Chemistry Reference
In-Depth Information
Note that the two-electron states are symmetrized, except the
A
2
combination.
The symmetrized states will combine with singlet spin states, while the
A
2
state
will be a triplet. One thus has:
√
2
x(
1
)x(
2
)
y(
1
)y(
2
)
√
2
α(
1
)β(
2
)
β(
1
)α(
2
)
1
1
1
A
1
=
+
−
√
2
(xα)(xβ)
+
(yα)(yβ)
1
=
√
2
(xα)(yβ)
+
(yα)(xβ)
1
1
B
1
=
(xα)(xβ)
+
(yα)(yβ)
√
2
−
1
1
B
2
=
3
A
2
=
(xα)(yα)
The
1
A
1
and
1
B
2
states are the
zwitterionic states
, while the
1
B
1
and
3
A
2
states
are called the
diradical
states. It is clear from the expressions that in both cases
the two radical carbon sites are neutral. The zwitterionic states are easily polar-
izable though.
6.6 The carbon atoms form two orbits. The
p
z
orbital on the central atom is in
the center of the symmetry group and transforms as
a
2
. The three methylene
orbitals are in
C
2
v
sites, transforming as the
b
2
irrep of the site group, i.e., they
are antisymmetric with respect to
σ
h
and symmetric with respect to
σ
v
.The
induced representation is
a
2
+
e
b
2
C
2
v
↑
D
3
h
=
(11)
The SALCs are entirely similar to the hydrogen SALCs in the case of am-
monia; this implies, for instance, that the component labeled
x
is symmetric
under the vertical symmetry plane through atom A. It will be antisymmetric
for the twofold-axis going through atom A since the relevant orbital is of
p
z
type:
√
3
|
p
C
1
|
Ψ
a
=
p
A
+|
p
B
+|
√
6
2
p
C
1
|
Ψ
x
=
|
p
A
−|
p
B
−|
√
2
|
p
C
1
|
Ψ
y
=
p
B
−|
The
a
2
or
bi
tals interact to yield bonding and antibonding combinations at
±
√
3
β
. Since the graph is bipartite, the remaining
e
orbitals are neces-
E
=
α
