Nonbonding overlap

Fig. 4-10.—The effect of hybridization of a w orbital. At the left is shown the angular dependence of orbital strength for a pure pic orbital, px (z axis vertical). At the right is shown a 7r orbital with 4.5 percent d character. It is seen that the d character increases overlap of the orbital with a similar orbital to the right (bonding overlap) and decreases overlap with a similar orbital to the left (nonbonding overlap).

Nonbonding overlap is significantly larger for 1 and leads to a shift of electron density into the three-membered ring. This is one important aspect of the VB calculations of Karadakov and coworkers (not mentioned by the authors)51, which becomes obvious when looking at the VB hybrid orbitals depicted in Figure 8. 

Figure 12 Different types of overlap encountered in the solid-angle measure, (a) In the process of projection, overlap that does not appear in the ligand appears in the projection. This overlap is called nonbonded overlap, (b) When two atoms physically overlap, the overlap in the projection is called bonded overlap. (From Ref. 48.)...

Condensed polycyclic benzenoid aromatic hydrocarbons are customarily regarded as planar molecular structures because of the geometrical constraints of carbon atoms in a state of sp2 hybridization. A well-known exception is the class of compounds called the helicenes (18) for which the nonbonded overlap of two terminal benzenoid rings in a cata-condensed structure, as in structure 1, forces a molecule into a nonplanar helical structure. A second exceptional class of compounds is related to corannulene (2) and other an-nulenes of this type (19, 20). In corannulene, strain associated with the pericondensed five- and six-membered rings requires adoption of a bowlshaped structure (20, 21). For both structures 1 and 2 the aromatic character of the benzenoid rings is retained to an appreciable extent. 

The qualitative energy levels of appropriate to P, T and G N2H would be radically different had we assumed that nonbonded overlap of the hydrogen Is AO s Is zero. In such an event, we would have obtained the symmetry orbitals shown In Figure 3b. Note that now excitation or deexcitation can no longer be defined simply because all four MO s are degenerate. We will see that assumption of one or the other MO patterns makes a "night-day" difference Insofar as the final prediction of the preferred geometry of N2H Is concerned. 

Since it is alway possible to replace N and/or H by some other atom or group so that geminal nonbonded overlap tends to zero and determine how the conformational equilibrium is affected by such a change, it is evident that MOVB theory lead to hard testable conclusions. 

Once we have properly understood why N2H is gauche, the reason for the fact that N2p shows no comparable preference for the gauche geometry becomes self-evident. Specifically, because of the smaller spatial extension of the fluorine valence AO s, geminal nonbonded overlap between F and F in N2p is much smaller than between H and H in N2H (see Table 1). As a result, the motivation for the T G transformation largely ceases to exist and N2p tends to adopt a T, rather than a G, geometry for reasons explained above. In addition, the N-N bond becomes... 

Minimization of nonbonded overlap repulsion. None, assuming nonbonded AO overlap to be zero. Minimization of nonbonded overlap repulsion. Minimization of coulomb repulsion... 

First some technical details If we symbolize each propellane by ML3M (M = C, Ge and L = CH2, CO), the basis AO s are the valence AO s of each M and the n and 2p AO s of each L with a total of 14 electrons. The bond diagram for 2(012)3 and drawings of the orbitals can be found in our previous published work. In Fig. 31, we indicate the type of each set of ligand MO s (n-type and 2p-type) assuming for simplicity, zero L—L nonbonded overlap. 

Refinements in three-dimensional space typically start from distance geometry structures, and attempt both to preserve the covalent geometry of the protein and to satisfy the constraints derived from the NMR measurements. The function to be optimized is almost always a sum of terms representing the energetics of the molecule per se and the experimental constraints. The molecular terms may be represented by simplified functions that maintain bond distances and angles and prevent nonbonded overlaps or by use of more realistic molecular mechanics expressions. 

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