Model Energy Landscapes

Pablo G. Debenedetti
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA and Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

Frank H. Stillinger
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

M.S. Shell
Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA

Received: July 18, 2003, in Final Form: October 10, 2003

Abstract: The multidimensional potential-energy "landscape" formalism offers useful insights into the properties of supercooled liquids and glasses. However, its mathematical fundamentals present formidable subtlety and complexity. In the interests of developing a useful approximation for the statistical mechanics of landscapes, we have developed a simple family of models describing the energy-depth distribution of landscape basins. Our analysis begins with the "Gaussian" model that has been advocated in the recent literature, a physically appealing and thermodynamically rather accurate description that straightforwardly predicts a positive-temperature ideal glass transition. Careful enumeration of low-lying basins reveals however that the Gaussian model requires modification in the form of a logarithmic correction. Consequently, we have carried out algebraic and numerical analyses of a logarithmically modified Gaussian model, including depth dependence of the mean intrabasin vibrational free energy. The logarithmic modification has the effect of eliminating the positive-temperature ideal glass transition of the precursor pure-Gaussian model. Nevertheless, it is sufficiently similar to that unmodified model at and above any kinetic glass transition temperature to be able to represent measurable calorimetric data with reasonable accuracy.