Chemistry Reference
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Figure 2.28
Coordinate system (top), energy levels (left) and real H
uckel MOs
¼
(right) for cyclobutadiene (ring with N
4)
uckel MOs for cyclobuta-
diene are sketched in Figure 2.28. To simplify the drawing, the 2p
The coordinate system, energy levels and H
€
AOs in
the MOs are viewed from above the zx molecular plane, so that only the
signs of the upper lobes are reported. We note that
p
f
2x
is a function having
the same transformation properties as the x coordinate, yz being a nodal
plane for this MO.
f
2y
is a function having the same transformation
properties as the y coordinate, zx now being the nodal plane for this MO.
f
2x
and
f
2y
are the pair of HOMO MOs belonging to the doubly
degenerate energy level
«
2
¼ «
3
which transform as the pair of basic
vectors
e
x
and
e
y
of the D
2h
symmetry (Magnasco, 2009a) to which the
s
skeleton of cyclobutadiene belongs. They are therefore orthogonal and
not interacting, as can be seen immediately:
1
4
1
4
ð
hf
2x
jf
2y
i¼
h
x
1
x
2
x
3
þx
4
jx
1
þx
2
x
3
x
4
i ¼
1
1
þ
1
1
Þ¼
0
ð
2
:
277
Þ
