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

Abstract

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.

Metal–Metal Bond in the Light of Pauling’s Rules

“…A similar analysis of the effective BOs for various atomic pairs obviously confirmed the validity of Equation (2) for both localized and delocalized bonds [ 13 ]. The BV parameters of the TM–TM bonds obtained by fitting the exponential curves allow for a simple but careful calculation of the effective BOs from the TM–TM distances by Equation (2) [ 14 , 15 , 16 ].…”

“…The approximate values of R 0 ij for the TM pairs were also calculated using empirical constants proposed by O’Keeffe and Brese in 1991 for most of the chemical elements ( b ij of 0.37 Å is assumed to be the same for all the i and j pairs) [ 24 ]. It was shown that all three methods (based on BO conservation, on quantum chemistry data and O’Keeffe’s constants) result in the close values of the BV parameters [ 16 ], but the first approach seems the most reliable for the moment. In particular, the evaluation of BV parameters from quantum chemical data could largely benefit from the (hopefully future) availability of a large set of BO data computed using wavefunctions of comparable quality and a single BO recipe.…”

“…In contrast, the Pauling rules and the BVM were for a long time deemed as inapplicable to compounds with delocalized bonds, e.g., metal cluster compounds (i.e., materials with metal–metal, TM–TM (TM = transition metal), interactions) [ 4 , 7 ]. Only recently, the efficacy of the model for such compounds was shown [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ].…”

Redox Potential and Crystal Chemistry of Hexanuclear Cluster Compounds

“…For ionic solids, coordination compounds etc., it is well known that the BVM provides accurate values of the ionic charges in the form of bond valence sum (BVS) [ 19 ]. In our previous works we showed that the BVM is also very effective in the case of cluster compounds [ 20 , 21 ].…”

A supported Cr–Cr sextuple bond in an all-metal cluster

“…[12][13][14] As a multiple bonding prototype, the chromium dimer has been widely studied, especially since Nguyen et al synthesized the first stable Cr-Cr quintuple bonding [Cr 2 (Ar′) 2 ] complex in 2005, 14 which still holds the record of the highest bond order among the stable molecules. 7,9,[15][16][17][18][19][20][21][22][23][24][25][26][27][28] Since then, there are burgeoning research studies on the characterization and exploration of Cr-Cr and other high multiplicity metal-metal bonding structures. Notably, sextuple bonds were only considered to exist in naked Mo 2 and W 2 dimers on the theoretical shelf, [28][29][30] while the radial distribution maxima of the 3d orbitals of Cr lie in the same region as those of the inner 3s and 3p orbitals, resulting in two intrinsically weak δ overlaps and they were only suggested to be quadruple.…”