Increased-valence-structure

Where appropriate, increased-valence structures [2-5] will be used to provide qualitative VB representations of electronic structure. Increased-valence structures involve localised one-electron and fractional electron-pair bonds, as well as "normal" electron-pair bonds [2-5]. These features will be re-described by reference to HCNO. 

Kekule, Dewar and increased-valence structures for HCNO... 

The electronic structures of C2-symmetry N6 and quasi-linear (CNO)2 have attracted some attention recently [8,9]. The results of ab initio MO studies [8,9] indicate that these two species are respectively unstable and bound relative to their N2 and CNO dissociation products. The VB structures that we shall use to represent the primary features of the electronic structures of N6 and (CNO)2 are examples of increased-valence structures [2-5], Such structures may be generated from familiar (Kekul6-type) Lewis structures by delocalising non-bonding electrons into bonding localised MOs (LMOs). 

When Heitler-London AO-type wavefunctions (i.e.. ..aabP +. ..baaP in which a and b are AOs) are used to represent electron-pair 7i c(CN) and 7i y(CN) bonds, it can be deduced [2,4,16, cf. also Eq.(ll) below] that VB structure 7 is equivalent to resonance between the Kekule Lewis structure 3 and the Dewar or "long-bond" Lewis structures 11-13. Only nearest-neighbour spin-pairing is indicated in increased-valence structures [2-5,10]. When the "long" or formal bonds are omitted from structures 11-13, these structures are designated as singlet diradical structures [2-4]. 

Because 7 = 3<- ll<- 12<- 13, increased-valence structure 7 involves fractional kx(CN) and 7iy(CN) electron-pair bonds [2,4,10-14,16]. Therefore its C-N bond-number, or bond-order is less than 3. A thin bond line is used to represent a fractional electron-pair bond [2-4]. An N-O double bond, which consists of an electron-pair a bond, and one-electron nx and ny bonds, is also present in this VB structure. With these bond properties, the N-0 and C-N bond-lengths that are implied by increased-valence structure 7 are in accord with the following observations with regard to its bond-lengths [171 ... 

The corresponding wavefunction for the 7i-electrons of increased-valence structure 7 is given by Eq.(9),... 

For quasi-linear (CNO)2, as ONC-C N O, the Kekule and increased-valence structures 14 and 15... 

The Kekule-type Lewis structure 24 is a component of the primary increased-valence structure 25. The presence of lone-pair electrons on the Nc and N c atoms of structure 24 correlates with the calculated bending that occurs at these atoms to generate the C2 geometry. For (CN0)2, the Nc and N c atoms of N6 are replaced by the carbon atoms, and the absence of lone-pair electrons for these atoms in the Lewis structure 14 permits the molecule to adopt either a linear or a quasi-linear geometry. 

Increased-valence structure 36 for N20(CooV) is analogous to increased-valence structure 7 for isoelectronic HCNO. It has been used recently to develop a VB representation for the N20(CooV) - N20(cyclic,C2V) —> NON(Dooh) isomerization process [32]. In Ref. [10], comparisons are made between 36 and other VB structures with apparently quinquevalent nitrogen atoms, and in Section 4.3, 36 provides the VB representation for N2O when it is formed in NCO-NO and OCN-NO2 decomposition reactions. 

The increased-valence structures 39 and 45 for CH2N2 and CH3NO2 are generated from the Kekule-type Lewis structures 37 and 42 via the one-electron delocalisations that are indicated in structures 47 and 48. More... 

Alternative VB representations for the cycloaddition process are displayed and discussed in Refs. [2,10,19,34], Some of them also include the less-important increased-valence structures, such as 8-10 here, in the resonance schemes. Recent MO [35] and spin-coupled VB [36] studies for this process do not give consideration to the concerted diradical formulation. The VB studies of Ref. [37] correspond to the concerted diradical mechanism discussed in Ref. [34]. 

Increased-valence structure 79 retains the double-bond character for each of the O2 moieties. This structure also involves fractional intermolecular 0=0 bonds - their a and n bond-numbers are both equal to 0.25 [43] - thereby implying that the latter bonds should be substantially longer than normal 0=0 bonds. These bond properties are in accord with calculated estimates of the 0-0 bond-lengths for O4 (1.21 and 3.2-3.5 A [43]). However the results of ST0-6G VB calculations show that the and n y-n y spin-pairings alone are... 

By analogy with S2O2 and O4, an S = 0 state for Fen02FeH, with an increased-valence structure of type 65, but with opposed spins for the two... 

With S=S replacing 0=0 in VB structure 78, the primary increased-valence structure for C2 symmetry S2O2 is obtained [2,4,51]. 

One-electron and three-electron chemical bonding, and increased-valence structures... 

Valence bond and molecular orbital approaches to descriptions of one-electron bonds and Pauling three-electron bonds are reviewed, and attention is given to the incorporation of Pauling three-electron bonds into the valence bond structures for molecular systems that involve four-electron three-centre, five-electron three-centre and six-electron four-centre bonding units. Many of these valence bond structures are examples of increased-valence structures. Examples are provided for a few of the large number of phenomena that involve these types of bonds and valence bond structures. 

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. 

THREE-ELECTRON BONDS AND INCREASED-VALENCE STRUCTURES FOR FOUR-ELECTRON THREE-CENTRE BONDING... 

Because the three-electron bond structure is equivalent to resonance between structures Xa and Xb, it follows from eq.(3) that resonance between the Lewis structures XIX (or XVII) and XVIII is equivalent to use of the VB structure XX. In XX, a thin Y-A bond line is used to indicate that the Y-A bond-number in this structure is fractional, i.e. its bond-number is less than the value of unity that obtains for the Kekule Lewis structure XVIII [4-6,46]. (The fractionality is a consequence of the absence of a Y-A bond in structure XVII [4-6,46].) Valence bond structure XX is an example of an increased-valence structure for a four-electron three-centre bonding unit [4-6,37,38]. It may always be generated from the Lewis structure of type XVIII by delocalizing a non-bonding b electron into the bonding MO v fab, as is indicated in XXI — XX... 

INCREASED-VALENCE STRUCTURES AND MULLIKEN-DONOR-ACCEPTOR COMPLEXES ... 

Valence-bond structure XXVI is an example of an increased-valence structure when LMOs are used to accommodate the three (fractional) bonding electrons [38], Elsewhere, it has been deduced that the A-atom valence is able to exceed unity in each of the VB structures XX [46] and XXVI [38], Increased-valence structures of the type XXVI will be used in the discussion of Sn2 reactions which is provided in the next section. 

OCIOCIO2 has been identified recently [54], The resulting (equivalent) VB representations [53] involve either nine Lewis structures, or four increased-valence structures, each of which involves two three-electron bonds, or one increased-valence structure with four three-electron bonds. The latter increased-valence structure is displayed in Figure 9, together with an increased-valence structure in which the locations of the three-electron bonds have been interchanged [53],... 

Figure 10. Construction of increased-valence structures for NO2 and N2O4 from Lewis and three-electron bond structures.

Example of increased-valence structures, and the Lewis structures and three-electron bond structures from which they may be derived, are displayed in Figure 10 for NO2 and N2O4. These two molecules involve four-electron three-centre and five-electron three-centre bonding units. N2O4 also possesses six-electron four-centre bonding units that are components of a ten-electron six-centre bonding unit. 

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