从环状聚合物分子动力学得到的微正则速率：直接射击法、定相法和最大熵法
Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches
摘要：
我们解决的微正则反应速率的计算过程中涉及显着的核量子效应，使用环聚合物分子动力学（RPMD），电子非绝热跃迁和不。在说明了天真的自由粒子直接射击的方法，其中的内环聚合物模式的温度被设置为平移能量标度的缺点，我们调查替代策略的基础上的表达的微正则速率的热反应速率的逆拉普拉斯变换。结果表明，简单的应用程序的静止相位近似（SPA）显着提高了使用RPMD的微正则速率的性能，特别是在低能量区域，隧道占主导地位。使用SPA作为贝叶斯先验，然后使用最大熵反演的热反应速率，电子绝热和非绝热模型系统，获得数值上精确的RPMD微正则速率。最后，直接拍摄的方法被重新使用的内部环聚合物模式的SPA确定的温度，导致一个简单的，直接的模拟方法，提高精度的隧道制度。
英文摘要：
We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates, for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime.
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