基于量子瞬子近似的反应速率计算的路径积分维里估计
Path-integral virial estimator for reaction rate calculation based on the quantum instanton approximation
摘要：
量子瞬子近似是一种量子过渡态理论，其使用反应通量关联函数及其在时间零处的低阶导数来计算化学反应速率。在这里，我们提出了几个路径积分估计后者的数量，其特征在于通量关联函数的初始衰减曲线。与内能或热容计算一样，在蒙特卡罗计算中，不同的估计量产生不同的方差（因此具有不同的收敛特性）。在这里，我们得到一个维里型估计，通过使用坐标缩放过程，而不是积分的部分，这允许更多的计算效益。我们还考虑了两种不同的方法来处理通量算子，即，局部路径和全局路径方法，其中后者以使用二阶势导数为代价实现较小的方差。数值试验进行了一维Eckart障碍和模型质子转移反应在极性溶剂中，这说明了减少方差的维里估计相应的热力学估计。
英文摘要：
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial-type estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
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