The Chemical Bond and s-d Hybridization in Coinage Metal(I) Cyanides

We present a four-component relativistic density functional theory study of the chemical bond and s-d hybridization in the group 11 cyanides M-CN (M = Cu, Ag, and Au). The analysis is carried out within the charge-displacement/natural orbital for chemical valence (CD-NOCV) scheme, which allows us to single out meaningful contributions to the total charge rearrangement that arises upon bond formation and to quantify the components of the Dewar-Chatt-Duncanson bonding model (the ligand-to-metal donation and metal-to-ligand back-donation). The M-CN bond is characterized by a large donation from the cyanide ion to the metal cation and by two small back-donation components from the metal toward the cyanide anion. The case of gold cyanide elucidates the peculiar role of the relativistic effects in determining the characteristics of the Au-C bond with respect to the copper and silver homologues. In AuCN, the donation and back-donation components are significantly enhanced, and the spin-orbit coupling, removing the degeneracy of the 5d atomic orbitals, induces a substantial split in the back-donation components. A simple spatial analysis of the NOCV-pair density, related to the ligand-to-metal donation component, allows us to quantify, with unprecedented accuracy, the charge rearrangement due to the s-d hybridization occurring at the metal site. The s-d hybridization plays a key role in determining the shape and size of the metal; it removes electron density from the bond axis and induces a significant flattening at the metal site in the position trans to the ligand. The s-d hybridization is present in all noble metal complexes, influencing the bond distances, and its effect is enhanced for Au, which is consistent with the preference of gold to form linear complexes. A comparative investigation of simple complexes [AuL]^+/0 of Au⁺ with different ligands (L = F^-, N-heterocyclic carbene, CO, and PH₃) shows that the s-d hybridization mechanism is also influenced by the nature of the ligand.