Alchemical Response Parameters from an Analytical Model of Molecular Binding

We present a parameterized analytical model of alchemical molecular binding. The model describes accurately the free energy profiles of linear single-decoupling alchemical binding free energy calculations. The parameters of the model, which are physically motivated, are obtained by fitting model predictions to numerical simulations. The validity of the model has been assessed on a set of host-guest complexes. The model faithfully reproduces both the binding free energy profiles and the probability densities of the perturbation energy as a function of the alchemical progress parameter $\lambda$. The model offers a rationalization for the characteristic shape of the free energy profiles. The parameters obtained from the model are potentially useful descriptors of the association equilibrium of molecular complexes.