Digonal hybridization

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... 

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. 

As a result of complex formation, the normally linear digonally hybridized triple bond bends to approximately 145°. Two 7i-bonds in the triple bond coordinate to two Co atoms, respectively, as shown by 130. In the following discussion, the simplified form 131 is used instead of 130 in most cases for simplicity. 

Divalent beryllium bonds through two equivalent sp, or digonal, hybrids. The appropriate ionization energy therefore is not that of ground state beryllium, s 2s, but an average of those energies necessary to remove electrons from the promoted, valence state ... 

Since the AOs of the hybridized basis are now properly directed along the z axis, we see that in the range 0 < w < 45° (namely, from pure p to equivalent digonal hybrids) /3a, decreases and /3, h increases from the value assumed for co = 0. The transformed Hiickel matrix ... 

Hiickel (4n + 2) rule Monocyclic planar (or almost planar) systems of trigonally (or sometimes digonally) hybridized atoms that contain [An + 2) Jt-electrons (where n is a nonnegative integer) will exhibit aromatic character. The rule is generally limited ton = 0-5. 

A localized MO view of nitrogen can be arrived at with the help of GO s obtained by hybridizing those canonical GO s which gave rise to the occupied delocalized MO s. The lowest two MO s i//1 and p in Fig. 7 were generated by an s and a px GO, respectively. We hybridize these two to yield the digonal hybrids... 

Schematic illustration of the formation of sp digonal hybrid orbitals by combination of an j and a p orbital.

An atom, X, using a pair of such sp or digonal hybrid orbitals, will form two equivalent bonds to two other atoms or univalent groups, Y, giving a linear YXY molecule. The gaseous halides (though not the solid compounds) of most of the Group II elements have linear structures which may be attributed to the sp hybridization of the metal atoms. Of course, a completely... 

A classical transformation combining two structures is via fusion. For two cycles each with an adjacent pair of sites each combined with no more than two other nonhydrogenic atoms an edgefusion merges the two pairs to a single pair as in Figure 29. Thence this is applicable to the presently considered structures if one initially has two pairs of adjacent digonally hybridized sites. It is realized that the two cycles involved in fusion need not be simple cycles but could have other attachments (away from the fusion). 

Other types of fusion are possible, particularly site-fusion where two digonally hybridized sites are merged and ring-fusion where two like-sized rings are merged together. But this usually leads to tetrahedrally hybridized sites not considered within the focus of the present discussion. 

Let s and d be the hybridization parameters which define the digonal hybrid bond orbital, i the ionicity parameter of the bond, and 7T the eventual double-bond character the field gradient is then found to be ... 

The electron pair (1) may be described by a two-electron function such as Eq. (30), built up by a combination of the %b orbital (tetrahedral or trigonal) of the carbon atom with a digonal hybrid Xa of the chlorine atom of the t q)e ... 

The pair (2) may be described by a second digonal hybrid of the chlorine atom, orthogonal to the first.f Finally, the two remaining pairs may be represented, in a first approximation, by the orbitals and 3/ , of the chlorine atom. 

Since there are only two covalent bonds to the Be atom, the maximum angle separating the axes of the two hybrid AO s should be 180 (Fig. 19.4), which is the observed value. Because of this orientation, the sp hybrid orbitals are also called DIGONAL HYBRID ORBITALS. 

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