Decoding the energy landscape: extracting structure, dynamics and thermodynamics

Abstract

Describing a potential energy surface in terms of local minima and the transition states that connect them provides a conceptual and computational framework for understanding and predicting observable properties. Visualizing the potential energy landscape using disconnectivity graphs supplies a graphical connection between different structure-seeking systems, which can relax efficiently to a particular morphology. Landscapes involving competing morphologies support multiple potential energy funnels, which may exhibit characteristic heat capacity features and relaxation time scales. These connections between the organization of the potential energy landscape and structure, dynamics and thermodynamics are common to all the examples presented, ranging from atomic and molecular clusters to biomolecules and soft and condensed matter. Further connections between motifs in the energy landscape and the interparticle forces can be developed using symmetry considerations and results from catastrophe theory.

Crossing the dividing surface of transition state theory. I. Underlying symmetries and motion coordination in multidimensional systems

“…1,2 Potential wells are studied by vibrational spectroscopy, which is based on models whose validity is in principle limited to displacements of infinitesimal amplitude in a harmonic force field. These restrictions are unacceptable in the study of reaction dynamics, which focuses on another kind of stationary points, namely saddle points.…”

Potential energy landscapes for the 2D XY model: Minima, transition states, and pathways

“…These graphs reveal that the landscape is funnelled in each case, with a well-defined global minimum, and small downhill barriers connecting this structure to the higher-energy configurations. Hence all of these 2D XY landscapes belong to the class of systems identified as good 'structure seekers', which includes 'magic number' atomic and molecular clusters, naturally occurring proteins, and self-assembling mesoscopic systems, including crystals [2,4,42,45]. Minimization from random starting points confirms that the global minimum is readily located in each case; the funnelled organisation of the landscape is reinforced by the existence of relatively large basins of attraction for the global minima compared to the higher energy minima, and this effect grows with increasing lattice size.…”

“…Locating low-lying minima for these 2D XY models should therefore be relatively straightforward: relaxation following the intrinsic dynamics of the system should lead to the global minimum for temperatures of physical interest. This is the pattern that we associate with good structure-seeking systems [2,4,42,45], including 'magic number' clusters such as buckminsterfullerene, self-assembling mesoscopic structures such as virus capsids, crystallisation, and proteins that fold into functional native states on in vivo time scales.…”

“…An extensive framework of conceptual and computational tools has been developed corresponding to the potential energy landscape approach [1][2][3][4][5], with applications to many-body systems as diverse as metallic clusters, biomolecules, structural glass formers, and coarse-grained models of soft and condensed matter. In all these examples, stationary points of a high-dimensional potential energy function are considered.…”

Beyond crystals: the dialectic of materials and information

“…One general concept that is proving useful to understand the basis for the particular structure of a crystal is that of an energy or structural landscape [34]. The potential energy function has local minima separated by energy barriers, and predictions can be made from knowledge of its stationary points, their topology and connectivity.…”