Relaxation Augmented Free Energy Perturbation

We re-examine the concept of free energy calculation via a single-step free energy perturbation (sFEP) method, which frequently fails to converge due to the problem of insufficient sampling. We find a close resemblance between the operation in sFEP and the vertical transition between two different electronic states in quantum mechanics. The insufficent sampling problem then has a vivid physical interpretation as lacking the relaxation process after perturbation. Upon augmenting the traditional sFEP with the relaxation process, the new method agrees well with the exact solution, shedding new light on the underlying physics in free energy calculations.