Bellucci Michael A, Trout Bernhardt L
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Chem Phys. 2014 Aug 21;141(7):074110. doi: 10.1063/1.4893216.
We present a new string method for finding the most probable transition pathway and optimal reaction coordinate in complex chemical systems. Our approach evolves an analytic parametric curve, known as a Bézier curve, to the most probable transition path between metastable regions in configuration space. In addition, we demonstrate that the geometric properties of the Bézier curve can be used to construct the optimal reaction coordinate near the most probable reaction path, and can further be used to devise a ranking vector capable of identifying precisely which collective variables are most important for governing the transition between metastable states. We discuss the algorithmic details of the Bézier curve string method, analyze its stability, accuracy and efficiency, and illustrate its capabilities using model potential energy functions. In particular, we use the degree elevation property of Bézier curves to develop an algorithm that adaptively learns the degree polynomial necessary to accurately represent the most probable transition path. Subsequently, we apply our method to the isomerization of alanine dipeptide, and demonstrate that the reaction coordinate obtained from the Bézier curve string method is in excellent agreement with the optimal reaction coordinate constructed from an aimless shooting and maximum likelihood procedure. Finally, we apply our method to a large complex system and study the homogenous nucleation of benzene from the melt. In these two examples, we illustrate that the ranking vector correctly identifies which collective variables govern these chemical transitions.
我们提出了一种新的字符串方法，用于在复杂化学系统中寻找最可能的过渡路径和最优反应坐标。我们的方法将一种称为贝塞尔曲线的解析参数曲线演化到构型空间中亚稳区域之间的最可能过渡路径。此外，我们证明了贝塞尔曲线的几何性质可用于在最可能反应路径附近构建最优反应坐标，并可进一步用于设计一个排序向量，该向量能够精确识别哪些集体变量对于控制亚稳状态之间的过渡最为重要。我们讨论了贝塞尔曲线字符串方法的算法细节，分析了其稳定性、准确性和效率，并使用模型势能函数说明了其能力。特别是，我们利用贝塞尔曲线的升阶性质开发了一种算法，该算法能自适应地学习准确表示最可能过渡路径所需的多项式次数。随后，我们将我们的方法应用于丙氨酸二肽的异构化，并证明从贝塞尔曲线字符串方法获得的反应坐标与通过无目标射击和最大似然程序构建的最优反应坐标非常吻合。最后，我们将我们的方法应用于一个大型复杂系统，并研究了苯从熔体中的均匀成核。在这两个例子中，我们说明了排序向量正确地识别了哪些集体变量控制了这些化学转变。
