Density-functional study of the ground- and excited-spin states of [M2Cl9]3–(M = Mo or W) face-shared dimers: consequences for structural variation in A3M2Cl9 complexes
The optimized geometries and relative energies for the ground- and excited-spin states (Smax= 0–3) of [M2Cl9]3–(M = Mo or W) have been determined from density-functional calculations. For both systems the calculations predict a dramatic increase in metal–metal distance, with a corresponding increase in M–Clb–M bridge angle, as the dimer spin state (Smax) increases. The terminal MCl3 groups on the other hand are relatively insensitive to changes in the M–M separation. For both [Mo2Cl9]3– and [W2Cl9]3– the spin-singlet structure (Smax= 0) is predicted to be the most stable species when using the local-density approximation (LDA), in agreement with experiment. In contrast, when non-local gradient corrections to the total energy are incorporated, both the spin-quintet (Smax= 2) and -septet (Smax= 3) species are predicted to be more stable than the spin singlet for [Mo2Cl9]3–. The calculated (LDA) singlet geometry for [W2Cl9]3– is in very good agreement with the observed structure whereas for [Mo2Cl9]3– the geometry of the spin-triplet species is closer to experiment. Incorporation of relativistic effects is more significant for [W2Cl9]3– resulting in a further destabilization of the higher-spin states, particularly the spin-quintet and -septet species, relative to the singlet configuration. Fragment analysis showed that the metal–metal and metal–bridge contributions to the total bonding in the higher-spin species counteract each other. The destabilization due to loss of metal–metal bonding in the higher-spin states is greater than the stabilization gained from the enhanced metal–bridge interaction. However, the reduction in the M–M interaction is more pronounced for [W2Cl9]3– and thus its higher-spin states are less accessible than for [Mo2Cl9]3–, accounting for the more dramatic variation in M–M distances observed in A3Mo2Cl9 complexes.