Relationships between Different Types of Delocalized Systems

16 Relationships between Different Types of Delocalized Systems 

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. 

FIGURE 1.40. (a, b) Overlap of carbon 2p AOs in cyclopropenium, seen from (a) the side and (b) above (c) overlap of B and H AOs in three-center bonds of diborane (d, e) overlap of carbon 2p AOs in the allyl anion, seen from (d) the side and (e) above overlap of carbon 2p AO with AOs of I and Cl in the transition state of Fig. 1.39. 

Since the choice of signs or phases of our basis set AOs that we use to construct MOs is arbitrary, it is convenient to use some convention in choosing them to avoid unnecessary confusion. An obvious choice is to pick the phases in such a way that AOs overlap in phase, i.e., positive parts of AOs overlap with positive parts and negative parts with negative parts. 

In most cases, we can carry out this program completely so that there are no phase dislocations where AOs overlap out of phase with one another this was true in the cases indicated in Figs. 1.36-1.40. As indicated, we can pick the signs (phases) of the AOs so that positive overlaps with positive and 

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