Hückel 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

 

The secular determinant for 1,3-butadiene is:

 

 

where the numbering of the atoms is:

 

 

Solving the secular determinant gives the MO energies...