title: Graph-based analysis of kinetics on multidimensional potential-energy surfaces.
abstract: The aim of this paper is twofold: one is to give a detailed description of an alternative graph-based analysis method, which we call saddle connectivity graph, for analyzing the global topography and the dynamical properties of many-dimensional potential-energy landscapes and the other is to give examples of applications of this method in the analysis of the kinetics of realistic systems. A Dijkstra-type shortest path algorithm is proposed to extract dynamically dominant transition pathways by kinetically defining transition costs. The applicability of this approach is first confirmed by an illustrative example of a low-dimensional random potential. We then show that a coarse-graining procedure tailored for saddle connectivity graphs can be used to obtain the kinetic properties of 13- and 38-atom Lennard-Jones clusters. The coarse-graining method not only reduces the complexity of the graphs, but also, with iterative use, reveals a self-similar hierarchical structure in these clusters. We also propose that the self-similarity is common to many-atom Lennard-Jones clusters.
authors.affiliation: Department of Physics, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu 525-8577, Japan. okushima@ike-dyn.ritsumei.ac.jp
authors.forename: T
authors.initials: T
authors.lastname: Okushima
authors.forename: T
authors.initials: T
authors.lastname: Niiyama
authors.forename: K S
authors.initials: KS
authors.lastname: Ikeda
authors.forename: Y
authors.initials: Y
authors.lastname: Shimizu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D007700:Kinetics; D008962:Models, Theoretical