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Module 2 : Molecular Structure

Lecture 9 : Polyatomics

9.3

Hybridization.
Hybridization is a ubiquitous concept in molecular chemistry. A pictorial description runs like this. As four hydrogen approach a carbon atom, one of the 2s electrons of C gets "promoted" to a vacant 2p giving four unpaired electrons. These four orbitals rearrange into a regular tetrahedral arrangement and combine with the four 1s orbitals of the four hydrogens to give a tetrahedral CH₄. Remember orbitals are mathematical functions. In quantum chemistry (the subarea of chemistry which studies the bonding in molecules using quantum mechanical principles), the bonding MOs are calculated for the most stable configuration of a molecule and from these levels (when the results agree with spectroscopic and other thermal data), inferences regarding hybridization are conclusively drawn. In LiF we have already seen sp hybrids.

In H₂O we mentioned hybrids formed by combining one s and three p orbitals on O. These are referred to as sp³ hybrids. These occur in all saturated carbon compounds. The tetrahedral bonding in a saturated carbon atom is a result of this hybridization. The four combinations for the four sp³ hybrids are given below.
h₁ = 2s +2p_x + 2p_y +2p_z	(9.4a)
h₂ = 2s + 2p_x - 2p_y - 2p_z	(9.4b)
h₃ = 2s - 2p_x - 2p_y - 2p_z	(9.4c)
h₄ = 2s - 2p_x + 2p_y - 2p_z	(9.4d)

The angle between any two sp³ hybrids can be found by the same argument. Take two sp³ hybrids (Eq 9.4). Two unit vectors along the hybrids h₁ and h_₂ are and . The dot product is -1/ 3 and cos ^-1 (-1/ 3) = 109^o 28' which is the tetrahedral angle.

It should be noted that all hybrid combinations are not completely regular. E.g. in CH₃Br, the hybrid in the direction of Br is likely to be more directed (due to the electronegativity of Br) towards Br than the others towards hydrogens. The actual coefficients of e.q. 9.3 and 9.4 in these molecules are obtained from detailed calculations.

In this lecture, we have considered hybridization among s and p orbitals. In molecules wherein there is participation of d orbitals, other combination such as pd, sp³d² and so on naturally emerge.