High-level ab initio calculations have been carried out to evaluate the lifetimes of complexes formed by the association of Cu2+ to water, ammonia, and hydrogen cyanide. The corresponding binding energies were evaluated at the CCSD(T)6-311+G(3df,2pd) level of theory. The potential-energy curves corresponding to their dissociation into Cu+ + L+ (L=H2O, NH3, and HCN) were obtained at the CCSD(T)6-311+G(3df,2p) level on BHLYP6-311+G(d,p) optimized geometries. Lifetimes were calculated using the exterior complex scaling and the semiclassical WKB methods. Although all the complexes investigated are thermodynamically unstable with respect to their dissociation into Cu+ + L+ in a typical Coulomb explosion, the activation barrier is high enough to accommodate several vibrational resonances, with very large lifetimes. As a matter of fact, if the three complexes are produced in the lowest vibrational levels, they behave as totally bound (with almost infinite lifetime) species.