A method to calculate the probability distribution for systems with large energy barriers

Abstract

A new way to calculate free energy differences in a molecular system is presented. The fundamental idea involves using a modified Monte Carlo procedure to automatically generate an umbrella sampling potential. This potential will have the property of making all conformations of the molecule equally probable at convergence. Thus the final umbrella potential will be equal to the negative value of the potential of mean force. Two examples will be given. In the first example, simulations of 1,2-dimethoxyethane have been performed in gas phase with the new method and the standard Metropolis algorithm. In the second approach we have applied the proposed scheme to study the effective interaction between two hard walls mediated by hard spheres. The newly developed technique has been compared with a standard Metropolis algorithm and with a direct integration of the force exerted on the walls. Comparison between the three techniques reveals that the new method converges much faster to a correct potential of mean force than standard techniques, provided that the studied barriers are much higher than kT.