Linear combination of atomic orbitals to give hybrid orbitals is possible for orbitals of similar energy (such as the 2
s and 2
p orbitals for B, C, and N).
Linear combination is
simple addition and subtraction of wavefunctions.
The number of different ways in which a set of atomic orbitals can be added or subtracted depends on the number in the set. Thus the
number of hybrid orbitals formed equals the number of atomic orbitals used.
The simplified cartoon below shows linear combination of the wavefunctions for one 2
s and 2
p orbital.
On combination, reinforcement occurs when blue overlaps with blue; cancellation occurs where blue overlaps with yellow. Thus the two
sp hybrid orbitals have the same shape but point away from one another.
 | + |  | = |  |
| 2s orbital | | 2p orbital | | 2s + 2p |
 |  |
| | sp orbital 1 |
| + | | = |  |
| 2s orbital | | 2p orbital | | 2s + 2p |
|  |
| | sp orbital 2 |
Thus an
sp hybridized atom has four orbitals available for bonding. As we will see, the two
sp orbitals are used in σ bonds, and the two
p orbitals are used in π bonds.
