We report free energy perturbation (FEP) molecular dynamics (MD) simulations of the relative binding free energies of three spherands and alkali metal ions (Li+, Na+, K+). The calculated free energies all favor Na+ binding and are in reasonable agreement with experiment for two of the hosts but not the third. The third host, a mixed anisole-phenanthroline-spherand, was calculated to be significantly selective for binding Na+ over K+ and Li+, whereas experiments suggest little or no selectivity between K+, Na+, and Li+. Our attempts to improve the calculations by using different charge fitting schemes and by simulating the experimental conditions (addition of picrate(-) anion, simulations in chloroform) did not resolve the discrepancy. The fact that our simulations work in two cases but not the third (the third spherand contains subunits present in the two other spherands) suggests that there may be significant differences in the nature of the host-guest complexes in the third case.