Charge-overlap study of multiple metal-metal bonding and conjugation in linear chains of transition-metal atoms

Abstract

For a comparative study of bonding, the dsp excited configuration, pertinent to linear digonal hybrids, was imposed on metals of three transition series. Computations of u, r, and 6 overlap of the s, p, and d orbitals in this configuration were made for selected metals, at the usual metallic distance, the distance in A3B superconducting alloys, and the distance for known multiple metal bonds in complexes. The computation made use of single-{ Slater orbitals derived from the same Burns rule for all. Subsequently, molecular orbital calculation of o, r, and 6 bonding for a repeating unit, -(M2)in an infinite chain was made by using an extended Hiickel method and the Mulliken-Wolfsberg and Helmholz approximation. The (same) parameter, K = 1.75, used for all metals was first tested for N2 and P2. The bond stabilization relative to the ground-state atoms, proportional to overlap, was used to approximate the bond dissociation energy. A new attempt was made to justify and to delineate the approximation involved and to show that the neglected two-electron integrals as well as the nuclear repulsion tend to cancel. Coulomb integrals were approximated by valence-orbital ionization energies (VOWS), which for self-consistency were all obtained from existing z-series expansion of the Hartree-Fock SCF energies of the atoms and their ions of appropriate configuration. The dsp configuration energies were also obtained from the same HF-SCF calculations. In cases where data were not available and for the third series the dnsp energies were obtained from weighted averages of spectroscopic term energies given by Moore. Overlap data here support dp hybridization assisted by sp in bonding that is principally do plus d r and d6. The bond strength as well as bond order for a chain peaks at group 6, drops at the first column of group 7, and rises again at group 8. The relative bond strength for do vs. d r vs. d6 bonds was estimated by the ratio of relative stabilizations. Pictures of conjugate bonds and their resonance in a chain, consistent with the translational symmetry of the repeating unit, -(M2)-, and with the conservation of azimuthal angular momentum were drawn. The study suggests that, for a chain of neutral transition-metal atoms, the most favorable multiple bonding occurs for group 5 and group 6 elements (more so for the second series than for the first), the largest number of resonance-conjugation hybrids exists for group 5, and the highest bond order occurs for group 6 atoms.