Equilibrium exchange enhances the convergence rate of umbrella sampling

Umbrella sampling, a technique for sampling energetically unfavorable states by computer simulation, is subject to systematic sampling errors arising from quasi-nonergodicity. In order to address this problem, we compare free energy profiles generated along the backbone dihedral angles φ and ψ of alanine dipeptide in water using umbrella sampling successively with and without the provision of equilibrium exchange between umbrellas. The results show that the addition of equilibrium exchange to umbrella sampling alleviates these errors by restoring the utilization of transition paths that leave and reenter the specified sampling region.