Cuprophilic interactions in neutral perpendicular model dimers of the type (CH3CuX)2 (X = OH2, NH3, SH2, PH3, N2, CO, CS, CNH, CNLi) were analyzed by ab initio quantumchemical methods. The basis set superposition error for the weakly interacting CH3CuX subunits is significant and is discussed in detail. A new correlation-consistent pseudopotential valence basis set for Cu. derived at the second-order Møller-Plesset level suppresses considerably the basis set superposition error in Cu-Cu interactions compared to the standard Hartree-Fock optimized valence basis set. This allowed the first accurate predictions of cuprophilicity, which has been the subject of considerable debate in the past. The dependence of the strength of cuprophilic interactions on the nature of the ligand X was addressed. The Cu-Cu interaction increases with increasing sigma-donor and pi-acceptor capability of the ligand and is approximately one-third of the well-documented aurophilic interactions. By fitting our potential-energy data to the Hershbach-Laurie equation, we determined a relation between the Cu-Cu bond length and the Cu-Cu force constant; this is important for future studies on vibrational behaviour. The role of relativistic effects on the structure and the interaction energy is also discussed. Finally we investigated cuprophilic interactions in (CH3Cu)4 as a model species for compounds isolated and characterized by X-ray diffraction.