Chen L Y, Horing N J M
Department of Physics, University of Texas at San Antonio, San Antonio, Texas 78249-0697, USA.
J Chem Phys. 2006 Apr 28;124(16):164102. doi: 10.1063/1.2188943.
When a minimum on the potential energy surface is surrounded by multiple saddle points with similar energy barriers, the transition pathways with greater prefactors are more important than those that have similar energy barriers but smaller prefactors. In this paper, we present a theoretical formulation for the prefactors, computing the probabilities for transition paths from a minimum to its surrounding saddle points. We apply this formulation to a system of 2 degrees of freedom and a system of 14 degrees of freedom. The first is Brownian motion in a two-dimensional potential whose global anharmonicities play a dominant role in determining the transition rates. The second is a Lennard-Jones (LJ) cluster of seven particles in two dimensions. Low lying transition states of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics nor of the product states they lead to. The probabilities are computed for paths going from an equilibrium ensemble of states near a given minimum to the surrounding transition states. These probabilities are directly related to the prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from transition states, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.
当势能面上的一个最小值被多个具有相似能垒的鞍点包围时，具有较大前因子的跃迁路径比那些具有相似能垒但前因子较小的跃迁路径更为重要。在本文中，我们给出了前因子的理论公式，计算从一个最小值到其周围鞍点的跃迁路径概率。我们将此公式应用于一个二维自由度系统和一个十四维自由度系统。第一个系统是二维势场中的布朗运动，其整体非谐性在确定跃迁速率中起主导作用。第二个系统是二维空间中由七个粒子组成的 Lennard-Jones（LJ）团簇。确定了 LJ 团簇的低能跃迁态，它们可以直接从一个最小值到达而无需经过另一个最小值，且无需对其特征或它们所导致的产物态做任何假设。计算了从给定最小值附近的平衡态系综到周围跃迁态的路径概率。这些概率与速率公式中的前因子直接相关。这种速率前因子的确定包含了所有非谐性，无论其与跃迁态是近还是远，这在 LJ 团簇非常复杂的能量景观以及许多其他复杂系统中都是相关的。
