The One-electron Bond

As a tribute to Pauling s contributions, I shall restate and summarize some of the implications for bonding theory that arise when the three-electron bond is incorporated as a mainstream component for VB descriptions of the electronic structures of electron-rich molecules. Attention will be focussed on increased-valence structures for molecular systems that involve four-electron three-centre and six-electron four-centre bonding units. However initially, consideration will be given to the one-electron bond, for which Pauling also provided some attention to both the theory and examples of systems that involve this type of bond in their VB structures. As indicated in ref. [8(a)], experimentally one-electron bonds and three-electron bonds are abundant and well-characterized for odd-electron systems. 

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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 energy of the one-electron bond in the lithium molecule ion is calculated with consideration of the s-p separation to be 1.19 e. v and the hybrid bond orbital involved is shown to involve about equal contributions from the 25 and 2p orbitals of the lithium atom. 

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. 

In the following sections of this chapter there are given, after an introductory survey of the types of chemical bonds, discussions of the concept of resonance and of the nature of the one-electron bond and the electron-pair bond. 

In this section we make the first chemical application of the idea of resonance, in connection with the structure of the simplest of all molecules, the hydrogen molecule-ion, Hj, and the simplest of all chemical bonds, the one-electron bond, which involves one electron shared by two atoms. 

In this discussion another type of interaction between the hydrogen atom and ion has been neglected to wit, the deformation (polarization) of the atom in the electric field of the ion. This has been considered by Dickinson,22 who has shown that it contributes an additional 10 kcal /mole to the energy of the bond. We may accordingly say that of the total energy of the one-electron bond in (61 kcal/mole) about 80 percent (50 kcal/mole) is due to the resonance of the electron between the two nuclei, and the remainder is due to deformation. 

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). 

The one-electron bond in the hydrogen molecule-ion is about half as strong as the electron-pair bond in the hydrogen molecule (Do . 60.95 kcal/mole for H/, 102.62 kcal/mcle for Hr—Secs. 1-4, 1-5) and, since the same number of atomic orbitals is needed for a one-electron ixmd as for an electron-pair bond, it is to be expected that in general molecules containing one-electron bonds will be less stable than those in which all the stable bond orbitals are used in electron-pair-bond formation. Moreover, there is a significant condition that must be satisfied in order for a stable one-electron bond to be formed between two atoms namely, that the two atoms be identical or closely similar (Sec. 1-4). For these reasons one-electron bonds are rare—much rarer, indeed, than three-electron bonds, to which similar restrictions apply. 

Similar excited states have been observed for diatomic molecules of the alkali metals. They may be interpreted as involving a molecule-ion, such as Li, with a one-electron bond, plus a loosely-bound outer electron. The internuclear distances are about 0.3 A greater than for the corresponding normal states 2 2.94 A lor Lij (2.672 A for Lit), 3.41 A for Na (3.079 A for Nat), and 4.24 A for K (3.923 A for Kt). The values of the bond energies for the one-electron bonds, as indicated by the vibrational levels, are about 60 percent of those for the corresponding electron-pair bonds. 

Notice the close similarity of this argument to that given for the one-electron bond in Sec. 1-4. 

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. 

Some substituted cyclopropanes have been shown to undergo nucleophilic addition of suitable solvents (CH3OH) [231]. For example, the electron transfer reaction of phenylcyclopropane (47, R = H) with p-dicyanobenzene resulted in a ring-opened ether (48), formed by anfi-Markovnikov addition. More recently, the reaction of a 2,3-dimethyl derivative (47, R = CH3) was shown to occur with essentially complete inversion of configuration at carbon, suggesting a nucleophilic cleavage of the one-electron bond [233]. This result is significant, since it requires an intermediate with the unperturbed stereochemistry of the parent molecule. 

The first and foremost rule is that the entire matrix element between two VB determinants is signed as the corresponding determinant overlap and has the same power in AO overlap. For example, the overlap between the two determinants of a HL bond, ab and ab is S lh. Hence, the matrix element is negatively signed and given as — 2(3ai,5 ai) since (3a/, is proportional to Sab, both the matrix element and the determinant-overlap involve AO overlap to the power of 2. For the one-electron bond case (Eq. 3.46), the overlap between the determinants is + Sah and the matrix element + (3afo. 

The borate salts (Scheme 7) constitute an analogous group of electron donors [8,29,121]. In this case, PET from the anions to cationic acceptors (Sect. 2.2.1) produces a radical cations, (or alternatively, if a Jt-reservoir is available a n radical cation may be formed). If one of the substituents is an alkyl group the one-electron bond breaks rapidly (possibly in a dissociative process), forming a radical and a neutral. These systems also find applications in imaging. 

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