Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801, USA.
Faraday Discuss. 2016 Dec 22;195:81-92. doi: 10.1039/c6fd00142d.
The quantum-classical path integral (QCPI) offers a rigorous methodology for simulating quantum mechanical processes in condensed-phase environments treated in full atomistic detail. This paper describes the implementation of QCPI on system-bath models, which are frequently employed in studying the dynamics of reactive processes. The QCPI methodology incorporates all effects associated with stimulated phonon absorption and emission as its crudest limit, thus can (in some regimes) converge faster than influence functional-based path integral methods specifically designed for system-bath Hamiltonians. It is shown that the QCPI phase arising from a harmonic bath can be summed analytically with respect to the discrete bath degrees of freedom and expressed in terms of precomputed influence functional coefficients, avoiding the explicit enumeration of forced oscillator trajectories, whose number grows exponentially with the length of quantum memory. Further, adoption of the blip decomposition (which classifies the system paths based on the time length over which their forward and backward components are not identical) and a cumulative treatment of the QCPI phase between blips allows elimination of the majority of system paths, leading to a dramatic increase in efficiency. The generalization of these acceleration techniques to anharmonic environments is discussed.
量子经典路径积分（QCPI）为模拟凝聚相环境中的量子力学过程提供了一种严格的方法，这些过程以全原子细节进行处理。本文描述了在系统-浴模型上实现 QCPI 的方法，该模型常用于研究反应过程的动力学。QCPI 方法将与受激声子吸收和发射相关的所有效应作为其最粗糙的极限纳入其中，因此在某些情况下，它可以比专门针对系统-浴哈密顿量设计的基于影响函数的路径积分方法更快收敛。结果表明，来自谐波浴的 QCPI 相位可以根据离散浴自由度进行解析求和，并以预先计算的影响函数系数表示，从而避免了强制振荡器轨迹的显式枚举，其数量随量子记忆长度呈指数增长。此外，采用斑点分解（根据其前后分量不同的时间长度对系统路径进行分类）和斑点之间的 QCPI 相位的累积处理，可以消除大多数系统路径，从而显著提高效率。讨论了将这些加速技术推广到非谐环境的方法。
