Exploring high-dimensional energy landscapes

Maps are not reserved for geography. Chemical reactions, atomic diffusion and protein folding all involve atomic displacements determined by the topography of a complex energy landscape. These landscapes are largely unexplored, and our first priority is to identify their key features: the energy minima and the connecting paths between them. Such a study represents a formidable task. The effort needed to map a space increases exponentially with its dimensionality and becomes rapidly out of reach for the high-dimensional problems of interest in physics, chemistry and biology. Therefore, we have to satisfy ourselves with only a very crude knowledge of these energy landscapes. Recently, many researchers have been developing algorithms for exploring and mapping the potential energy landscapes of systems as diverse as polypeptides, chemical reactions, Lennard-Jones clusters and silica glass. In this article, we address some of the general issues and present an algorithm, called the activation-relaxation technique (ART), which we developed for mapping high-dimensional landscapes.