Bond-valence model for metal cluster compounds. II. Matrix effect

The bond-valence model was commonly considered as inappropriate to metal cluster compounds, but recently it was shown that the model provides unique information on the lattice strains and stabilization mechanisms in (TM)₆-chalcohalides, M_x(TM)₆L_y (TM = transition metal, L = the chalcogen and/or halogen ligands; M = counter-cation). The previous study was mainly devoted to the non-uniform distribution of the anion valences (bond-valence sums) around clusters. This and the previous paper are focused on two additional phenomena: (i) a steric conflict between counter-cations and the cluster-ligand framework resulting in `common' lattice strains [previous paper: Levi et al. (2013). Acta Cryst. B69, 419-425], and (ii) steric conflict between the small (TM)₆-cluster and the large coordination polyhedron around the cluster or so-called matrix effect (this paper). It was shown that both phenomena can be well described by changes in the bond-valence parameters. This paper demonstrates that the matrix effect results in high strains in the TM-L bonds in most of the (TM)₆-chalcohalides (TM = Nb, Mo, W and Re). In spite of this, the violations for the total TM valence are minimal, because the cluster stretching is fully or partially compensated by compression of the TM-L bonds. As a result, the influence of the matrix effect on the material stability is rather positive: it decreases the volume of the structural units and in many cases ensures a more favorable distribution of the bond valences around TM atoms, stabilizing the cluster compound.