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The distribution of di-, tri-, and tetracoordination among the d(10) ions of the group 11 metals is theoretically analyzed by means of density functional calculations on more than 150 model complexes of general formula [MX(m)L(n)](1-m) (where M = Cu, Ag, or Au; L = NH(3) or PH(3); X = Cl, Br, or I; m + n = 2-4). The energy of a ligand association reaction has been found to be practically determined by two contributions: the interaction energy and the energy of deformation of the metal coordination sphere. The larger deformation energy of gold complexes compared to copper and silver ones explains the predominance of dicoordination among Au(I) complexes, in comparison with Cu(I) and Ag(I), for which dicoordination is far less common than tri- and tetracoordination. Other experimental trends can be explained by looking at the fine details of these two energetic components.

The nature of the multicenter, long bond in neutral phenalenyl dimers is analyzed in detail and compared to the multicenter, long bond in [TCNE](2)(2-). These dimers are prototypes of multicenter, long bond in dimers of neutral and anion radicals. This was done by examining the number of electrons (m) and atomic centers (c) involved in the long bond for these dimers, as well as identifying the dominant attractive components of their interaction energy (SOMO-SOMO bonding, dispersion, and the sum of the exchange-repulsion and electrostatic components) in accord with Pauling's focus on total bond energies. The long bond in [TCNE](2)(2-) is a 2e(-)/4c bond, the electrostatic component is repulsive, and the dominant attractive component is the dispersion component (-27.7 kcal/mol), about two times larger than the bonding component. In phenalenyl dimers the dispersion component (-31.7 kcal/mol) is about 2.5 times stronger (than the SOMO-SOMO bonding component; hence, the multicenter, long bond in these dimers is closer to a van der Waals bond than to a covalent bond. Consequently, it possesses a two-electrons/fourteen center 2e(-)/14c bond, rather than the 2e(-)/12c bond suggested by the SOMO-SOMO bonding component. The covalent-like properties in phenalenyl dimers result from the dominant dispersion component that enable the fragments to approach each other so that their SOMOs overlap and produce a qualitative MO diagram identical to that found in conventional covalent bonds.

The 2.89-A intradimer separation for cofacial [TCNE]2(2-) (TCNE = tetracyanoethylene) dimers is twice that of conventional C-C bonds but approximately 0.6 A shorter than the sum of the van der Waals radii. Experimental and computational studies best characterize the intradimer bonding as a 2-electron-4-center (2e(-)-4c) C-C bonding interaction (or bond). This nonconventional bonding exhibits unique spectroscopic properties (new, lower energy electronic absorption, new nuCC and new and shifted nuCN and deltaCCN vibrational absorptions, and characteristic 13C NMR chemical shifts) and is diamagnetic. [TCNE]2(2-) is a prototype of a growing number of organic compounds that are best described by multicenter C-C bonding.