MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules

Many of the most common molecular simulation methods, including Monte Carlo (MC) and molecular or stochastic dynamics (MD or SD), have significant difficulties in sampling the space of molecular potential energy surfaces characterized by multiple conformational minima and significant energy barriers. In such cases improved sampling can be obtained by special techniques that lower such barriers or somehow direct search steps toward different low energy regions of space. We recently described a hybrid MC/SD algorithm [MC(JBW)/SD] incorporating such a technique that directed MC moves of selected torsion and bond angles toward known low energy regions of conformational space. Exploration of other degrees of freedom was left to the SD part of the hybrid algorithm. In the work described here, we develop a related but simpler simulation algorithm that uses only MC to sample all degrees of freedom (e.g., stretch, bend, and torsion). We term this algorithm MC(JBW). Using simulations on various model potential energy surfaces and on simple molecular systems (n-pentane, n-butane, and cyclohexane), MC(JBW) is shown to generate ensembles of states that are indistinguishable from the canonical ensembles generated by classical Metropolis MC in the limit of very long simulations. We further demonstrate the utility of MC(JBW) by evaluating the room temperature free energy differences between conformers of various substituted cyclohexanes and the larger ring hydrocarbons cycloheptane, cyclooctane, cyclononane, and cyclodecane. The results compare favorably with available experimental data and results from previously reported MC(JBW)/SD conformational free energy calculations.