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.

The angle between any two sp³ hybrids can be found by the same argument. Take two sp³ hybrids. Two unit vectors along the hybrids h₁ and h₂ 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 next case of hybridization is sp2, which predominantly occurs in carbon compounds containing double bonds.The best example is ethene CH2 = CH2. Each carbon atom is "connected" to three "centers", one adjacent carbon and two hydrogens.

To get 3 equivalent orbitals in 3 directions in a plane, one s (2s) and two 2p (2p_x and 2p_z) orbitals in the xz plane are used. The three sp² orbitals on the first carbon are:

Figure 1 Hybrid Orbitals.

Orbital h₁ is directed towards the second carbon to its right. Orbitals h₂ and h₃ are directed towards negative z. To get the angle between the orbitals, treat the p orbitals as vectors. The s orbitals are spherically symmetrical and independent of direction. They are like scalars and do not contribute to directionality. If z axis is and x axis is , then the unit vectors corresponding to h₂ and h₃ are -1/ 2 and -1/ 2 -( ) . The dot product or cos ( , the angle between the two vectors) is ( 1/4-3/4).

Since cos = -1/ 2, = 120^o, which is the angle between the two sp² hybrids. The same angle is found between any pair among the three hybrids. Among the four electrons in C, three can be placed, with one electron in each orbital to bind with an adjacent C or two hydrogens. All these three hybrid orbitals are in the molecular plane of C₂H₄. The fourth electron is in the p_y orbital which is in a plane perpendicular to the molecular plane. This electron binds with its counterpart on the other carbon atom to give a bond, which is the double bond in C₂H₄.

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