Theoretical Approaches to Direct Exchange Couplings between Divalent Chromium Ions in Naked Dimers, Tetramers, and Clusters

Direct exchange interactions between divalent chromium ions in naked dimers, tetramers, and clusters were investigated theoretically. The orbital energy gaps, occupation numbers, and bond orders for the naked Cr(II)−Cr(II) dimer (1) were calculated by ab initio UHF MO and density functional (DFT) methods. All these calculations indicated that the orbital energy gaps are very small for 1, and therefore the occupation numbers of the bonding σ, π, and δ molecular orbitals and formal quadruple bond orders were largely reduced because of strong electron correlation effects. The UHF and DFT MO calculations were also performed for the linear naked Cr(II) tetramer to elucidate possible electronic structures of the d−d conjugated systems. The energy differences among singlet, triplet, and quintet states for 1 were calculated from the total energies obtained by the CASCI and CASSCF methods based on the UHF and DFT natural orbitals (UNO). The reliability of the Heisenberg model Hamiltonian was elucidated from variations of these calculated effective exchange integrals with the interatomic distance. The calculated Jab values are compared with the experimental results for several binuclear Cr(II) complexes with different interatomic distances. The Heisenberg spin Hamiltonian was used to discuss the spin alignments in large d−d conjugated Cr(II) clusters and a possibility of the macroscopic quantum spin tunneling in mesoscopic magnetic systems.