Digonal orbitals

The sp orbital (known as a digonal orbital) is a merger of an s and a p orbital which consists of two lobes, one large and one small, as illustrated in Fig. 2.18. An sp bond consists of two sp orbitais which, because of mutual repulsion, form an angle of 180° and, consequently, the sp molecule is linear. The bond, like all overlap bonds, is a sigma (a) bond and has high strength. The sp orbitals account fortwo of the electrons of the carbon atom. The other two valence electrons are free, delocalized pi n) orbited electrons which are available to form subsidiary pi (n) bonds in a manner similar to the sp hybridization. 

Figure 4.1 Mixing of atomic orbitals to give hybrid orbitals capable of generating digonal 2-coordination. (From J.E. Huheey, Inorganic Chemistry, Harper and Row, London, 1975. Reprinted by permission of Addison-Wesley Educational Publishers Inc.)...

It certainly does not seem that these interactions continue in solution, so that their magnitude is weaker than solvation forces. Theoretical explanation has suggested that the unused, filled, 6s-5dz2 hybrid (section 4.1) interacts with vacant 6px,py orbitals at right angles to the digonal bonds (Figure 4.49). 

Figure 3.17 Geometry of hybrid orbitals, (a) digonal sp hybrids oppositely directed along the same axis (b) trigonal sp2 hybrids pointing along three axes in a plane inclined at 120° (c) tetrahedral sp3 hybrids pointing towards the comers of a regular tetrahedron. (Reproduced with permission from R. McWeeny, Coulson s Valence, 1979, Oxford University Press, Oxford.)...

There exists no uniformity as regards the relations between localized orbitals and molecular symmetry. Consider for example an atomic system consisting of two electrons in an (s) orbital and two electrons in a (2px) orbital, both of which are self-consistent-field orbitals. Since they belong to irreducible representations of the atomic symmetry group, they are in fact the canonical orbitals of this system. Let these two self-consistent-field orbitals be denoted by Cs) and (2p), and let (ft+) and (ft ) denote the two digonal hybrid orbitals defined by... 

Similar, but different, redeployment is envisaged when a carbon atom combines with three other atoms, e.g. in ethene (ethylene) (p. 8) three sp hybrid atomic orbitals disposed at 120° to each other in the same plane plane trigonal hybridisation) are then employed. Finally, when carbon combines with two other atoms, e.g. in ethyne (acetylene) (p. 9) two sp hybrid atomic orbitals disposed at 180° to each other digonal hybridisation) are employed. In each case the s orbital is always involved as it is the one of lowest energy level. 

The first three geometries involve the tetrahedral, trigonal, and digonal hybrids discussed above and the fourth involves the use of pure s and p orbitals as discussed on page 149. The last structure contains three equivalent bonds at mutual angles of 60 and a fourth bond at an angle of approximately 145° to the others. U is impossible to construct s-p hybrid orbitals with angles less than 90°, and so structure V is ruled out. In this sense it may be sard that hybridization does not allow" structure V, but it may not be said that it "chooses ore of the others. Carbon hybridizes sp, sp2, and spJ in various compounds, und the choice of sp3 in methane is a result of the foot that the tetrahedral structure is the most stable possible. 

Atomic orbitals of this mixed type are usually referred to as hybrids (or more specifically digonal dimensional model, they reinforce on one side of the nucleus and partly cancel on the other. Hence the transformation is from the delocalised s and p description to a description in terms of two equivalent orbitals, localised cn opposite sides of the nucleus. Again a similar transformation may be applied to a 4 X 4 determinant describing a system with two electrons in each of these orbitals. 

The greater stability of the digonal vinyl cation 161 than of the bridged cation 162 would imply that, at least in the gas phase, race-mization is involved as stereochemical course of any reaction with nucleophiles since both lobes of the empty p-orbital of 161 are available for a nucleophilic attack. Efforts to rationalize (Bumelle, 1964) early reports of stereospecific trans addition to acetylene derivatives have recently been complemented by a theoretical calculation of the energy profile for addition of hydrogen fluoride to acetylene in the gas phase (Hopkinson et at., 1971). The results of these calculations suggest that the bridged cation is possibly a transition state and not an intermediate. 

Our initial interest in this area arose from the observation that the orbitals of the commonly accepted planar geometry of the parent nitrile ylide do not correctly account for the cycloaddition regioselectivities observed for these species. Thus, as shown by the examples in Fig. 14, the digonal carbon is the nucleophilic center of the molecules, whereas the HOMO of the planar species has the largest coefficient at the trigonal carbon, which should, therefore, be the more nucleophilic center of the molecule. However, full optimization of the geometry of nitrile ylide using the... 

Fig. 9. The digonal twist motion interconverting square-planar (Dti,) and tetrahedral (Trf) structures by D d and showing orbital correlations.

These are illustrated in Fig. 41 and are called digonal sp hybrids they are exactly similar or equivalent except in orientation. Clearly, a plausible description of the za MO in HF could be obtained by overlapping h with the hydrogen Is AO and using hg as the lone pair orbital, ya. This would not be the best description because there is no reason, here, for choosing a pair of exactly similar hydrids but it is still qualitatively useful. More generally. 

With the admission of d orbitals the number of principal types of hybridisation is increased from 4 (pure p, digonal, trigonal, tetrahedral) to over 40 fortunately only a few of these lead to systems of strong bonds. 

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