Path Integral Simulations
Path Integral Simulations
复制标题
路径积分模拟
DOI：
10.1016/b978-0-12-409547-2.11614-2
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Motoyuki Shiga
中科院分区：
文献类型：
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作者：
Lei Yan;Yoshiyuki Yamamoto;Motoyuki Shiga;Osamu Sugino;Motoyuki Shiga
路径积分（PI）模拟是一种基于费曼虚时间路径积分理论的方法。 1–3 该方法提供了热平衡中复杂分子系统的量子玻尔兹曼统计的精确数值解。 PI 模拟技术有多种，4-12，但本文重点关注路径积分分子动力学 (PIMD)、13-16 路径积分蒙特卡罗 (PIMC)、17-21 路径积分混合蒙特卡罗 (PIHMC)、16、22-26 质心分子动力学 (CMD)、27-32 和环聚合物分子动力学 (RPMD)。 33–36 近年来，PI 模拟已被应用到 AMBER、37 CPMD、38 i-PI、39 PIMD、40 和 PINY 等软件中。 41PIMD 是一种采用分子动力学作为采样技术来计算统计平均值的方法。与 PIMD 类似的是 PIMC 和 PIHMC 方法，其中分别采用蒙特卡罗和混合蒙特卡罗作为采样技术。 PIMD、PIMC 和 PIHMC 的共同之处在于它们生成的轨迹不传达时间演化信息。然而，PIMD 的 CMD 和 RPMD 扩展能够生成具有近似量子时间相关函数的轨迹。因此，CMD 和 RPMD 结果被称为准经典或半经典动力学。 PI模拟的概要如下。我们引入一个经典系统，其统计行为与原始量子系统相同。正如下面将要提到的，经典系统对应于许多复制系统的项链状物体。然后，我们使用分子动力学计算经典系统的统计平均值，以获得原始量子系统的统计平均值。
Path integral (PI) simulation is a method based on Feynman’s imaginary time path integral theory. 1–3 The method provides numerically exact solutions with respect to quantum Boltzmann statistics of complex molecular systems in thermal equilibrium. There are a variety of PI simulation techniques, 4–12 but this paper focuses on path integral molecular dynamics (PIMD), 13–16 path integral Monte Carlo (PIMC), 17–21 path integral hybrid Monte Carlo (PIHMC), 16, 22–26 centroid molecular dynamics (CMD), 27–32 and ring polymer molecular dynamics (RPMD). 33–36 In recent years PI simulation has been implemented into software such as AMBER, 37 CPMD, 38 i-PI, 39 PIMD, 40 and PINY. 41PIMD is a method in which molecular dynamics is employed as a sampling technique to compute statistical averages. Akin to PIMD are PIMC and PIHMC methods where Monte Carlo and hybrid Monte Carlo, respectively, are employed as sampling techniques. PIMD, PIMC and PIHMC are common in the sense that they generate trajectories that do not convey information on time evolution. However the CMD and RPMD extensions of PIMD are able to generate trajectories with approximate quantum time correlation functions. Thus CMD and RPMD results are referred to as quasiclassical or semiclassical dynamics. The outline of PI simulations is as follows. We introduce a classical system whose statistical behavior is identical as that of the original quantum system. As will be mentioned below, the classical system corresponds to a necklace-like object of many replicated systems. We then compute the statistical average of the classical system using molecular dynamics to obtain the statistical average of the original quantum system.