Three-center MO model

Figure 3.84 An illustration of the Pimentel-Rundle three-center MO model of hypervalency, showing equilibrium valence AO (xa-/b-Xc) overlap patterns for (a) 2pF—2pF—2pF NAOs of the trifluoride ion, F3 and (b) 2pF—lsp—2pF NAOs of the bifluoride ion, FHF-.

The electronic structures of borane clusters were first successfully described using localized three-center- and two-center-two-electron bonds. These treatments have been replaced by the cluster electron-counting rule based on MO methods hence, why bother with the three-center bond model in a book about clusters Let s consider why there is value in a more localized approach. 

The VSEPR model works at its best in rationalizing ground state stereochemistry but does not attempt to indicate a more precise electron distribution. The molecular orbital theory based on 3s and 3p orbitals only is also compatible with a relative weakening of the axial bonds. Use of a simple Hiickel MO model, which considers only CT orbitals in the valence shell and totally neglects explicit electron repulsions can be invoked to interpret the same experimental results. It was demonstrated that the electron-rich three-center bonding model could explain the trends observed in five-coordinate speciesVarious MO models of electronic structure have been proposed to predict the shapes and other properties of non-transition element... 

Both the three-center bond model and the correlation diagram treatment, as just outlined, omit all central-atom orbitals except the s and p orbitals of the valence shell. Indeed the three-center bond model neglects even the s orbital except as a storage place for one electron pair. They can be described as very restricted or incomplete MO treatments. They are also inexact, even within their self-imposed limits, since numerical accuracy is neither sought nor obtained in their usual applications. It would not, of course, be sensible to strive for numerical precision after such sweeping assumptions have been made at the outset. On the other hand, the hybridization or directed valence treatment assumes very full involvement of outer d orbitals whenever more than four pairs of electrons must be accommodated. This extreme assumption is also unlikely to be accurate. Finally, the VSEPR model resorts to a simple electrostatic model, which, however successful it may be, can scarcely be taken literally. 

Qualitative MO descriptions consider the interaction of the F2p orbital with one of the antibonding 11 orbitals of O2, see [23 to 25]. Because of the high electronegativity of the F atom, very little electron density is released into n resulting in a weak 0-F bond (a (p-ji )o bond) and only a small reduction of the 0-0 bond order [26]. This model, however, was criticized and replaced by another three-center bonding model [34]. 

Pimentel employed this three-center, four-electron (3c/4e) MO model to discuss the bonding in triiodide (I3-), bifluoride (FHF-), and other prototypical hypervalent species. In triiodide and other trihalides, for example, the relevant AOs are the (pa, Pb, Pc) orbitals along the bonding axis,... 

Answer. The HOMO of I- is a filled 5p AO whereas the LUMO of I2 is the highest lying a-antibonding MO shown in Figure 1.3. Best overlap of the donor and acceptor orbitals will be achieved in a linear structure. As [13] is ahomonuclear compound this HOMO-LUMO analysis cannot be pushed too far and we will defer presentation of the MOs of a species like [L] until we develop a model for three-center bonds later in the chapter. 

Let us compare the MO descriptions of six and four sep R4E4 tetrahedral clusters. In Figure 2.5 the cluster MO energies for E = C and E = Ga are shown alongside the localized descriptions discussed above. The number of filled and unfilled MOs is equal for E = C a consequence of the two-center-two-electron bond model. Conversely, the number of filled MOs is less than the number of empty MOs for E = Ga a consequence of the three-center-two-electron bond model. Note also that an e symmetry pair of orbitals lies in between lower-energy filled orbitals and... 

Subsequently Cotton et al. [55] confirmed a short CH-Mo distance of 2.2 A in the Mo complex from X-ray crystallographic analysis and proposed the current three-center/two-electron (3c-2e) bonding model. More direct evidence... 

Of course, the octet is usually not actually violated. Multicenter bonding models require some MOs that are essentially nonbonding and concentrated only on the substituents, and thus, the number of electrons in the valence shell of the central atom rarely exceeds the octet. However, here we should distinguish, between what Musher [61] more than 40 years ago termed hypervalent compounds of first and second kind, respectively. In the first class, the central atom is not in its maximum oxidation state, and thus, the central-atom s-character concentrates in a Ip. Then, as we have discussed in detail above, the bonds are made mainly from np-orbitals of the central atom, and thus, the assumptions of the usual three-center-four-electron bonding models are nicely fulfilled. In contrast, hypervalent compounds of the second kind exhibit the maximum oxidation state and, thus, necessarily involve the ns-orbitals fuUy in bonding. One thus sees (i) extensive hybridization defects... 

The model most widely used to explain hypervalence is the three-center, four-electron (3c-4e) model of Rundle and Pimentel [5]. Coulson [31] analyzed the 3c-4e model and suggested a valence bond resonance model that shares some similarities with the MO model. Under this model, the bond is posited to arise primarily from resonance between F-X F and F X -F charge structures (with contributions from other charge configurations). Weinhold and Landis [32] incorporated natural bond orbital analysis and natural resonance theory in what is perhaps the most... 

Both unsymmetrical species F—F—0 (bent) and F—0=F (bent) were predicted [13] on the basis of the MO calculation for diatomic OF (see p. 67), which may form a weak o bond by overlap of a p orbital of a highly electronegative atom with one lobe of its jt orbital. However, this bonding model was criticized and replaced by a three-center model which does not support the unsymmetrical FFO species [16]. Heats of formation, calculated by the MNDO method [14] for (symmetrical) FOF (18.2 kcal/mol) and for FFO (125.8 kcal/mol), show the former to be the more stable species [15]. 

In the previous section, we met three situations where the localized bond model fails. In each case, we had to represent bonding in terms of MOs covering three or more atoms, formed by overlapping of AOs on them. Now the general rules for formation of such many-center MOs are basically the same as for normal two-center bonds. The AOs involved must be of comparable energies (i.e., all from valence shell AOs of the participating atoms) and they must overlap in space. How they overlap is not important. There is no basic distinction between the 7r-type overlap of p AOs in benzene (Fig. 1.37), the linear a-type overlap in the transition state of Fig. 1.39, and the nonlinear a-type overlap of AOs in diborane (Fig. 1.36). All three situations are equivalent in terms of MO theory. The distinction between them arises solely from quantitative considerations of the efficiency of overlap and the energies of the orbitals involved. 

Another approach for studying the electronic structure of boranes uses the localized three-center bonds arising from the Lipscomb topological models (section II.A) as the basis set for Huckel-type MO computations. Kettle and Tomlinson showed that this method leads to the same pattern of MO energy levels as the LCAO methods of Lipscomb. Subsequent work showed that this method is a topologically correct extension of Hiickel theory to three dimensions. 

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