The MP2 intermolecular interaction energies of the title complexes were calculated with the Dunning’s correlation consistent basis sets (cc-pVXZ, X=D, T, Q, and 5) and the interaction energies at the basis set limit were estimated. The second-order Mo/ller–Plesset (MP2) interaction energies greatly depend on the basis sets used, while the Hartree–Fock (HF) energies do not. Small basis sets considerably underestimate the attractive interaction. The coupled cluster single double triple [CCSD(T)] interaction energies are close to the MP2 ones. The expected CCSD(T) interaction energies of the H2O–MeOH, H2O–Me2O, H2O–H2CO, MeOH–MeOH, and HCOOH–HCOOH complexes at the basis set limit are −4.90, −5.51, −5.17, −5.45, and −13.93 kcal/mol, respectively, while the HF/cc-pV5Z energies are −3.15, −2.58, −3.60, −2.69, and −11.29 kcal/mol, respectively. The HF calculations greatly underestimate the attractive energies and fail to predict the order of the bonding energies in these complexes. These results show that a large basis set and the consideration of an appropriate electron correlation correction are essential to study interactions of hydrogen bonding complexes by ab initio molecular orbital calculation.