Yan Yaming, Xu Meng, Liu Yanying, Shi Qiang
Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China.
J Chem Phys. 2019 Jun 21;150(23):234101. doi: 10.1063/1.5096214.
There has been a long history of applying the generalized master equation (GME) to study charge carrier and exciton transport in molecular systems. Yet exact memory kernels in the GME are generally difficult to obtain. In this work, exact memory kernels of the Nakajima-Zwanzig-Mori GME for a one dimensional Holstein type of model are calculated by employing the Dyson relation for the exact memory kernel, combined with the hierarchical equations of motion method. Characteristics of the exact memory kernels, as well as the transition rate constants within the Markovian approximation, are then analyzed for different sets of parameters ranging from the hopping to bandlike transport regimes. It is shown that, despite the memory effect of the exact kernels, the Markovian approximation to the exact GME can reproduce the diffusion constants accurately. We also investigate the validity of the second and fourth order perturbation theories with respect to the electronic coupling constant in calculating the rate constants and the diffusion constant. It is found that, due to the cancellation of errors, the second order diffusion constant gives a reasonable estimate of the exact one within a wide range of electronic coupling constants.
将广义主方程（GME）应用于研究分子系统中的电荷载流子和激子输运已有很长的历史。然而，GME中精确的记忆核通常很难获得。在这项工作中，通过将精确记忆核的戴森关系与运动方程的层级方法相结合，计算了一维荷斯坦型模型的中岛 - 兹万齐格 - 森GME的精确记忆核。然后针对从跳跃到带状输运区域的不同参数集，分析了精确记忆核的特性以及马尔可夫近似内的跃迁速率常数。结果表明，尽管精确核存在记忆效应，但对精确GME的马尔可夫近似能够准确地重现扩散常数。我们还研究了在计算速率常数和扩散常数时，关于电子耦合常数的二阶和四阶微扰理论的有效性。结果发现，由于误差的抵消，二阶扩散常数在很宽的电子耦合常数范围内对精确扩散常数给出了合理的估计。
