Second-order Moller-Plesset (MP2) calculations (using the approximate resolution of the identity, RI-MP2), explicitly correlated MP2 (MP2-R12) calculations, and coupled-cluster calculations including all single and double excitations with a perturbative estimate of triple excitations [CCSD(T)] are performed to study the interaction of molecular hydrogen with the small molecules HF, H2O, NH3, and LiOH. Different adsorption positions are studied. In the cases of H2O and NH3, the most favorable configuration places H-2 in an end-on fashion on the O or N atom, respectively. In the cases of HF and LiOH, the H-2 molecule takes a side-on position on the H atom of HF or the Li atom. With respect to MP2 calculations in a triple-zeta basis, both the enlargement of the basis set and the extension of the correlation treatment (CCSD(T) vs MP2) increase the interaction energy. The basis set limit CCSD(T) estimates of the interaction energy of H-2 with the HF, H2O, NH3, and LiOH molecules amount to 4.40, 2.67, 3.02, and 10.74 kJ mol(-1), respectively. The interaction energy for the simultaneous interaction of H-2 with two LiOH molecules does not significantly exceed the value obtained for the interaction with a single LiOH molecule. Furthermore, the interaction energies (by MP2) of H-2 with glycine, the glycine dimer, and imidazolium chloride amount to 2.78, 5.00, and 6.30 kJ mol(-1), respectively.