We present calculations for the nonbonded interactions in the dimeric complexes: methane dimer, ammonia dimer, water dimer, H2O .(NH3), CH4.(NH3), and (FHF)(-) as a function of theory level (HF, DFT(B3LYP), MP2, LMP2, MP3, MP4, CCSD(T), and others) and basis set (6-31G**, cc-pVXZ, X = D, T, Q, 5). Dimer minimum energy structures are determined at the MP2 theory level for the cc-pVTZ basis set employing analytical second derivatives. For HF and DFT levels of theory, methane dimer and one structure of CH4.(NH3) are not bound. The basis set superposition error (BSSE) begins to converge (becomes systematically small) for basis sets larger than cc-pVTZ. For hydrogen-bonded systems, most levels of theory seem to give reasonable estimates of the experimentally known binding energies, but here, too, the BSSE overwhelms the reliability of the binding energies for the smaller basis sets. The CH4.(NH3) dimer has two minimum energy conformations with similar binding energies, but very different BSSE values especially for small basis sets (cc-pVXZ, X less than or equal to T). On the basis of these calculations, we present a discussion of ab initio calculations of nonbonded interactions for molecules, such as phenethylamine, that have different conformations. Suggestions for possible next steps in the calculation of nonbonded interactions are presented.