On the short-time limit of ring polymer molecular dynamics
On the short-time limit of ring polymer molecular dynamics
复制标题
DOI：
10.1063/1.2357599
复制
发表时间：
2006-09-28
影响因子：
4.4
通讯作者：
Manolopoulos, David E.
中科院分区：
文献类型：
--
作者：
Braams, Bastiaan J.;Manolopoulos, David E.
我们研究了一类近似量子动力学技术的短时精度，其中包括质心分子动力学（CMD）和环聚合物分子动力学（RPMD）方法。这两种方法都基于路径积分分子动力学（PIMD）技术，用于计算量子力学系统的精确静态平衡特性。对于涉及位置或动量线性函数算子的 Kubo 变换实时相关函数，RPMD 和（绝热）CMD 近似的不同之处仅在于 PIMD 中采用的环形聚合物珠系统的人造质量矩阵的选择。因此，这种类型的一般方法的明显变形是将 PIMD（或 Parrinello-Rahman）质量矩阵的元素视为一组可调整的参数，可以选择这些参数来提高所得近似值的精度。我们在此表明，当用于选择质量矩阵的标准是 Kubo 变换相关函数的短时精度时，此 ansatz 唯一地导致 RPMD 近似。特别是，我们表明，对于一般非简谐势，RPMD 位置自相关函数中的引导误差为 O(t(8))，速度自相关函数中的误差为 O(t(6))。 CMD 近似中的相应误差分别为 O(t(6)) 和 O(t(4))。 (c) 2006 年美国物理研究所。
We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively. (c) 2006 American Institute of Physics.