To perfect a method for building a theoretical hydrogen-bond basicity scale, the enthalpy of hydrogen bonding between methanol and thirteen neutral and anionic bases (MeOH, MeNH2, Me2NH, Et2NH, Me3N, Et3N, Br-, CN-, SH-, Cl-, HCOO-, MeO-, F-) was calculated by DFT and ab initio methods. The theoretical results were compared to selected experimental ones. It appears that B3LYP/6-31+G(d,p) calculations are satisfactory for optimizing the geometry of complexes and giving a general order of basicity. However, they are deficient for reproducing the large effect of alkyl groups on the hydrogen-bond basicity of amines. This deficiency is explained by intermolecular perturbation theory calculations, which show that the alkylation of nitrogen dramatically increases the dispersion energy component not taken into account by the B3LYP functional. Of the methods considered, only MP2/aug-cc-pVTZ calculations are capable of reproducing the binding enthalpy within the experimental error for the first-row acceptor atoms N, O, and F, and of accounting for dispersion effects created by alkylation at the hydrogen-bond acceptor site.