Exploration of coarse free energy surfaces templated on continuum numerical methods

Abstract

The characterization of a process in physics or chemistry through a set of collective variables (distances between atoms, orientational order parameters, dihedral angles) can be of great help in understanding the reaction mechanism. In particolar, a key role is played by the free energy surface as a function of these collective variables (“coarse” free energy), and the development of efficient methods of exploration of this surface in order to find minima and saddle points is an important issue. To this end, for example, the ideas of metadynamics were recently proposed [LP02, ILP03]. In this paper we propose a method for exploring the coarse free energy surface limiting the necessary calculations as much as possible, without explicitely resorting to a coarse non-Markovian metadynamics, and using the ideas of continuum numerical methods. We choose as a test case the free energy surface of the 38 atoms Lennard-Jones cluster, which presents an interesting double-funnel structure.