Axial hybrid orbitals

Now the two axial hybrid orbitals, each of which has one electron, overlaps with the 3px orbital (singly-filled) of two Cl-atoms to form two IC1 s-bonds. Due to the presence of Ips, IC12- ion assumes linear (symmetrical) shape... 

Although the spatial arrangement of six electron pairs round I-atom is octahedral, due to the presence of two lone pairs of electrons in the axial hybrid orbitals, the shape of IC14- ion gets distorted and becomes square planar as shown in Fig. 

The hybrid orbital has cylindrical symmetry, and accordingly the introduction of d character and f character in the axial bond itself does not lead to an interaction dependent on the relative azimuthal orientation of the two groups. 

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. 

The axially symmetric metal carbonyl fragments M(CO)n (n = 1, 3, 4) have three outpointing hybrid orbitals with a high proportion of s and p orbital character, which are suitable for forming cluster skeletal molecular orbitals (77, 78, 238). The number and radial characteristics of these frontier molecular orbitals, which are illustrated schematically in Fig. 26a, are reminiscent of the frontier orbitals of a main group diatomic hydride fragment E—H, where E = C or B (Fig. 26b). To describe this similarity the term isolobal has been introduced (77). Molecular orbital... 

The or-MOs are bonding type with axial symmetry. They are formed by overlap of s or pt orbitals or hybrid orbitals like sp, sp, sp8, etc. along the direction of the bond. They form strong single bonds with two spin paired electrons localized between the combining atoms. 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

However, there is no reason at all to assume ha and hb are made up of only pz and dz2 orbitals The dz2 orbital can also contribute to the equatorial hybrids, and the s orbital can also contribute to the axial hybrids. In fact, if we use only the s and pz orbitals for the axial hybrids, and the dz2, px, and p-y for the equatorial hybrids, we then have... 

At r, the and p Bloch sum interactions are not symmetry allowed. Nor is the hybridization between the d and py Bloch sums. The d orbital at the origin does, however, have a tt antibonding interaction with the axial p orbitals (not shown) directly above and below it. In other words, the d orbital at the origin only interacts with two of the six first-nearest neighbor oxygen atoms. 

Although it will not be important for our purposes, the dsp3 hybrid orbital set is different from the hybrids we have considered so far in that the hybrid orbitals pointing to the vertices of the triangle (often called the three equatorial hybrid orbitals) are slightly different in shape than the other two (the axial orbitals). This situation stands in contrast to the sp, sp1, and sp3 hybrid sets in which each orbital in a particular set is identical in shape to the others. 

Most sets of hybrid orbitals are equivalent and symmetric, that is, four sp orbitals directed to the comers of a regular tetrahedron, six tPsp orbitals to the corners of an octahedron, etc. (n the case of hybrids the resulting orbitals are not equivalent. In the trigonal bipyramidal arrangement three orbitals directed trigonally form one set of equivalent orbitals (these may be considered sp hybrids) and two orbitals directed linearly (and perpendicular to the plane of the first three) form a second set of two (these may be considered dp hybrids). The former set is known as the equatorial orbitals and the latter as the axial orbitals. Because of the nature of the different orbitals involved, bonds formed from the two are intrinsically different and will have different properties even when bonded to irJenlica] atoms. For example, in molecules like PFj bond lengths differ for axial and equatorial bonds (see Chapter 6). 

FIGURE 8.30 (a) Hybrid orbitals formed from linear combinations of Pm P>r and orbitals. The pair of orbitals that point along the positive and negative z-axes are the same except for their orientation in space they are called axial orbitals. The set of three orbitals in the x-y plane are equivalent to one another and are called equatorial orbitals, (b) This set of hybrid orbitals can be used to describe the bonding in PF5, for example. 

As shown in Figure 8.30a, these orbitals point to the vertices of a trigonal bipyramid there are three equivalent equatorial hybrids and two eqnivalent axial hybrids. Examples of molecules whose shapes are described by dsp hybridization inclnde PF5, which you have seen in Section 3.9, and CnCl C PF5 is shown in Fig-nre 8.30b for comparison with the set of dsp hybrid orbitals. 

BiXs has three equatorial bonds, made from the usual sp hybrid orbital, and two axial bonds which use the three-center four-electron bonding, two electrons from the p orbital of bismuth and two electrons from the X ligands [94B-N]. In the three-center four-electron bonding, the central atom should be positively charged. This has been confirmed for MH5 (M = P, As, Sb, Bi) with recent ab initio calculation [95JA11790]. 

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