Department of Physics, Indiana University - Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.
J Chem Phys. 2017 Mar 28;146(12):124128. doi: 10.1063/1.4979058.
Calculating the kinetic rates for rare transitions is an important objective for molecular simulations. Here I prove equalities that relate the transition rates to the equilibrium free energy and the statistics of the transition paths. In particular, the durations of the transition paths within given intervals of the reaction coordinate provide the kinetic pre-factor in the rate formula. Based on the available free energy, the transition rates can further be rigorously calculated by initiating forward and backward simulations and evaluating the duration of each transition path. Validation on a model system confirms that the approach correctly predicts the transition rates from the simulations and demonstrates that whereas the relations here are general and valid for any chosen reaction coordinate, a good reaction coordinate will enable a more efficient sampling of the transition paths and thus a more reliable rate calculation.
计算稀有跃迁的速率是分子模拟的一个重要目标。在这里，我证明了一些等式，它们将跃迁速率与平衡自由能和跃迁路径的统计量联系起来。具体来说，反应坐标给定区间内跃迁路径的持续时间为速率公式提供了动力学前因子。基于可用的自由能，可以通过启动正向和反向模拟并评估每个跃迁路径的持续时间来严格计算跃迁速率。对模型系统的验证表明，该方法可以正确地从模拟中预测跃迁速率，并证明尽管这里的关系是通用的，并且适用于任何选定的反应坐标，但一个好的反应坐标将能够更有效地对跃迁路径进行采样，从而更可靠地计算速率。
