As part of an extended fundamental study on the interaction of molecular hydrogen with the surfaces of potential storage materials, this work describes the interaction of dihydrogen with bare alkaline cations (Li+, Na+, K+, Rb+) by means of ab initio and density functional calculations. The effects of method and basis set are evaluated, and an estimate of the electrostatic contributions to the binding energy is evaluated. All methods predict a t-shaped coordination geometry, in accord with the quadrupolar nature of the molecule. The binding energies at the MP2/aug-cc-pVQZ (MP2-Møller-Plesset method truncated at second order) level ranges between 24 kJmol for Li+ and 5 kJmol for Rb+. Basis set size has minor effect on the binding energy of the complexes, although the poorer sets have severe limitations in the description of the electrostatics of the isolated molecule. The electrostatic contribution to the binding energy calculated from the electrostatic properties of the isolated molecule are in fact strongly basis set dependent. Their careful analysis shows that the predominant terms of the interaction are those due to the quadrupole and dipole-polarizability terms. The vibrational spectra of the adducts are evaluated and compared with a large set of experimental and theoretical results from the literature. This review highlights a linear correlation between the frequency shift and the binding energy, which is valuable in the understanding of adsorption phenomena by means of spectroscopic methods.