Odd-electron bond

Odd-electron bonded species represent a very special class of radicals with unique characteristics. Many of them, perhaps even the majority have been evaluated using radiation chemical, particularly pulse radiolysis methods. 

however, only fair to acknowledge the vital input this field has received from complementary studies conducted especially with photochemical, ESR, electrochemical and theoretical means. Sulfur-centered radicals and radical ions turned out to be probably the most informative species in this respect and, accordingly, will serve as basis for the following evaluation of the characteristic features of such bonds. In general, the principles to be presented and discussed for the sulfur-centered species apply, however, also to any heteroatom-heteroatom interaction as will be shown for selected examples with Group III and Group V-VII elements. 

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Section 3.2 includes an extensive discussion on the formation of odd-electron bonds, ion pairing, and the distonic stabilization of ion-radicals at the expense of separation between their spins and charges. Section 3.3 deals with ion-radicals from the class of even spin-charge distribution. This class occnrred more frequently in scientific works of past decades. However, the reader will find newly developed manifestations of the principle of the released electron, concerning spread conjugation and the fates of ion-radical precursors with increased dimensionality. 

P. C. Hiberty, S. Humbel, D. Danovich, and S. Shaik,/. Am. Chem. Soc., 117, 9003 (1995). What Is Physically Wrong with the Description of Odd-Electron Bonding by Hartree-Fock Theory A Simple Nonempirical Remedy. 

A typical situation, where the VB wave function is written as a resonance hybrid, is odd-electron bonding (le or 3e bonds). For example, ale bond A B is a situation where only one electron is shared by two centers A and B (Eq. 3.46), while three electrons are distributed over the two centers in a 3e bond AB (Eq. 3.47) ... 

These equations for odd-electron bonding energies are good for cases where the forms are degenerate or nearly so. In cases where the two structures are not identical in energy, one should use the perturbation theoretic expression (3). 

The BOVB method has been successfully tested for its ability to reproduce dissociation energies and/or dissociation energy curves, close to the results (or estimated ones) of full Cl or to other highly accurate calculations performed with the same basis sets. A variety of two-electron and odd-electron bonds, including difficult test cases as F2, FH, and F2 (38,42), and the H3M-C1 series (M = C, Si, Ge, Sn, Pb) (39,43,44) were investigated. 

The importance and physical nature of dynamic correlation is even better appreciated in the case of 3e bonds, a type of bond in which the electron correlation is entirely dynamic, since there is no left-right correlation associated with odd-electron bonds. As noted earlier, the Hartree Fock and simple VB functions for 3e bonds (hence, GVB, SC, or VBSCF) are nearly equivalent and yield about similar bonding energies. Taking the F2 radical anion as an example, it turns out that, compared to the experimental bonding energy of... 

These levels are tested below on bond energies and/or dissociation curves of classical test cases, representative of two-electron and odd-electron bonds. 

Alongside electron-pair bonds, odd-electron bonds play an important role in chemistry, and constitute therefore a compulsory test case for any computational method. Odd-electron bonds can be represented as two resonating Lewis structures that are mutually related by charge transfer, as shown in (13) for two-center, one-electron (2c,le) bonds and in (14) and (15) for typical two-center, three-electron (2c,3e) bonds. 

Moreover, suMur-centered radicals and radical ions often represent a special class of radicals with odd-electron bonds and they can serve as convenient models for the evaluation of the characteristic features of such bonds. 

The actual electronic structure of (RSSR) is especially interesting. Key feature is a 2o/10 bond between the two sulfur atoms, rendering [RS.. SR]-an even more appropriate and informative notation.55,56 While further details on this three-electron bond will be dealt with in the odd electron bonds section vide infra), the following is of immediate interest. The combined effect of the two bonding o-electrons and the one antibonding a electron affords a formal bond order of 1/2. This, in turn, provides the rationale for the above equilibrium and relative ease of redissociation of the newly formed sulfur-sulfur bond. The same [RS. . SR] species is, incidentally, formed in the reduction of disulfides by hydrated electrons. Thiyl radicals and disulfide radical anions thus are two conjugate forms of the one-electron redox intermediate between thiols and disulfides. 

The disulfide radical anions (RSSR) are characterized by a relatively strong and thus easily detectable optical absorption. Depending on the nature of R absorption maxima range from 380 to 430 nm (for more details see section dealing with odd electron bonds ) and extinction coefficients are about (8-9)xl03 M-1 cm-. 71... 

All the sulfur-centered radical cations mentioned above exhibit moderate to strong optical absorptions allowing convenient detection and study of their properties by pulse radiolysis. In case of (R2S)2 and (RSSR) " the main absorption bands are located in the near UV and visible part of the spectrum. Since they are related to the special features of the odd-electron bonds it is again appropriate to present and discuss further details later. 

Odd-electron bonds between other identical heteroatoms... 

The bonding in O2 is illustrated in Scheme 3.R.3b. It is seen that the two O atoms form one electron-pair bond (the connecting line in 0—0) by clicking one of the connectivities of each O. The remaining connectivity on each O engages a lone pair on the other O and forms an odd-electron bond (three-electron bond). An odd-electron bond is considered to be equivalent to half of an electron-pair bond. Thus, we have a normal electron-pair bond and two odd-electron bonds, and this is equivalent to having two electron-pair bonds. 

The two odd-electron bonds retain the two unpaired electrons. We drew near those unpaired electrons arrows pointing in the same direction. As we explained in the Retouches in the previous lectures, an unpaired electron is a little magnet due to its spin. The spin has a direction up or down, which is indicated by the direction of the arrow. During the covalent bond pairing, these little magnets are arranged so that they cancel each other. However, when the electrons remain unpaired, like in Scheme 3.R.3b, the spin is not cancelled, and the molecule attains a magnetic property. 

As a consequence of the BOVB procedure, the active orbitals (those involved in the bond) can use this extra degree of freedom to adapt themselves to their instantaneous occupancies. The spectator orbitals (not involved in the bond) can fit the instantaneous charges of the atoms to which they belong. Thus, all the orbitals follow the charge fluctuation that is inherent to any bond by undergoing instantaneous changes in size and shape, hence the name breathing orbitals . The same philosophy imderlies the description of odd-electron bonds, in terms of two VB structures. 

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