Tetrahedral hybridization

Shape tetrahedral Hybridization sp3 Bond angles 109.5° Nonpolar... 

Figure 5.1 Tetrahedral hybrid orbitals sp. (A) Section along development axis. (B) Spatial form and orientation of hybrid orbital Tci (from Harvey and Porter, 1976 redrawn and reproduced with permission).

We saw in 11-3 that a set of equivalent tetrahedral hybrid orbitals could also be constructed from a set of s, d, d s, and d, orbitals. Mathematical expressions for these hybrids (sd1) can be obtained from eqns (11-5.14) by changing p, to d, p to d., and pf to d, . That these are the correct changes can be deduced from the fact that the operators Oc>, 0Cjb, and Oc acting on the column matrix... 

The description of the bond orbitals of the carbon atom as sp8 tetrahedral hybrid orbitals is satisfactory in many respects, but it can be improved. One improvement is that of concentrating the orbitals more closely about the bond direction by the introduction of some d and/character.21... 

The values of 6 are estimated by methods described in the Appendix this gives 6 = 0.455 for the sp oxygen hybrid orbital and 8 = tt/4 for the sd vanadium hybrid orbital The tetrahedral hybrid, 6 — 7r/6, is used for the water oxygen c orbital... 

As an example, consider methane. If the carbon atom L-shell orbitals are arranged as tetrahedral hybrids, we can take the tat, t td configuration and combine this with an 3aSbScSd configuration of the four hydrogen atoms. Table 1 shows some numbers of states associated with these orbitals. It is... 

Table 1 Numbers of states under various constraints for methane and four tetrahedral hybrids and four H-atom orbitals.

HFC. The carbon orbitals are formed into the standard tetrahedral hybrids, pointing at the H atoms. There are 14 covalent basis functions and the this row gives the relative energy for the 14 term wave function. 

Two molecular fragments are isolobal if the number, symmetry properties, shapes, and approximate energies of their frontier orbitals are the same. They may or may not also be isoelectronic. For example, the HB and HC fragments are isolobal (but not isoelectronic), whereas the H2C and H2N moieties are both isolobal and isoelectronic. These relationships are illustrated in Fig. 1-23. As shown there, the symbol is used to express isolobality. Also shown in Fig. 1-23 is the idea that we may choose to picture the isolobality in more than one way. Thus, for the HB and HC fragments, we can either envision one sp hybrid orbital whose axis is colinear with the H—B or H—C bond, plus two p orbitals perpendicular to this axis, or we may envision a state of full hybridization, where the frontier orbitals in each case are three of the four in a set of sp3 tetrahedral hybrids. The orbitals whose similarity is critical in determining isolobality are called the frontier orbitals. 

In order to derive the tetrahedral hybrid electron functions we shall follow the method of Pauling and show that the linear combination of one s and three p wave functions give maximum stability of the bond. The linear combination has the form ... 

Fifl. 8. (a) The spherically symmetrical Is orbital for H (b) tetrahedral hybrid orbitals for B (c) trigonal hybrid orbitals for B, showing the 7r-orbital extending above and below the plane of the sp hybrids... 

Figure 10.4 Formation of four sp tetrahedral hybrid orbitals.

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