated with application to dissipative symmetric and asymmetric two-level systems.
我们提出了一种量子经典方法，用于传播与多原子（大分子或溶剂）环境耦合的系统的密度矩阵。系统通过全路径积分进行处理，而环境的动力学则根据经典轨迹进行近似。我们得到了量子经典路径积分（QCPI）表达式，其中轨迹可以在规则的时间间隔内经历到其他量子态的跃迁，但这些跃迁的累积概率受到状态间耦合的局部强度以及溶剂重组能的大小的控制。如果环境坐标中的量子效应相对较弱，则便宜的随机跳跃近似可以准确地描述动力学。我们描述了一种系统的迭代方案，通过逐渐考虑非局部的“量子记忆”效应来包含溶剂的量子力学修正。随着所包含的记忆长度接近环境的退相干时间，迭代 QCPI 过程收敛到完整的 QCPI 结果。该方法通过应用于耗散对称和不对称的双能级系统进行了说明。
