As a simple example, we will expand our molecular
orbital as a linear combination of just two atomic orbitals (this could, for
example, be the two 1s AOs in the
hydrogen molecule):
(5)
Now substituting into eq. 2 we obtain:
(6)
Eq. 6 now simplifies to give:
(9)
This can be rewritten in the form:
(10)
Now differentiating eq.10 with respect to c1
we obtain:
(11)
We now set 
to obtain:
(12)
If we differentiate eq.10 with respect to c2
we obtain the equation :
(13)