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 (2px and 2pz) orbitals in the xz plane are used. The three sp2 orbitals on the first carbon are:
h1 =
[s +
pz]
h2 =
[ s -
( )( pz ) +
( px )]
(9.5)
h3 =
[ s -(
) ( pz ) -
( px )]
Figure 9.4 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, = 120o, 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 py 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.
[s +
pz] 
)( pz ) +
( px )]
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). 
bond, which is the double bond in C2H4.
