Pauling 3-Electron Bonds and Increased-Valence Structures

We are now ready to examine in detail the incorporation of the Panling 3-electron bond stmcture A B into the valence-bond structures for electron-rich molecules that involve 4-electron 3-centre and 6-electron 4-centre bonding units. To do this, we may nse any of three alternative methods. In this Chapter, we shall 

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Pauling 3-Electron Bonds and Increased-Valence Structures for N2O4... 

We are therefore led to conclude that all increased-valence structures for 4-electron 3-centre bonding units can have Pauling 3-electron bonds as components of their valence-bond structures. And because the phenomenon of 4-electron 3-centre bonding occurs extremely frequently, it follows that the relevance of Pauling 3-electron bond and increased-valence theory for qualitative valence-bond descriptions of electronic structure is very great. The need for an increased-valence theory has also been implied by Bent in his review on inter- and intramolecular donor and acceptor complexes. 

Relative to the octet Lewis octet structures (1) and (4), structures (2) and (5) as well as structures (3) and (6) exhibit increased-valence , i.e. more electrons participate in bonding than does occur in structures (1) and (4). In this Chapter (and throughout this book), we refer to valence bond structures that involve one or more Pauling 3-electron bonds as increased-valence structures. 

The geometry for a cis dimer of SO has been reported (Table 11-4), with S-S and S-0 bond-lengths of 2.025 and 1.458 A. The SO monomer, with two Pauling 3-electron bonds in its valence-bond structure (31), has a bond-length of 1.481 A. On dimerization, increased-valence structure (59), with fractional S-S o- and 7i-bonds, is obtained. Inspection of structures (31) and (59) makes clear why the SO bond-lengths for the monomer and dimer are similar, and why the S-S bond for the dimer (with an S-S bond-number < 2 in structure (59)) is appreciably longer than the length of 1.89 A for the double-bond of S2. 

For 6-electron 4-centre (and longer JV-centre) bonding units, similar types of properties exist for most of the increased-valence structures. For example, by spin-pairing the odd-electrons of the Pauling 3-electron bond stmctures A B and C i), increased-valence structure A - B—C - D for 6-electron 4-centre bonding units is obtained. This structure summarizes resonance between the Lewis... 

Resonance between the Pauling 3-electron bond structures (7) and (8) (or (9) and (10)) do not account for one NOj bond-property. The N-O bond-lengths of 1.19 A are similar to Pauling s estimate of 1.20 A for an N-O double bond (cf 1.214 A for CHjN = O f. However, resonance between stractures (7) and (8), each of which has seven bonding electrons, would imply that the N-O bonds for NO2 should be longer than double bonds. To obtain an additional bonding electron in each structure, it is necessary to utilize the increased-valence procedures that we shall describe in Chapters 11 and 12. 

In Fig. 11-3, the orbital occupations and electron spins are displayed for two equivalent Pauling 3-electron bond structures A-B and C-D. When the atomic orbitals of these two structures overlap, spin-pairing of their (antibonding) unpaired-electrons generates the increased-valence structure (46), for which a total of four electrons can participate in fractional A-B, A-C, A-D, B-C, B-D and C-D bonding . 

The third method for generating increased-valence structures utilizes the molecular orbital description of the Pauling 3-electron bond in terms of bonding and antibonding orbitals. 

For increased-valence structure (13), the bonding and antibonding molecular orbitals for the Pauling 3-electron bond components of stractures (16) and (17) are given by Eqs. (11) and (20) when A and D, and B and C are pairs of equivalent atoms. We shall now use these orbitals to deduce that the B and C valencies of increased-valence structure (13) can exceed unity in value. 

It seems now that both Samuel and Wheland held the widespread opinion that valence-bond structures for diamagnetic molecules must only have electron-pair bonds. Samuel and Wheland had attempted to transform the molecular orbital configurations for N2 and NO so that they would obtain electron-pair bonds for N2O. But neither worker used the correct procedure to obtain valence-bond stractures from diatomic molecular orbital configurations with one or more singly-occupied anti-bonding molecular orbitals. The technique that should be used was developed by Linnett in 1956 , and then by Green and Liimett in 1960 °, and it has formed the primary Pauling 3-electron bond basis for the increased-valence theory we use in this book. When this theory is applied to the excited Nj and NO... 

Because I2 has a single bond, the extra electron of I must occupy an antibonding molecular orbital. Therefore, the valence-bond structure for 1 must be the Pauling 3-electron bond structure ("I I ). By spin-pairing the unpaired electrons of Ij and McjN", we may represent MejN — 1 by the increased-valence structure (3), and describe (approximately) the electronie stmcture of the complex in terms of resonance between structures (2) and (3). 

Resonance between stractures (l)-(4) generates two Pauling 3-electron bonds as in (5), with the spin distributions of (6) and (7), in which the crosses (x) and circles (o) represent electrons with +V2 and -I/2 5 spin quantum numbers. The molecular orbital configuration for each of the structures (5)-(7) involves two B-C and two A-D bonding electrons, and one B-C and one A-D antibonding electron. On spin-pairing the two antibonding electrons, increased-valence structure (8) is obtained. 

As discussed in both volumes, singlet diradical structures help the standard Kekule-type structures to internet. Resonance between these two types of Lewis structures generates electronic hypervalence - for example a possible valence greater than four for the central nitrogen atom of N2O - and is needed to ensure that valence-bond formulations of mechanisms for Sn2 and 1,3-dipolar cycloaddition reactions are those for concerted reactions. Also, as will be shown in Chapter 25, Pauling 3-electron bonds are components of increased-valence struetures for (non electron-rich) 3-electron 3-centre bonding units. 

For the ground-states of other electron-rich molecules, the results of valence-bond calculations from different laboratories - see for example references 24-29 of Chapter 2 - also indicate also indicate that long-bond structures are more important than is usually supposed, and therefore they need to be included in qualitative valence-bond descriptions of their electronic stmcture. This book describes how this can be done, and some of the resulting consequences for the interpretation of the electronic structure, bond properties and reaction mechanisms for various electron-rich molecules. When appropriate, molecular orbital and valence-bond descriptions of bonding are compared, and relationships that exist between them are derived. Considerable attention is given to the use of Pauling 3-electron bonds (A--B as A-B) for providing qualitative valence-bond descriptions of electronic structure. The increased-valence structures for electron-rich molecules - for example... 

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