Density Functional Studies of a Heisenberg Spin Coupled Chromium−Semiquinone Complex and Its Chromium−Catechol Analog

The electronic structure of [Cr(tren)(3,6-DTBSQ)]2+, where tren is tris(2-aminoethyl)amine and 3,6-DTBSQ is 3,6-di-tert-butylorthosemiquinone, has been studied by self-consistent-field non-local gradient-corrected density functional theory. The results are consistent with a Heisenberg exchange formulation where a Cr(S = 3/2) ion is antiferromagnetically coupled to the semiquinone(S = 1/2) giving rise to a S = 1 ground state. Population analyses were carried out which show net α and β spin densities at the chromium ion and semiquinone, respectively. Some orbital interactions have been identified that allow partial delocalization from the semiquinone toward the chromium ion giving rise to an antiparallel alignment of their electron spins. The isotropic exchange constant J of the Heisenberg Hamiltonian ℋex = J S 1·S 2 has been determined from the self-consistent-field energies at the U-BLYP/6-311** and U-B3LYP/6-311** levels and is consistent with previously reported magnetic susceptibility data. The triplet state wave function shows some spin contamination from the higher-lying quintet state. Accordingly, approximate spin and energy projections were performed to account for the quintet admixture. Some magneto-structural correlations between the Cr−OSQ and OSQ−CSQ bond lengths and the magnitude of J have also been investigated. It was found that J decays in a nearly exponential fashion with increasing bond distances. The electronic structure of the free semiquinone ligand has also been studied and correlated to its bonding with chromium. Finally, a single-crystal X-ray structure of the related complex [Cr(tren)(3,6-DTBCat)]+ was obtained and used to carry out similar self-consistent-field calculations. Analysis of the quartet ground state wave function of the catecholate complex produced spin densities consistent with a Cr(S = 3/2)−catechol(S = 0) formulation.