Determination of free energy profiles by repository based adaptive umbrella sampling: bridging nonequilibrium and quasiequilibrium simulations.

We propose a new adaptive sampling approach to determine free energy profiles with molecular dynamics simulations, which is called as "repository based adaptive umbrella sampling" (RBAUS). Its main idea is that a sampling repository is continuously updated based on the latest simulation data, and the accumulated knowledge and sampling history are then employed to determine whether and how to update the biasing umbrella potential for subsequent simulations. In comparison with other adaptive methods, a unique and attractive feature of the RBAUS approach is that the frequency for updating the biasing potential depends on the sampling history and is adaptively determined on the fly, which makes it possible to smoothly bridge nonequilibrium and quasiequilibrium simulations. The RBAUS method is first tested by simulations on two simple systems: a double well model system with a variety of barriers and the dissociation of a NaCl molecule in water. Its efficiency and applicability are further illustrated in ab initio quantum mechanics/molecular mechanics molecular dynamics simulations of a methyl-transfer reaction in aqueous solution.