Three electron bonds

Addition of small amounts of (CH3)2S (5 x 10 5 — 5 x 10"4m) to deoxygenated solutions of 3m HC104 and 0.5m DMSO leads to replacement of the 285 nm absorption by 465 nm absorption which is known to belong to the complexed three-electron-bonded radical cation of the disulfide47. 

The Helium Molecule and Molecule-ion.—The simplest example of a molecule containing a three-electron bond is the helium molecule-ion, in which a Is eigenfunction for each of two identical atoms is involved. The two unperturbed states of equal energy are He He+ and He-+ He. The formation of this molecule might be represented by the equation He Is2 >5 + He+ Is 5 —>- He (Is + ls) 2 Three dots in a horizontal line placed between the two atomic symbols may be used to designate a three-electron bond He He+. 

Evidence has been advanced8 that the neutral helium molecule which gives rise to the helium bands is formed from one normal and one excited helium atom. Excitation of one atom leaves an unpaired Is electron which can then interact with the pair of Is electrons of the other atom to form a three-electron bond. The outer electron will not contribute very much to the bond forces, and will occupy any one of a large number of approximately hydrogen-like states, giving rise to a roughly hydrogenlike spectrum. The small influence of the outer electron is shown by the variation of the equilibrium intemuclear distance within only the narrow limits 1.05-1.13 A. for all of the more than 25 known states of the helium molecule. 

I believe that the explanation of these facts is provided by the three-8 W. Weizel, Z. Physik, 59,320 (1929). Weizel and F. Hund [ibid., 63, 719 (1930) ] have discussed the possible electronic states of the helium molecule. Neither one, however, explains why He Is2 + He+ Is form a stable molecule-ion, nor gives the necessary condition for the formation of a three-electron bond. In earlier papers they assumed that both atoms had to be excited in order to form a stable molecule [W. Weizel, ibid., 51,328 (1928) F. Hund, ibid., 51, 759 (1928)]. 

It may be mentioned that the three-electron bond developed above is not present in the benzene molecule, for which certain investigators have suggested the structure... 

We have seen that a three-electron bond is less stable than an electron-pair bond, so that this structure would provide a very unstable rather than a very stable benzene ring. 

It is shown that a stable shared-electron bond involving one eigenfunction for each of two atoms can be formed under certain circumstances with either one, two, or three electrons. An electron-pair bond can be formed by two arbitrary atoms. A one-electron bond and a three-electron bond, however, can be formed only when a certain criterion involving the nature of the atoms concerned is satisfied. Of these bonds the electron-pair bond is the most stable, with a dissociation energy of 2-4 v. e. The one-electron bond and the three-electron bond have a dissociation energy... 

In Sections 42 and 43 we shall describe the accurate and reliable wave-mechanical treatments which have been given the hydrogen molecule-ion and hydrogen molecule. These treatments are necessarily rather complicated. In order to throw further light on the interactions involved in the formation of these molecules, we shall preface the accurate treatments by a discussion of various less exact treatments. The helium molecule-ion, He , will be treated in Section 44, followed in Section 45 by a general discussion of the properties of the one-electron bond, the electron-pair bond, and the three-electron bond. 

The revision leads to a difference of 0.06 A. between the interatomic distance in the normal oxygen molecule and the sum of the double-bond radii. This may be attributed to the presence of an unusual structure, consisting of a single bond plus two three-electron bonds. We assign this structure both to the normal 2 state, with ro = 1.204 A., and to the excited 2 state, with ro = 1.223 A., the two differing in the relative spin orientations of the odd electrons in the two three-electron bonds. We expect for the double-bonded state the separation n 1.14 A. 

In sharp contrast to the stable [H2S. .SH2] radical cation, the isoelectron-ic neutral radicals [H2S.. SH] and [H2S. .C1] are very weakly-bound van der Waals complexes [125]. Furthermore, the unsymmetrical [H2S.. C1H] radical cation is less strongly bound than the symmetrical [H2S.. SH2] ion. The strength of these three-electron bonds was explained in terms of the overlap between the donor HOMO and radical SOMO. In a systematic study of a series of three-electron bonded radical cations [126], Clark has shown that the three-electron bond energy of [X.. Y] decreases exponentially with AIP, the difference between the ionisation potentials (IP) of X and Y. As a consequence, many of the known three-electron bonds are homonuclear, or at least involve two atoms of similar IP. 

