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Quantum mechanical ab initio calculations are reported for the Cu and Cu+ complexes with acetylene and ethylene and for the dicopper-substituted ethylenes C2H2Cu2 and di- and tetracopper-substituted ethanes C2H4Cu2 and C2H2Cu4. The geometries were optimized at the MP2 level of theory while the bond energies are predicted at CCSD(T) using relativistic effective core potentials with valence basis sets of TZ + P quality for copper. The calculated copper-acetylene and copper-ethylene complexes have C2v symmetry, which is in agreement with experimental evidence. The metal-ligand bond energies of the charged species Cu+ (C2H2) (De = 40.6 kcal mol−1) and Cu+(C2H4) (De = 43.9 kcal mol−1) are significantly higher than predicted in most previous studies. The neutral complexes Cu(C2H2) and Cu(C2H4) are much more weakly bonded. There are four energy minima with C2v symmetry on the C2H2Cu2 potential energy surface which have rather strong CuC bonds. The geminal isomer of dicopper-substituted ethylene is 2.8 kcal mol−1 lower in energy than the trans form and 6.4 kcal mol−1 more stable than the cis form. The global minimum structure is an end-on bonded Cu2 complex with acetylene, which is 5.9 kcal mol−1 lower in energy than 1,1-dicopperethylene. Strong CuC bonds are also predicted for the dicopper- and tetracopper-substituted ethanes. Two energy minima are found on the C2H4Cu2 potential energy surface. The anti form of C2H4Cu2 is 4.5 kcal mol−1 lower in energy than the gauche form. There are also two energy minima on the C2H2Cu4 potential energy surface. The gauche form of tetracopperethane is calculated as only 0.3 kcal mol−1 more stable than the anti form. It is suggested that the deformed structure 5d of C2H2Cu4 with two copper atoms bridging the carbon atoms may be used as a model for the interactions between acetylene adsorbed on a copper(III) surface. The nature of the CuC bonding was analysed using the NBO partitioning scheme and the topological analysis of the electronic charge distribution. The charged complexes Cu+(C2H2) and Cu+ (C2H4) have a T-shaped rather than a cyclic electronic structure. They are held together mainly by Coulombic interactions. The neutral complexes Cu(C2H2) and Cu(C2H4) show cyclic electronic structures. The weak CuC bonds of the neutral complexes Cu(C2H2) and Cu(C2H4) are caused by dispersion forces. The rather strong CuC bonds of the copper-substituted ethylenes and ethanes are strongly polarized towards the carbon end. Relativistic effects yield clearly shorter CuC and CuCu bonds.