The structures and the binding free energies between the protonated amino acids, glycine and alanine, with one, two, and three water molecules were extensively studied by ab initio molecular orbital and density functional theory calculations, at the HF/6-31G(d), B3LYP/6-311++G(d,p), and MP2/6-311++G(d,p) levels, respectively. Higher level calculations such as CCSD(T) and newly developed DFT methods with BSSE corrections were also explored in the evaluation of these non-covalent interactions. All the optimized conformers were confirmed as local minimum structures from frequency calculations. The computed binding enthalpies, entropies and free energies were compared to the latest experimental values from electrospray ionization high pressure mass spectrometry obtained by the scientists of the National Institutes of Health.