Chemistry Reference
In-Depth Information
whose roots (eigenvalues, left in the top row of Figure 7.2) are x
¼
1,
while the normalized eigenvectors (the MOs of the top row of Figure 7.3)
are given by the (2
2) unitary matrix
0
@
1
A
1
2
1
p
p
C
¼ð
c
1
c
2
Þ¼
ð
7
:
55
Þ
1
2
1
2
p
p
7.4.2 The Allyl Radical (N
¼
3)
€
uckel secular equation for N
¼
3is
The H
x 10
1
x 1
01
x
¼
x
ð
x
2
1
Þþ
x
¼
x
ð
x
2
D
3
¼
2
Þ¼
0
ð
7
:
56
Þ
+
-
+
N
= 2
+
.
.
.
+
-
-
-
φ
1
φ
2
N
= 3
+
.
-
.
+
+
+
+
-
+
.
-
-
-
-
-
+
-
+
φ
1
φ
2
φ
3
N
= 4
+
.
+
.
+
.
-
.
+
+
+
-
-
-
-
+
-
-
-
+
φ
1
φ
2
+
+
-
+
-
-
+
-
.
.
.
.
.
.
.
+
+
-
+
-
-
+
-
φ
3
φ
4
Figure 7.3 H
€
uckel MOs for a linear chain with N
¼
2
;
3
;
4
