Two-Center/Three-Electron Sigma Half-Bonds in Main Group and Transition Metal Chemistry

Abstract

First proposed in a classic Linus Pauling paper, the two-center/three-electron (2c/3e) σ half-bond challenges the extremes of what may or may not be considered a chemical bond. Two electrons occupying a σ bonding orbital and one electron occupying the antibonding σ* orbital results in bond orders of ∼0.5 that are characteristic of metastable and exotic species, epitomized in the fleetingly stable He2(+) ion. In this Account, I describe the use of coordination chemistry to stabilize such fugacious three-electron bonded species at disparate ends of the periodic table. A recent emphasis in the chemistry of metal-metal bonds has been to prepare compounds with extremely short metal-metal distances and high metal-metal bond orders. But similar chemistry can be used to explore metal-metal bond orders less than one, including 2c/3e half-bonds. Bimetallic compounds in the Ni2(II,III) and Pd2(II,III) oxidation states were originally examined in the 1980s, but the evidence collected at that time suggested that they did not contain 2c/3e σ bonds. Both classes of compounds have been re-examined using EPR spectroscopy and modern computational methods that show the unpaired electron of each compound to occupy a M-M σ* orbital, consistent with 2c/3e Ni-Ni and Pd-Pd σ half-bonds. Elsewhere on the periodic table, a seemingly unrelated compound containing a trigonal bipyramidal Cu3S2 core caused a stir, leaving prominent theorists at odds with one another as to whether the compound contains a S-S bond. Due to my previous experience with 2c/3e metal-metal bonds, I suggested that the Cu3S2 compound could contain a 2c/3e S-S σ half-bond in the previously unknown oxidation state of S2(3-). By use of the Cambridge Database, a number of other known compounds were identified as potentially containing S2(3-) ligands, including a noteworthy set of cyclopentadienyl-supported compounds possessing diamond-shaped Ni2E2 units with E = S, Se, and Te. These compounds were subjected to extensive studies using X-ray absorption spectroscopy, X-ray photoelectron spectroscopy, density functional theory, and wave function-based computational methods, as well as chemical oxidation and reduction. The compounds contain E-E 2c/3e σ half-bonds and unprecedented E2(3-) "subchalcogenide" ligands, ushering in a new oxidation state paradigm for transition metal-chalcogen chemistry.

Spectroscopic observation of two-center three-electron bonded (hemi-bonded) structures of (H2S)n+ clusters in the gas phase

“…Until now, the sulfur–sulfur hemi-bond has been characterized only by EPR and UV-vis (transient) absorption. 16–18 However, it is very difficult to directly extract structural information from these types of experiments. Spectroscopic evidence in the gas phase has been highly requested to examine the theoretical predictions of the sulfur–sulfur hemi-bond.…”

Odd‐Electron Bonds

“…Above all, much of the late Dieter Asmus' seminalw ork [4][5][6][7][8][9][10][11][12][13] has apparently been forgotten, [72] but also the pioneering experimental studies of Meot-Ner, [19] Pauling [3] and Hiberty's [29] rationalization of oddelectron bond energiesi nt erms of valence-bond theory and Bock [34] and Nelsen's [35] fundamental studies on three-electron p-bonds are apparently no longerp resenti no ur general picture of bondingt heory.T his short review attempts to remind us of these classical examples of physicalo rganic chemistry, which taken on an even more importantr ole as the importance of radicals and radical ions is increasingly recognized in both biology and photovoltaics and whose importance in transition-metal chemistry has recently been reviewed. [73] Computational Section All calculations used the Gaussian 09 series of programs. [74] Geometries of the one-and three-electron hydride complexes shown in Figure 1w ere optimized at the QCISD [61] /6-311 + G(d,p) [65,66] level andc haracterizeda sm inimab yc alculating theirn ormalv ibrations within theh armonica pproximation at thes amel evel of theory.T he speciesg iven in Ta ble2 were optimizeda tt he MP2 [75] /6-31G(d) [76][77][78] levelo ft heorya nd theirn ormalv ibrationsc alculated.…”

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

“…We remark that the emergence of a resonance associated with the symmetrization of the many-body wave function in two-center/three-electron bonded systems is well known [33][34][35] in theoretical chemistry and in particular in the valence-bond treatment of the three-electron bond which controls the formation of molecules Figure 1. Energy versus −1/g spectra, SPDs (green surfaces), and spin-resolved CPDs (red surfaces) of N=4 strongly repelling 6 Li atoms in a double-well confinement with a parallel arrangement of the two 1D traps, as a function of the interwell separation d and/or interwell barrier V b .…”