Lapelosa Mauro, Abrams Cameron F
Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut St., Philadelphia, Pennsylvania 19104.
Comput Phys Commun. 2013 Oct;184(10):2310-2315. doi: 10.1016/j.cpc.2013.05.017.
Rare events between states in complex systems are fundamental in many scientific fields and can be studied by building reaction pathways. A theoretical framework to analyze reaction pathways is provided by transition-path theory (TPT). The central object in TPT is the committor function, which is found by solution of the backward-Kolmogorov equation on a given potential. Once determined, the committor can be used to calculate reactive fluxes and rates, among other important quantities. We demonstrate here that the committor can be calculated using the method of finite elements on non-uniform meshes. We show that this approach makes it feasible to perform TPT calculations on 3D potentials because it requires many fewer degrees of freedom than a regular-mesh finite-difference approach. In various illustrative 2D and 3D problems, we calculate the committor function and reaction rates at different temperatures, and we discuss effects of temperatures and simple entropic barriers on the structure of the committor and the reaction rate constants.
复杂系统中状态间的罕见事件在许多科学领域都至关重要，可通过构建反应路径来进行研究。过渡路径理论（TPT）提供了一个分析反应路径的理论框架。TPT的核心对象是反应概率函数，它通过在给定势场上求解反向柯尔莫哥洛夫方程得到。一旦确定，反应概率函数可用于计算反应通量和速率以及其他重要量。我们在此证明，反应概率函数可使用非均匀网格上的有限元方法来计算。我们表明，这种方法使得在三维势场上进行TPT计算变得可行，因为与常规网格有限差分方法相比，它所需的自由度要少得多。在各种二维和三维示例问题中，我们计算了不同温度下的反应概率函数和反应速率，并讨论了温度和简单熵垒对反应概率函数结构和反应速率常数的影响。
