Chemistry Reference
In-Depth Information
cyclic butadiene, hexatriene and benzene, taken as representatives of
linear chains with N
¼
2
6.
For these systems, we shall solve in an elementary way for both eigen-
values and eigenvectors of theH
;
3
;
4
;
6 and rings (closed chains) with N
¼
4
;
uckel matrixH, obtaining in thisway the
orbital energy levels and the schematic shapes of the MOs shown in
Figures 7.2-7.7. General, and more powerful, techniques of solution are
due to Lennard-Jones (1937) and will be used later in Section 7.5.
€
7.4.1 Ethylene (N
¼
2)
The H
€
uckel secular equation for N
¼
2is
¼
x
2
x
1
D
2
¼
1
¼
0
ð
7
:
54
Þ
1
x
x
-√2
LUMO
-1
LUMO
0
HOMO
1
HOMO
√2
N
= 2
N
= 3
x
-2
LUMO
-1.618
-0.618
LUMO
0
HOMO
0.618
HOMO
1.618
2
N
= 4
(Chain)
N
= 4
(Ring)
Figure 7.2 H
€
uckel orbital energies for a linear chain with N
¼
2
;
3
;
4 and a ring with
N
¼
4
