Relative free energies of complexation of Na+, K+ and Rb+ cations by the 222 cryptand have been calculated in water and in methanol. This was achieved by "slow growth MD mutations" using the perturbation thermodynamic cycle. Starting with the experimental structure of the K+ subset-of 222 cryptate we calculate that, in gas phase and in solution, 222 prefers intrinsically Na+. In solution, taking into account the relative solvation free energies, we find a peak of binding selectivity for K+, in qualitative agreement with experiment. Calculated relative free energies of transfer from water to methanol of the free cations and of their cryptates compare also reasonably well with experiment. However, calculations starting from another cryptate type structure give rather different energies, which questions the predictive power of FEP calculations when restricted to small simulation times, and when the experimental structures are not available!