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

Abstract

The optimized geometries and relative energies for the ground- and excited-spin states (S_max= 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–Cl_b–M bridge angle, as the dimer spin state (S_max) 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 (S_max= 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 (S_max= 2) and -septet (S_max= 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.