A generalized class of strongly stable and dimension-free T-RPMD integrators
A generalized class of strongly stable and dimension-free T-RPMD integrators
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DOI：
10.1063/5.0036954
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发表时间：
2020-11
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影响因子：
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通讯作者：
Jorge L. Rosa-Ra'ices;Jiace Sun;Nawaf Bou-Rabee;Thomas F. Miller
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文献类型：
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作者：
Jorge L. Rosa-Ra'ices;Jiace Sun;Nawaf Bou-Rabee;Thomas F. Miller
最近的工作表明，强稳定性和维数自由度是恒温环聚合物分子动力学（T-RPMD）和路径积分分子动力学的鲁棒数值积分所必需的，否则标准积分器会表现出非遍历性和其他病态[R. Korol等人，J. Chem. Phys. 151，124103（2019）和R. Korol等人，J. Chem.Phys.152，104102（2020）]。特别是，BCOCB计划，通过凯莱修改的标准BAOAB计划，具有一个简单的重新参数化的自由环聚合物子步骤，赋予强大的稳定性和维数的自由，并已被证明产生良好的数值精度在凝聚相系统与大的时间步长。在这里，我们介绍了一个更广泛的类T-RPMD数值积分器，表现出很强的稳定性和维数自由，无论奥恩斯坦-乌伦贝克摩擦时间表。除了考虑平衡精度和时间步长的稳定性，在以前的工作中，我们评估的基础上，他们的收敛速度的平衡和他们的效率，在评估平衡的期望值的积分。在广义类中，我们发现BCOCB对于各种与配置相关的可观测量量在准确性和效率方面具有上级，尽管广义类中的其他积分器对于与速度相关的量表现得更好。大量的数值证据表明，所述性能保证适用于液态水的强非谐情况。分析和数值结果表明，BCOCB优于其他已知的积分器的精度，效率和稳定性方面的时间步长的实际应用。
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.