Evidence for the encagement of atomic ions by water clusters in the gas phase has been reported previously on the basis of observation of especially stable magic-number clusters of the form M(+)(H2O)(n) for M(+) = Cs+ and K+, with n = 20. Using the same variable-temperature flow reactor experimental technique, the work is extended to the clustering of water to Li+, Rb+, and Na+. The experimental findings presented in the current paper show that all of the alkali metal cations except for sodium display a tendency to form distinct and reproducible magic number species at n = 20. Surprisingly, there is no indication in the experiments that the Na+(H2O)(20) cluster is magic. We also present herein the results of molecular dynamics calculations, which suggest that a pentagonal dodecahedral network of water molecules surrounding a central ion is a possible stable structure for M(+)(H2O)(20). In addition, we present results of free energy calculations which (1) corroborate the experimental observation that K+(H2O)(20) is a magic-number cluster and (2) suggest that, despite the fact that it is not an especially prominent species in the mass spectra, Na+(H2O)(20) is also a magic cluster in terms of its stability relative to clusters of proximate size.