Theoretical study of the relationship between the nearest-neighbor exchange coupling interactions and the number of peripheral complexes in the cyano-bridged CrMn6(CN)6 and CrMn2(CN)2 clusters.

A theoretical density functional study of the relationship between the nearest-neighbor constants and the number of peripheral complexes in the cyano-bridged [Cr[CNMn(salen)(H2O)]6]3+ and [(5-Brsalen)2(H2O)2Mn2Cr(CN)6] clusters is presented. Two approaches show that the antiferromagnetic coupling interactions between nearest neighbors decrease with the increase of the number of peripheral complexes, although the second approach provides better results using several exchange-correlation functionals. The first approach consisted of evaluating the exchange coupling constant J(ij) between two paramagnetic metal centers i and j in the hexanuclear molecule by calculating the energy differences between the highest and broken-symmetry spin states of a model molecule in which metal atoms except for i and j are substituted by diamagnetic Zn(II) cations, while the second consisted of calculating the different spin-state energies of hexanuclear complexes and using the Heisenberg Hamiltonian to obtain the exchange coupling constants between different metal centers. Moreover, Kahn's qualitative theory succeeded in being applied to interpret the trend.