Steric and Electrostatic Effects in Compounds with Centered Clusters Quantified by Bond Order Analysis

Steric and electrostatic effects affect the strength, energy, and reactivity of chemical bonds, but their quantification by density functional theory is not straightforward, even for simple molecules. In the previous works devoted to compounds with metal-metal bonds, we showed that these effects can be easily and properly described by the difference between formal and effective bond orders, the latter being calculated from the experimental bond lengths using exponential correlations and empirical bond valence parameters. This work applies for the first time the same method to halides with Z-centered M₆-clusters (Z represents main group elements like Be, B, C, and N or transition metals like Mn, Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, and Pt; M = Sc, Zr, Y, and Gd). It was shown that a spatial inconsistency between short M-Z bonds and relatively rigid anion close-packing results in the high strains in the individual bonds, but the total bond order sums calculated for the M atom in most of the halides are close to the number of its valence electrons. This bond order conservation associated with high deformability of electron clouds of M atoms explains the stability of the cluster compounds.