Directed orbitals

It is sometimes convenient to combine aos to form hybrid orbitals that have well defined directional character and to then form mos by combining these hybrid orbitals. This recombination of aos to form hybrids is never necessary and never provides any information that could be achieved in its absence. However, forming hybrids often allows one to focus on those interactions among directed orbitals on neighboring atoms that are most important. 

In the Hiickel treatment, atomic orbitals on nonadjacent atoms are assumed to have no interacticai. They are neither bonding nor antibonding. The concept of homoconjugation suggests that such orbitals may interact, especially in rigid structures which direct orbitals toward one another. Consider, for example, bicyclo[2.2.1]hepta-2,S-diene ... 

The diagrams also indicate why neutral c/oio-boranes BnHn4.2 are unknown since the 2 anionic charges are effectively located in the low-lying inwardly directed orbital which has no overlap with protons outside the cluster (e.g. above the edges or faces of the Bg oct edron). Replacement of the 6 Ht by 6 further builds up the basic three-dimensional network of hexaborides MB6 (p. 150) just as replacement of the 4 H in CH4 begins to build up the diamond lattice. 

Once again we see how the planar geometry is stabilized by removal of repulsive electrons from the d y (ligand-directed) orbital. The achievement of planar... 

We generate hybrid orbitals on inner atoms whose bond angles are not readily reproduced using direct orbital overlap with standard atomic orbitals. Consequently, each of the electron group geometries described in Chapter 9 is associated with its own specific set of hybrid orbitals. Each type of hybrid orbital scheme shares the characteristics described in our discussion of methane ... 

With a steric number of 5, chlorine has trigonal bipyramidal electron group geomehy. This means the inner atom requires five directional orbitals, which are provided hymsp d hybrid set. Fluorine uses its valence 2 p orbitals to form bonds by overlapping with the hybrid orbitals on the chlorine atom. Remember that the trigonal bipyramid has nonequivalent axial and equatorial sites. As we describe in Chapter 9, lone pairs always occupy equatorial positions. See the orbital overlap view on the next page. 

Frequently, directionality is a property attributed to the covalent bond which supposedly is taken to be the cause of the resulting structures. However, as the success of the valence electron pair repulsion theory shows, there exists no need to assume any orbitals directed a priori. The concept of directed orbitals is based on calculations in which hybridization is used as a mathematical aid. The popular use of hybridization models occasionally has created the false impression that hybridization is some kind of process occurring prior to bond formation and committing stereochemistry. 

Analogous considerations apply for tetracoordinate fragments M(CO)4. Fig. 30 shows some of the possible conformations of these fragments. As before, the directional orbitals that develop for particular values of the angle 6 (refer to Fig. 30) allow prediction of possible interaction with donors or of dimerization. Also, the level shifts for variation of 6 in both cases can be calculated, as well as for the squashing mode rearrangement of a tetrahedral into a square-planar coordination. The qualitative confomiational preferences implied by these patterns have been checked, as for the pentacoordinate case, by comprehensive EHT calculations for all dn systems of all conceivable symmetries. 

Although the exchange mechanism was originally formulated in terms of direct orbital overlap between the donor and acceptor chromophores, it is clear that it can be extended to cover the case of through-bond mediated EET. The reason is because TB coupling provides a mechanism for spatially extending the active orbitals of the two chromo-... 

The --system is certainly directional. That is, there is a p-orbital, which is shared between the trans ligand and the leaving group, which I will call L. This is the one-directional - orbital involving L. 

It is now possible to draw a correlation diagram between the states, as shown in Figure 7.13. The crucial feature to note here is that the Ax to Ax correlations which would seem to follow from direct orbital,correlations cannot and do not actually occur, because of what is called the noncrossing rule. Two states of the same symmetry cannot cross, in the manner indicated by the dotted lines, because of electron repulsion. Instead, as they approach they turn away from each other so that the lowest 4, states on each side are correlated with each other as shown by the full lines. The repulsive interaction is similar in essence to that involved in configuration interaction in naphthalene, as discussed in Section 7.6. Indeed, the noncrossing rule is no more than a special but straightforward instance of configuration interaction. 

We see that by alternately using a plus and minus in front of the 2p orbital we obtain an electronic density which is concentrated to the right or to the left of the original center of gravity. Forming such a directional orbital, however, requires energy. Figure 4-2 shows this schematically. 

Since the coefficients in (5) are each not less than the corresponding coefficient in (4), the desired directed orbitals are possible. In fact, since we have a choice between 5 and dt for the orbital... 

Quinone methides are strikingly different from the 1,2- and 1,4-isomers, because there is no direct orbital interaction between the meta-oxygen and carbon substituents at the benzene ring. Consequently, the neutral valence bond resonance form for the 1,3-quinone methide is a triplet biradical (Scheme 1). These 1,3-quinone methides are chemically more unstable and difficult to generate than their 1,2- and 1,4-isomers, which exist as stable neutral molecules.8... 

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