We report results of calculations of the difference between the Gibbs free energies of association of the p-sulfonatocalix[4]arene with the tetramethylammonium and methylammonium cations in acidic aqueous solution. Good agreement is observed between the free energy difference predicted using our perturbation algorithm and the experimental value. We show the relative importance of the potential of mean force (pmf) bond correction and of the van der Waals and electrostatic contributions to the total change in the Gibbs free energy of complexation. We also provide a microscopic interpretation of these contributions to the total Gibbs free energy during the mutation process. In addition, we examine the hydration of the guest and the host as a function of the nature of the perturbation.