Simple and effective application of the Wang-Landau method for multicanonical molecular dynamics simulation.

We propose a novel application of the Wang-Landau method (WLM) for multicanonical molecular dynamics (McMD) simulations. Originally, WLM was developed for Monte Carlo (MC) simulations. Fundamentally, WLM remarkably reduces simulation efforts because it estimates the optimal multicanonical energy function automatically. When WLM is applied to McMD, not only the multicanonical energy but also energy gradient must be estimated adequately. However, because of the rugged multicanonical energy function at the early simulation stage, applications of WLM for MD simulations are difficult and require a smoothing procedure: simulation efforts such as cubic-spline extrapolation and gathering multiple preruns are utilized for smoothing. We propose a simple and effective smoothing method that requires only one additional equation and two time-dependent parameters. As a result, our method produced the correct multicanonical energy function and succeeded in the flat sampling of a small biomolecule with reduced simulation effort.