Approximating Free Energy Surfaces

Abstract

This paper discusses the reformulation of an old problem in new terms. While configurational transitions have been traditionally explored using the concept of potential energy, we now look to interpret these transitions in terms of free energy. The study of free energy, however, is much more complicated than the corresponding inspection of potential energy and creative techniques must be employed in the determination of the free energy function over a given variable. In this paper we present three algorithms we have developed to approximate the free energy function for a given system in one dimension. Each method is then applied to a well known test case to determine its relative ability. Finally, we examine the ability of one of our methods to determine the free energy function for the hydrogen bond distance in the biomolecule Alanine Dipeptide and discover some promising results.