Chapter 18 - Energy Landscapes

Abstract

The thermodynamics and kinetics of condensed matter can be described in terms of its underlying energy landscape. Under constant volume conditions, the potential energy landscape maps the potential energy as a function of all 3N position coordinates of an N-atom system. Under constant pressure conditions, a (3N + 1)-dimensional enthalpy landscape can be used to capture changes in volume. The energy landscape of a system contains an exponentially large number of minima, known as inherent structures. Inherent structures are locally stable configurations of atoms. The collection of all points in the landscape that drain to a particular minimum is known as a basin. While the energy landscape itself does not change with temperature, the way in which a system samples the landscape depends on the available thermal energy. The primary assumption of the energy landscape approach is that the kinetics of the system can be separated into fast vibrations within a basin and less frequent inter-basin transitions. The inter-basin transitions are accomplished by overcoming a transition barrier, where the difference between the transition point energy and the inherent structure energy defines the activation barrier for the inter-basin transition. Application of the energy landscape approach involves mapping the continuous energy landscape to a discrete set of basins and the connecting transition points. The transitions points can be found using a variety of different approaches, including eigenvector-following with a Lagrange function, the activation-relaxation technique, and the nudged elastic band method. ExplorerPy is an open source software package for performing this mapping of any arbitrary potential energy landscape or enthalpy landscape.