An efficient umbrella potential for the accurate calculation of free energies by molecular simulation

Umbrella sampling has been widely used to calculate free energies in many chemical and biological applications because it can effectively bridge the systems of interest and sample in the united phase space that is essential to yield accurate results. Many algorithms have implemented the idea of umbrella sampling that greatly improves the calculation of free energies. An efficient umbrella potential not only can connect the systems of interest, but also can lower the energetic barriers and facilitate the sampling over the relevant phase spaces. Here we present such an umbrella potential that is built on the equations of the weighted histogram analysis method. The proposed umbrella potential can facilitate the sampling of the important phase spaces of the systems of interest, which ensures the accurate calculation of free energies. We test this umbrella potential using a harmonic-model system, a water system, and a Lennard-Jones system. We demonstrate that this umbrella potential is effective in the circumstances when the systems of interest do not exhibit overlap in their phase spaces.