School of Chemical Engineering, National Technical University of Athens, Zografou Campus, GR-15780 Athens, Greece.
J Chem Phys. 2013 Mar 28;138(12):12A545. doi: 10.1063/1.4792363.
An alternative graphical representation of the potential energy landscape (PEL) has been developed and applied to a binary Lennard-Jones glassy system, providing insight into the unique topology of the system's potential energy hypersurface. With the help of this representation one is able to monitor the different explored basins of the PEL, as well as how--and mainly when--subsets of basins communicate with each other via transitions in such a way that details of the prior temporal history have been erased, i.e., local equilibration between the basins in each subset has been achieved. In this way, apart from detailed information about the structure of the PEL, the system's temporal evolution on the PEL is described. In order to gather all necessary information about the identities of two or more basins that are connected with each other, we consider two different approaches. The first one is based on consideration of the time needed for two basins to mutually equilibrate their populations according to the transition rate between them, in the absence of any effect induced by the rest of the landscape. The second approach is based on an analytical solution of the master equation that explicitly takes into account the entire explored landscape. It is shown that both approaches lead to the same result concerning the topology of the PEL and dynamical evolution on it. Moreover, a "temporal disconnectivity graph" is introduced to represent a lumped system stemming from the initial one. The lumped system is obtained via a specially designed algorithm [N. Lempesis, D. G. Tsalikis, G. C. Boulougouris, and D. N. Theodorou, J. Chem. Phys. 135, 204507 (2011)]. The temporal disconnectivity graph provides useful information about both the lumped and the initial systems, including the definition of "metabasins" as collections of basins that communicate with each other via transitions that are fast relative to the observation time. Finally, the two examined approaches are compared to an "on the fly" molecular dynamics-based algorithm [D. G. Tsalikis, N. Lempesis, G. C. Boulougouris, and D. N. Theodorou, J. Chem. Theory Comput. 6, 1307 (2010)].
已经开发并应用了一种替代的势能景观（PEL）的图形表示方法，用于研究二元 Lennard-Jones 玻璃系统，提供了对系统势能超曲面独特拓扑结构的深入了解。通过这种表示方法，人们可以监测 PEL 中不同的探索盆地，以及如何——主要是何时——通过过渡使盆地子集相互通信，从而消除了先前时间历史的细节，即在每个子集中的盆地之间实现了局部平衡。通过这种方式，除了有关 PEL 结构的详细信息外，还描述了系统在 PEL 上的时间演化。为了收集有关通过过渡与彼此相连的两个或更多盆地的身份的所有必要信息，我们考虑了两种不同的方法。第一种方法基于考虑根据它们之间的跃迁率使两个盆地相互平衡其种群所需的时间，而不考虑景观其余部分引起的任何影响。第二种方法基于明确考虑整个探索景观的主方程的解析解。结果表明，这两种方法在 PEL 的拓扑和动态演化方面都得到了相同的结果。此外，引入了一个“时间不连通图”来表示源自初始系统的集中系统。集中系统是通过专门设计的算法[N. Lempesis、D. G. Tsalikis、G. C. Boulougouris 和 D. N. Theodorou，J. Chem. Phys. 135, 204507（2011）]获得的。时间不连通图提供了有关集中系统和初始系统的有用信息，包括定义“元盆地”作为通过相对于观察时间较快的跃迁相互通信的盆地集合。最后，将这两种方法与基于“实时”分子动力学的算法[D. G. Tsalikis、N. Lempesis、G. C. Boulougouris 和 D. N. Theodorou，J. Chem. Theory Comput. 6, 1307（2010）]进行了比较。
