The ground state structure, harmonic frequency, and dissociation energy for Ca . RG, Ca+. RG, and Ca2+. RG (RG=Ar and Ne) complexes are computed at four theoretical levels [HF, B3LYP, MP2, and MP2(full)] using three different basis sets. The most rigorous method employed was Moller-Plesset second order perturbation with valence plus core electron correlation using 183 basis functions for the calcium-neon complexes and 187 basis functions for the calcium-argon complexes. Correcting the dissociation energies, bond distances, and frequencies for basis set superposition error (BSSE) were done at the most rigorous level of theory by fitting the Morse function to the potential energy curves generated by the counterpoise procedure. At this level of theory, proceeding from the neutral to the doubly charged complexes, the calcium-neon bond distances range from 5.40 to 2.45 Angstrom with dissociation energies (De) from 0.03 to 5.86 kcal/mol. Likewise, the calcium-argon bond distances range from 5.00 to 2.70 Angstrom with dissociation energies from 0.23 to 16.80 kcal/mol as the metal charge increases. Good theoretical agreement is obtained with experimental data when available, while the remaining results can aid in the interpretation of future experiments. In all comparable cases where the calcium-rare gas complexes possess equivalent charge, the argon atom is bound tighter to the metal than the neon atom due to its larger atomic polarizability. An examination of the relationship between dispersion and charge-induced dipole forces is done using these calcium-rare gas complexes.