Trigonal bipyramidal arrangement hybrid orbitals

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 3.20 One of the five sp3d hybrid orbitals, and their five directions, that may be formed when d-orbitals are available and we need to reproduce a trigonal bipyramidal arrangement of electron pairs. 

SOLUTION According to Example 3.3, SF4 has a trigonal bipyramidal arrangement of electron pairs. We can construct five equivalent hybrid orbitals by mixing an s-orbital with three p-orbitals and one d-orbital. The result is five sp3d orbitals. 

Hybridization of five atomic orbitals occurs by a combination of one s orbital, three p orbitals, and one d orbital, giving five sp3d hybrid orbitals in a trigonal bipyramidal arrangement (Figure 7.12). Three of the hybrid orbitals lie in a plane at angles of 120°, with the remaining two orbitals perpendicular to the plane, one above and one below. 

A set of dsp3 hybrid orbitals on a phosphorus atom. Note that the set of five dsp3 orbitals has a trigonal bipyramidal arrangement. (Each dsp3 orbital also has a small lobe that is not shown in this diagram.)... 

Fig. 4.7 A schematic representation of sp d hybridization, (a) A combination of s, Px Py Pz and atomic orbitals gives a set of live sp d hybrid orbitals corresponding to a trigonal bipyramidal arrangement the axial sp d hybrid orbitals are directed along the z axis, (b) A combination of s, Px, Py, Pz and d i yi atomic orbitals gives a set of five sp d hybrid orbitals corresponding to a square-based pyramidal arrangement the axial sp d hybrid orbital is directed along the z axis.

The mixing of 5, p, Py, p and d i atomic orbitals gives a set of five sp d hybrid orbitals, the mutual orientations of which correspond to a trigonal bipyramidal arrangement (Figure 4.7a). The five sp d hybrid orbitals are not equivalent and divide into sets of two axial and three equatorial orbitals the axial orbital lobes lie along the z axis. The model of sp d hybridization can be used to... 

The dsp hybridized phosphorus atom in the PCI5 molecule uses its five dsp orbitals to share electrons with the five chlorine atoms. Note that a set of five effective pairs around a given atom always requires a trigonal bipyramidal arrangement, which in turn requires dsp hybridization of that atom. 

There are five pairs of electrons around P therefore, the electron pair arrangement is trigonal hipyramidal. P must use sp d hybrid orbitals when bonding to Br, because sp d hybrid orbitals have a trigonal bipyramidal arrangement (see Table 4.3). The hybridization process can be imagined as follows. 

The sp d orbitals have shapes similar to those we have seen for the sp, sp, and sp hybrid orbitals that is, one large lobe and one small lobe. In addition, the five hybrid orbitals adopt a trigonal bipyramidal arrangement, enabling us to ejqrlain the geometry and bond angles in PCI5 ... 

Note that the lone pairs are placed in the plane where they are 120 degrees apart. Accommodating five pairs at the vertices of a trigonal bipyramid can be explained if the xenon atom adopts a set of five dsp3 orbitals. Each fluorine atom has four electron pairs and can be assumed to be sp3 hybridized. The XeF2 molecule has a linear arrangement of atoms. 

Phosphorus peniafluoride ( >3/,). A Lewis structure for the PFj molecule requires ten electrons in the valence shell of the phosphorus atom and the use of 3s, 3p, and l>d orbitals and five cr bonds. It is impossible to form five bonds in three dimensions such that they are all equidistant from one another, but the trigonal bipyramidal (Fig. 6.1e) and square pyramidal arrangements tend to minimize repulsions. Almost every five-coordinate molecule (coordination compounds excepted) which has been carefully investigated has been found to have a trigonal bipyramidal structure. The structure of the PF5 molecule is shown in Fig. 6.1e sp d hybrid). The bonds are of two types axial, the linear F—P—F system and equatorial, the three P—F bonds forming a trigonal plane. 

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