Rosa-Raíces Jorge L, Sun Jiace, Bou-Rabee Nawaf, Miller Thomas F
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Department of Mathematical Sciences, Rutgers University Camden, Camden, New Jersey 08102, USA.
J Chem Phys. 2021 Jan 14;154(2):024106. doi: 10.1063/5.0036954.
Recent work shows that strong stability and dimensionality freedom are essential for robust numerical integration of thermostatted ring-polymer molecular dynamics (T-RPMD) and path-integral molecular dynamics, without which standard integrators exhibit non-ergodicity and other pathologies [R. Korol et al., J. Chem. Phys. 151, 124103 (2019) and R. Korol et al., J. Chem. Phys. 152, 104102 (2020)]. In particular, the BCOCB scheme, obtained via Cayley modification of the standard BAOAB scheme, features a simple reparametrization of the free ring-polymer sub-step that confers strong stability and dimensionality freedom and has been shown to yield excellent numerical accuracy in condensed-phase systems with large time steps. Here, we introduce a broader class of T-RPMD numerical integrators that exhibit strong stability and dimensionality freedom, irrespective of the Ornstein-Uhlenbeck friction schedule. In addition to considering equilibrium accuracy and time step stability as in previous work, we evaluate the integrators on the basis of their rates of convergence to equilibrium and their efficiency at evaluating equilibrium expectation values. Within the generalized class, we find BCOCB to be superior with respect to accuracy and efficiency for various configuration-dependent observables, although other integrators within the generalized class perform better for velocity-dependent quantities. Extensive numerical evidence indicates that the stated performance guarantees hold for the strongly anharmonic case of liquid water. Both analytical and numerical results indicate that BCOCB excels over other known integrators in terms of accuracy, efficiency, and stability with respect to time step for practical applications.
近期的研究表明，对于恒温环聚合物分子动力学（T-RPMD）和路径积分分子动力学的稳健数值积分而言，强大的稳定性和维度自由度至关重要，否则标准积分器会表现出非遍历性及其他病态问题[R. Korol等人，《化学物理杂志》151, 124103 (2019)以及R. Korol等人，《化学物理杂志》152, 104102 (2020)]。具体而言，通过对标准BAOAB方案进行凯莱修正得到的BCOCB方案，其特点是对自由环聚合物子步进行简单的重新参数化，从而赋予了强大的稳定性和维度自由度，并且在具有大时间步长的凝聚相系统中已被证明能产生出色的数值精度。在此，我们引入了一类更广泛的T-RPMD数值积分器，它们具有强大的稳定性和维度自由度，与奥恩斯坦-乌伦贝克摩擦时间表无关。除了像之前的工作那样考虑平衡精度和时间步长稳定性外，我们还根据积分器向平衡收敛的速率以及它们在评估平衡期望值时的效率来评估这些积分器。在这个广义类中，我们发现对于各种与构型相关的可观测量，BCOCB在精度和效率方面表现更优，尽管广义类中的其他积分器对于与速度相关的量表现更好。大量的数值证据表明，对于液态水的强非谐情况，所述的性能保证是成立的。分析和数值结果均表明，在实际应用中，就精度、效率和时间步长稳定性而言，BCOCB优于其他已知的积分器。
