Relaxation Augmented Free Energy Perturbation

We re-examine the concept of free energy calculation using the single-step free energy perturbation (sFEP) method, often referred to as the Zwanzig equation, which frequently fails to converge due to the problem of insufficient sampling. We find a close resemblance between the operation in sFEP and the Franck-Condon principle in quantum mechanics. The insufficient sampling problem then has a vivid physical interpretation as lacking the subsequent relaxation process after the perturbation. Upon augmenting the traditional sFEP with the relaxation process, the new method gives calculated free energies which agree well with the exact solution for two model systems, shedding new light on the underlying physics in non-equilibrium free energy calculations.