The symmetrically orthogonalized MOs
~
u
0
1
¼ u
0
ðp2Þ
E
À S 12 =2 u
0
ðp1Þ
E
and ~
u
0
2
¼ u
0
ðp 1 Þ
E
À S 12 =2 u
0
ðp 2 Þ
E
ð14:15Þ
keep their largest amplitudes on atoms p 1 and p 2 respectively. In such symmetrical
systems one may use symmetry arguments to obtain directly the coefficients of the
symmetry-adapted SOMOs. One of them is antisymmetric with respect to the
reflection plane, and attributing a coefficient 1 on the less connected atoms of major
color one obtains one SOMO located on the upper side atoms with alternant values.
The symmetrical one second one has larger amplitudes on the lower side atoms.
The generalization to longer acenes is straightforward. The symmetries of these
SOMO depend on the parity of the number of rings. For 2′a they are
-1
-1
1
1
-3
1
1
-3
2
2
-2
and the following ones for 3′a
1
1
1
-1
-1
2
0
-2
1
-1
-1
1
-1
1
From these symmetry-adapted SOMOs u
0
g and u
0
u , which are the canonical
(symmetry-adapted) SOMOs of the Hückel Hamiltonian, again obtained without
diagonalization, one may define the localized SOMOs
14 Magnetic Properties of Conjugated Hydrocarbons …
371