The importance of strict adherence to proper symmetry and careful examination of various Jahn-Teller isomers was demonstrated on geometrically optimized models of Cu(acac)(2)(3NOPy)(2) and Cu(acac)(2)(4NOPy)(2) complexes. It was shown that qualitatively the results are basis-set-independent. Spin density distribution and natural orbital analysis allowed rationalization of the stable spin states of the complexes. Based on comparison between the characteristics of the free radical-ligand and the complex with Cu(acac)(2), a protocol for molecular design of Cu(II) spin-hybrid systems with desired magnetic properties is suggested.