Chemistry Reference
In-Depth Information
So, we finally get:
c
6
c
1
¼
1
2
1
2
¼
c
2
c
1
¼
3
2
þ
1
2
¼
c
3
c
1
¼
1
;
1
;
2
1
¼
1
;
c
4
c
1
¼
c
5
c
1
¼
3
4
þ
1
4
¼
1
;
1
namely:
¼
;
¼
;
¼
;
¼
;
¼
c
2
c
1
c
3
c
1
c
4
c
1
c
5
c
1
c
6
c
1
Normalizing to unity we obtain:
1
6
c
1
þ
c
2
þ
c
3
þ
c
4
þ
c
5
þ
c
6
¼
6c
1
¼
p
1
1
c
1
¼
Y
Y
thereby giving for the eigenvector
f
6
corresponding to the last eigenvalue:
1
p
c
1
¼
c
2
¼
c
3
¼
c
4
¼
c
5
¼
c
6
¼
ð
2
:
316
Þ
Following what was said for cyclobutadiene, it is left as an easy exercise
for the reader to verify that all MOs, Equations (2.285), are normalized
and orthogonal and not interacting in pairs. Furthermore, even if their
form is different, each pair of MOs belonging to the respective degenerate
eigenvalue gives the same value for the corresponding orbital energy.
