p molecular orbitals for 1,3 butadiene

Using the “x” notation where we can write the secular equations in the form:

xc1	+	c2	+	0	+	0	=	0
c1	+	x c2	+	c3	+	0	=	0
0	+	c2	+	x c3	+	c4	=	0
0	+	0	+	c3	+	x c4	=	0

(1)

The secular determinant is:

(2)

where the picture of 1,3-butadiene, showing the numbering of the atoms is:

Solving the secular determinant gives the MO energies...