The three electron bond

The introduction of the idea of a three electron bond was an attempt to explain the existence of molecules with unpaired electrons within the framework of the Heitler-London treatment. According to Pauling the bond in occurs by the superposition of the two forms  

In a similar manner the nitric oxide molecule may be represented by resonance between the two forms  

A comparison of this structure with the electronic configuration according to the molecular orbital treatment brings out an important similarity. The molecular orbitals of nitric oxide are 

Since the (zcr) and (yor) orbitals cancel, these four electrons take no part in the bond and will be represented by the two electrons shown to the left of the nitrogen and two to the right of the oxygen in structure /. Of the remaining three orbitals, the ( or) and (doubly degenerate) arp 

The idea of a localized molecular orbital may be illustrated by the water molecule. The atomic orbitals available for the formation of molecular orbitals are the and 2p of oxygen and the two i jofthe two hydrogen atoms, 

The theory of localized molecular orbitals, although most successful when applied to the ground states of molecules containing not more than one double bond, ceases to be correct for excited states and for systems containing conjugated double bonds. The first of these cases may be illustrated by considering methane. If one of the electrons be excited, it is impossible to predict in which localized molecular orbital it will occur and 

The second situation referred to above, viz systems containing conjugated double bonds, is perhaps more important to the present discussion. The classical example of such a system is benzene. The molecular orbital treatment regards the six G—G bonds and the six G—H bonds as completely localized molecular orbitals compounded out of carbon sp2 hybrid atomic orbitals and the hydrogen s orbital. So far the treatment is identical with the electron pair theory, discussed in Chapter 4. The G—G bonds will be or bonds formed by the overlap of two sp2 hybrid atomic orbitals, one from each carbon atom and the C—H bonds will also be a bonds formed by the overlap of one sp2 hybrid atomic orbital of carbon with the s atomic orbital of hydrogen. The six carbon 2p atomic orbitals that remain will form completely non-localized molecular orbitals. Thus each 2pt electron will be regarded as existing in the field of six nuclei and will possess a wave function of the form  

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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... 

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. 

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 ... 

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. 

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). 

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. 

Scheme 3.30 depicts an intriguing case, when one-electron oxidation of the conformationally constrained exo-2-(carboxy)-en(i(9-2-(ammo)-en(i(9-6-(methylthio)-bicyclo[2.2.1]heptane gives rise to a cation-radical in which an amino- and not a carboxylate group participates in the three-electron bond with sulfur (Glass 1995). 

The onium form of the ethyl acetate cation-radical is more stable by 50 kJ moH than the corresponding carbonyl form (Rhodes 1988). The CHj fragment is stabilized by the three-electron bonding with the neighboring oxygen in the following manner -O.. CH2. Oxidation of the carbonyl... 

The aim ofthe present study is double i) to show that BET can be used as a tool for analyzing the adiabatic PESs and localizing the diabatic crossings which govern the overall electron changes ii) to provide a topological description of the three-electron bonds. 

When we consider the principal structures at the energy minimum geometry we see the three-electron bonds discussed above. These are shown in Tables 11.19 and 11.20. Considering the principal tableaux of either sort, we see there are two three-electron sets present, plaPxb and Py Pya- There is, of course, a normal two-electron a bond present also. When we move to the second structure, there are differences. 

VB description. Just as R—X is a representation of the two-electron bond, (R—X) is the representation we will use for the three-electron bond between R and X. In VB terms such a bond may be described by a linear combination of the configurations, R- X and R -X. Both of these configurations are repulsive with respect to R---X approach due to exchange repulsion. The exchange repulsion comes about from the overlap of two electrons, one on R and the other on X, possessing the same spin (Pauling and Wilson, 1935). The linear combination of the two VB forms may, however, lead to the formation of a stable three-electron bond. Let us see how this comes about. 

If the two VB forms describing the three-electron bond are very different in energy then, as indicated in Fig. 6a the bond is expected to break up spontaneously. This is indeed the case for [CH3 -C1] which decomposes spontaneously to CH3 and Cl" (Wang and Williams, 1980). As the R group is made more electronegative the relative contribution of R X increases so that a stable three-electron bond is generated. This is observed for [CFj- -Cl]- and [(CF3)3C—1], which both exhibit measurable lifetimes (Wang and Williams, 1980). 

VB-MO correspondence for three-electron bonds. The MO description of the ground state of the three-electron bonded species, (R—X)-, is a2a i.e. a doubly occupied a-orbital and a singly occupied a orbital. Substituting the hybrid orbital description of a and a into the MO description of the three-electron bond, we obtain (50). 

Electron transfer from N to RX generates the species N (R — X)-. The fate of this species depends on the stability of the three-electron bond R—X. 

The One-Electron Bond and the Three-Electron Bond Electron-deficient Substances... 

In a few molecules and crystals it is convenient to describe the interactions between the atoms in terms of the one-electron bond and the three-electron bond. Each of these bbnds is about half as strong as a shared-electron-pair bond each might be described as a half-bond.1 There are also many other molecules and crystals with structures that may be described as involving fractional bonds that result, from the resonance of bonds between two or more positions. Moat of these molecules and crystals have a smaller number of valence electrons than of stable bond orbitals. Substances of this type are called electron-deficient substances. The principal types of electron-deficient substances are discussed in the following sections (and in the next chapter, on metals). 

It may be pointed out that the one-electron bond, the electron-pair bond, and the three-electron bond use one stable bond orbital of each of two atoms, and one, two, and three electrons, respectively. 

The Helium Molecule-Ion.—The simplest molecule in which the three-electron bond can occur is the helium molecule-ion, HeJ, consisting of two nuclei, each with one stable Is orbital, and three electrons. The theoretical treatment7 of this system has shown that the bond is strong, with bond energy about 55 kcal/mole and with equilibrium internuclear distance about 1.09 A. The experimental values for these qualities, determined from spectroscopic data for excited states of the helium molecule, are a bout 58 kcal/mole and 1.080 A, respectively, which agree well with the theoretical values. It is seen that the bond energy in He He4 is about the same as that in H H+, and a little more than half as great as that of the electron-pair bpnd in H H. 

The properties of the molecule are accounted for by this structure. The extra energy of the three-electron bond stabilises the molecule relative to structure I to such extent that the heat of the reaction 2NO — > NaO is small,8 and the substance does not polymerize in the gas phase. 

N5sbO . The observed distance for NO is 1.151 A, somewhat larger than that expected for a 2 J bond it corresponds, when interpreted with use of an equation similar in form to Equation 7-7, to the bond number 2.31. We conclude that the difference in electronegativity of the two atoms decreases the contribution of structure II to such an extent that the three-electron bond is about a one-third bond, rather than a one-half bond. 

The explanation of this weak bond is provided by the stability of the three-electron bonds in the NO molecules that compose the dimer, which strive to prevent the two odd electrons from settling down on the... 

There is, of course, resonance of the double bonds between the alternative positions.) In the foregoing discussion of NO it was concluded that the occupancy of the nitrogen atom by the odd electron of the N 0 bond is about 65 percent. If the three-electron bond in NO2 is similar and the resonance for the two N02 molecules is unsynchronized, the odd electrons would have 42 percent simultaneous location on the nitrogen atoms, and hence the bond number 0.42 tvould be expected. This result agrees satisfactorily with the value 0.34 given by the bond length. 

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