Puddle-skimming: An efficient sampling of multidimensional configuration space

We examine the effectiveness of a simple method for surmounting energy barriers and enhancing the exploration of configuration space in Monte Carlo (MC) and molecular dynamics (MD) simulations. Proposed previously for treating surface diffusion M. M. Steiner, P.-A. Genilloud, and J. W. Wilkins, Phys. Rev. B 57, 10236 (1998), the method has widespread applicability and is particularly advantageous for systems with potential energy landscapes whose features are not known a priori. The algorithm requires selection of a single parameter, a “boost energy” EB. The MC or MD simulation is carried out on an effective potential energy function that is equal to the true potential energy when it is greater than EB, but is equal to EB otherwise. Since the effective potential energy is, therefore, never less than EB, deep energy minima are removed analogous to a rough landscape that has been flooded with water. The bias introduced by altering the potential energy function in this way is easily and rigorously removed “on-the-fly.” We test the method with a MD simulation of the equilibrium populations of conformations of n-pentane. The method recovers the canonical equilibrium distribution with dramatically increased sampling efficiency and modest additional computational overhead, over a range of temperatures. In cases for which the potential energy function can be written as a sum of terms, the energy boost can be applied to the selected terms rather than to the entire potential energy function. We illustrate this by application to the dihedral angle term only of the empirical n-pentane potential energy function and show that this further enhances sampling efficiency. The simple nature of this algorithm allows it to be readily scaled to high-dimensional systems. We discuss the prognosis for applying this method to more complex systems such as liquids and macromolecules.