Geometry-optimized structures, energies, and harmonic vibrational frequencies of closed-shell states of CuL+, (XCuL)-L-I, and (XCuL)-L-III fragments (L = CO, C2H4, C2H2; X = H-, F-, OH-, O2-, N3-) have been obtained at the MP2 level using valence-DZP-quality basis sets with effective core potentials. Natural population analyses have been used to interpret the nature of metal-ligand interactions. The computed data for all the Cu(I) species are along expected lines. interestingly, the formally high-oxidation-state species also have effectively d(10) configurations, with the electron deficiency localized in the ligands. As a result, the Cu-X bonds are long and, in a few cases, the ligand L dissociates during geometry optimization. In the computed minima, the Cu-L interaction energies are fairly large, primarily due to electrostatic interactions. The extent of pi-back-donation is generally low in "Cu(III)" systems. However, a strong pi-donor group enhances the ability of the metal to engage in d pi-p pi bonding with CO, C2M4, or C2H2, making it comparable to a typical (CuL)-L-I system in all respects. The trends are virtually identical in all three lowest energy closed-shell states of the ethylene and acetylene complexes.