Hybrid orbitals formation

Component atomic orbitals involved in hybrid orbital formation... 

Hybridization or hybrid orbital formation has proved to be an extremely helpful and instructive concept for understanding the structure and bonding in many covalent materials (solids and molecules). Here, we introduce the basic ideas of hybrid orbital formation with the single illustrative example of the group IV elements, C, Si, Ge, and Sn. All four elements have four valence orbitals with the valence configuration ns np (A in Figure 2.6). One finds that it is possible to make linear combinations of these four valence orbitals to yield a new set of hybrid orbitals. The particular set of hybrid orbitals relevant to the present discussion are the sp -hybrid functions. These four sp hybrid orbitals are linear combinations of the original orbitals and can be written down as... 

Figure 6.12 Formation of a bonding 3-centre B-H-B orbital j1/ from an sp hybrid orbital on each of B(l), B(2) and the H Is orbital, (KH). The 3 AOs have similar energy and appreciable spatial overlap, but only the combination Vr(Bl)-l-Vr(B2) has the correct symmetry to combine linearly with i/r(H).

When two sp-hybridized carbon atoms approach each other, sp hybrid orbitals on each carbon overlap head-on to form a strong sp-sp a bond. In addition, the pz orbitals from each carbon form a pz-pz it bond by sideways overlap and the py orbitals overlap similarly to form a py-py tt bond. The net effect is the sharing of six electrons and formation of a carbon-carbon triple bond. The two remaining sp hybrid orbitals each form a bond with hydrogen to complete the acetylene molecule (Figure 1.16). 

The formation of the BeF2 molecule can be explained by assuming that, as two fluorine atoms approach Be, the atomic orbitals of the beryllium atom undergo a significant change. Specifically, the 2s orbital is mixed or hybridized with a 2p orbital to form two new sp hybrid orbitals. (Figure 7.12). 

Formation of a <7-bond by donation from the 7r-orbital of ethene into a vacant metal dsp2 hybrid orbital... 

The promotion of electrons will occur if, overall, it leads to a lowering of energy by permitting the formation of more bonds. Hybrid orbitals are constructed on an atom to reproduce the electron arrangement characteristic of the experimentally determined shape of a molecule. 

So far, we have not considered whether terminal atoms, such as the Cl atoms in PC15, are hybridized. Because they are bonded to only one other atom, we cannot use bond angles to predict a hybridization scheme. However, spectroscopic data and calculation suggest that both s- and p-orbitals of terminal atoms take part in bond formation, and so it is reasonable to suppose that their orbitals are hybridized. The simplest model is to suppose that the three lone pairs and the bonding pair are arranged tetrahedrally and therefore that the chlorine atoms bond to the phosphorus atom by using sp hybrid orbitals. 

The carhon-carbon double bond in alkenes is more reactive than carbon-carbon single bonds and gives alkenes their characteristic properties. As we saw in Section 3.4, a double bond consists of a a-bond and a 7r-bond. Each carbon atom in a double bond is sp2 hybridized and uses the three hybrid orbitals to form three cr-bonds. The unhvbridized p-orbitals on each carbon atom overlap each other and form a Tr-bond. As we saw in Section 3.7, the carbon-carbon 7r-bond is relatively weak because the overlap responsible for the formation of the 7r-bond is less extensive than that responsible for the formation of the a-bond and the enhanced electron density does not lie directly between the two nuclei. A consequence of this weakness is the reaction most characteristic of alkenes, the replacement of the 77-bond by two new a-bonds, which is discussed in Section 18.6. 

To visualize bond formation by an outer atom other than hydrogen, recall the bond formation in HF. One valence p orbital from the fluorine atom overlaps strongly with the hydrogen 1 S orbital to form the bond. We can describe bond formation for any outer atom except H through overlap of one of its valence p orbitals with the appropriate hybrid orbital of the inner atom. An example is dichloromethane, CH2 CI2, which appears in Figure 10-11. We describe the C—H bonds by 5 -I S overlap, and we describe the C—Cl bonds by 5 - 3 p... 

It will thus be apparent why the use of hybrid orbitals, e.g. sp3 hybrid orbitals in the combination of one carbon and four hydrogen atoms to form methane, results in the formation of stronger bonds. 

The orbitals containing the bonding electrons are hybrids formed by the addition of the wave functions of the s-, p-, d-, and f- types (the additions are subject to the normalization and orthogonalization conditions). Formation of the hybrid orbitals occurs in selected symmetric directions and causes the hybrids to extend like arms on the otherwise spherical atoms. These arms overlap with similar arms on other atoms. The greater the overlap, the stronger the bonds (Pauling, 1963). 

Figure 1.12 The hypothetical formation of methane from an sp -hybridized carbon atom. In orbital hybridization we combine orbitals, not electrons. The electrons can then be placed in the hybrid orbitals as necessary for bond formation, but always in accordance with the Pauli principle of no more than two electrons (with opposite spin) in each orbital. In this illustration we have placed one electron...

For metal ions having configurations d°, d1, d1, or d. there will always be two of the d orbitals empty to form a set of d2sp3 hybrids. Therefore, we expect complexes of these metal ions to be octahedral in which the hybrid orbital type is d2sp3. If we consider Cr3+ as an example, the formation of a complex can be shown as follows ... 

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