Reconstructing the Density of States by History-Dependent Metadynamics

Abstract

We present a novel method for the calculation of the energy density of states $D(E)$ for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain $D(E)$ more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size $50\times 50$) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.