Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
J Chem Phys. 2012 Mar 28;136(12):124104. doi: 10.1063/1.3692803.
The dynamics of complex systems often involve thermally activated barrier crossing events that allow these systems to move from one basin of attraction on the high dimensional energy surface to another. Such events are ubiquitous, but challenging to simulate using conventional simulation tools, such as molecular dynamics. Recently, E and Zhou [Nonlinearity 24(6), 1831 (2011)] proposed a set of dynamic equations, the gentlest ascent dynamics (GAD), to describe the escape of a system from a basin of attraction and proved that solutions of GAD converge to index-1 saddle points of the underlying energy. In this paper, we extend GAD to enable finite temperature simulations in which the system hops between different saddle points on the energy surface. An effective strategy to use GAD to sample an ensemble of low barrier saddle points located in the vicinity of a locally stable configuration on the high dimensional energy surface is proposed. The utility of the method is demonstrated by studying the low barrier saddle points associated with point defect activity on a surface. This is done for two representative systems, namely, (a) a surface vacancy and ad-atom pair and (b) a heptamer island on the (111) surface of copper.
复杂系统的动力学通常涉及热激活势垒穿越事件，这些事件使系统能够从高维能量表面上的一个吸引域转移到另一个吸引域。这些事件无处不在，但使用传统的模拟工具（如分子动力学）来模拟它们具有挑战性。最近，E 和 Zhou [Nonlinearity 24(6), 1831 (2011)] 提出了一组动态方程，即最平缓上升动力学（GAD），用于描述系统从吸引域的逃逸，并证明 GAD 的解收敛于基础能量的指数为 1 的鞍点。在本文中，我们将 GAD 扩展到能够在有限温度下进行模拟，在这种模拟中，系统在能量表面上的不同鞍点之间跳跃。提出了一种使用 GAD 来采样位于高维能量表面上局部稳定构型附近的低势垒鞍点的有效策略。该方法的实用性通过研究与表面上点缺陷活性相关的低势垒鞍点来证明。对于两个代表性系统，即 (a) 表面空位和 adatoms 对以及 (b) 铜的 (111) 表面上的七聚体岛，都进行了这样的研究。
