.

$$S_{1-2} = S_{2-1} = \int p_2 ( p_z \sin \theta_{1-2} + p_y \cos \theta_{1-2}) d \tau$$ (2)

and since p₂ is a p_y orbital and orthogonal to p_z we know that the first term vanishes, so,

$$S_{1-2} = \int p_2 ( p_y \cos \theta_{1-2}) d \tau = <p_{y_2}\vert p_{y_1}> \cos \theta_{1-2}$$ (3)

since p₂ and p_y are identical, normalized p orbitals, parallel to each other, i.e., the standard Hückel assumption.

Normally, the exchange integrals are declared proportional to the overlap integrals, so we now turn our attention to these exchange integrals.