DV-Xα法
Electronic structures of three cubane-type sulfur-bridged molybdenum clusters [Mo4S4(H2O)12]4+(1A), [Mo4S4(H2O)12]5+(1B), and [Mo4S4(H2O)12]6+(1C) have been calculated by the spin-polarized discrete-variational Xα method. Magnetic measurements of Mg2[Mo4S4(edta)2].20H2O(2A'), Ca1.5[Mo4S4(edta)2].13H2O(2B'), and Na2[Mo4S4(edta)2].6H2O(2C') indicate that [Mo4S4(edta)2]4-(2A) and [Mo4S4(edta)2]2-(2C) are essentially diamagnetic, and [Mo4S4(edta)2]3-(2B) is paramagnetic with S=1/2. Although the ligands are different in the two groups 1A-1C and 2A-2C, electronic spectra of 1A and 2A, 1B and 2B, and 1C and 2C are similar to each other, and 1A and 1C are expected to be diamagnetic, and 1B paramagnetic. Both Td and D2d symmetries were applied to the calculation of the clusters. In Td symmetry, all the HOMO's of 1A, 1B, and 1C are t2 orbitals, which indicated that 1B and 1C are paramagnetic and 1A is diamagnetic: discrepancy occurs between the observation and the calculation in the case of 1C. Then D2d symmetry was adopted to 1A, 1B, and 1C(t2 orbital in Td symmetry splits into b2 and e orbitals in D2d symmetry), where spin polarization occurred in the case ob 1B only. The HOMOs of 1A, 1B, and 1C are e(occupied), e up(occupied), and b2(occupied), respectivery, which agrees with the experimental results. The Calculations explain successfully the experimental results of valence-band X-ray photoelectron spectra, and magnetic measurements.
