Accurate sampling using Langevin dynamics

We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J. Chem. Phys. 126, 014101 (2007)]. Our integrator leads to correct sampling also in the difficult high-friction limit. We also show how these ideas can be applied in practical simulations, using a Lennard-Jones crystal as a paradigmatic case.