The ab initio calculations of various three-electron hemibonded systems [122, 123] indicated that the inclusion of electron correlation corrections is extremely important for the calculation of three-electron bond energies. The Hartree-Fock (HF) error is found to be nonsystematic and always large, sometimes of the same order of magnitude as the bond energy. According to valence bond (VB) and MO theories, the three-electron bond is attributed to a resonance between the two Lewis structures... 

These two resonance hybrids are mutually related by charge transfer. Hib-erty, Shaik and co-workers [136] explained the HF bias in the three-electron bond energies in terms of two deficiencies ... 

This difference between these two carbenes can be attributed to the presence of the lone pair of electrons on nitrogen in 4b. Two-center, three-electron bonding in the molecular plane of 4b, involving the lone pair, produces some unpaired a spin density on nitrogen. Coulombic repulsion between the a and tt electrons of... 

Linus Pauling, "The Nature of the Chemical Bond. Applications of Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules," JACS 53 (1931) 13671400 also, "The Nature of the Chemical Bond. II. The One-Electron Bond and Three-Electron Bond,"... 

The Nature of the Chemical Bond. II. The One-Electron Bond and Three-Electron Bond." JACS 53 (1931) 32253237. 

Fig. 39). The ESR data for dimethylselenide dimer cation radical 107c are consistent with two-center three-electron bonding, in which two electrons are in a cr bond between the two chalcogens, while the third electron is in a o orbital. 

A review considering the generation and characterization of radical ions, their reactions, formation of species with three-electron bonds, and radical cations of strained systems has been published." The redox and acidity properties of a number of substituted benzene radical cations were smdied by pulse radiolysis. ... 

Because the three-electron-bonded radicals are formed at the cost of the removal of the nitrogen p-electron, such cation-radicals should be considered as p-acids. Of course, the formation and behavior of these p-acids have to be dependent on steric factors. Works by Tomilin et al. (1996, 2000), Bietti et al. (1998), Dombrowski et al. (2005), and Yu et al. (2007) should be mentioned as describing stereoelectronic requirements to formations and configurational equilibria of A-alkyl-substituted cation-radicals. 

This section is devoted to odd-electron multicenter bonds. Two-center three-electron bonds were described by Pauling (1931). Since the first prediction by Pauling, a great deal of interest has been expressed in such systems. The following text provides a list of important references. 

One-electron oxidation of l,6-diazabicyclo[4.4.4]tetradecane proceeds at a remarkably low rate. The cation-radical obtained contains a three-electron o bond between the two nitrogen atoms (Alder and Sessions 1979). In this case, the three-electron bond links the two nitrogens that are disjoined in the initial neutral molecule, at the expense of one electron from the lone electron pair of the first nitrogen and the two electrons of the second nitrogen, which lasts as if it is unchangeable. The authors named such a phenomenon as strong inward pyramidalization of the nitrogens with remarkable flexibility for the N—N interaction. This interaction results in 2a-la bond formation (Scheme 3.21). 

The molecular geometry, which allows optimal p orbital interaction to yield a three-electron bond, presumes an orientation of p orbitals belonging to each sulfur atom along the S S axis. This is the case of the chair-boat conformer of the 1,5-dithiacyclooctane cation-radical, the first structure in Scheme 3.22.In the 1,3-dithiacyclopentane cation-radical, the sulfurp orbitals are aligned almost perpendicular to the ring plane, and this prevents stabilization by the transannular interaction between the two sulfur atoms in the cycle. This unreal structure (the second structure in brackets in Scheme 3.22) cannot exist. However, the cation-radical of bis(2-methyl-1,3-dithianyl)methanol (the third structure in Scheme 3.22) was predicted to exist Li and Kutateladze (2003) calculated this structure as the most stable because it differs by a special orbital pattern from the structure in brackets. 

There are three possible types of three-electron bonds. Oxidation of a u bond leads to a cation-radical with a, u three-electron bond. This bond contains no antibonding electrons, and the total bond strength exceeds that of a double bond by the energy of half a n bond. Olefins can acquire the 2a—In bond on one-electron oxidation, the bond constructed from the electrons 2a and In. Oxidation of organic disulfides, RSSR, to their cation-radicals (RSSR) yields species in which the unpaired electron from the oxidized sulfur interacts with the unbound p-electron pair of the second sulfur (Glass 1999). This establishes a 2n-In bond on top of the already existing o bond. The overall bond strength of this five-electron (2a—2n-In ) bond also exceeds that of the normal... 

When geometric constrains preclude the participation of a neighboring group, the three-electron bond is not formed. Scheme 3.29 gives one such example, namely, exo-2-(caTboxy)-endo-6-(methylthio)-bicyclo[2.2.1]heptane. 

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