Chemistry Reference
In-Depth Information
O
2
has been often discussed in terms of Rydberg and valence [23, 83, 102, 104];
however, to understand electronic structures of O
2
correctly, discussion based on
the potential energy curve is essential [26, 34, 91, 103, 106-109].
A. Core-Valence Excitation
1. Electron Configuration
Oxygen molecule (O
2
) has a triplet ground state with two parallel spins in the
degenerate 1
π
gx
and 1
π
gy
orbitals: (1
σ
g
)
2
(1
σ
u
)
2
(1
π
gx
)
1
(1
π
gy
)
1
. Within the MO
picture, the ground-state wave function
3
G
is simply described by using the
α
and
β
spin functions
↑
↓
and
as follows:
3
G
(S
z
=
(2)1
π
gx
↑
(3) 1
π
gy
↑
1)
=
1
σ
↑
(1)1
σ
↓
(4)
=
cc
·
xy [
αβαα
]
1
π
gy
(
1
,
3
uy
)
where 1
σ
is one of the core (c) obitals 1
σ
g
and 1
σ
u
. The 1
σ
u
→
excited states have a configuration (1
σ
u
)
1
(1
π
gx
)(1
π
gy
)
2
:
3
x
(S
z
=
1)
=
c
·
yxy [
αβαα
]
=
cx
·
yy [
αα
·
αβ
]
·
αβ
)
/
√
2
3
x
(S
z
=
0)
=
cx
·
yy [(
αβ
+
βα
)
·
αβ
)
/
√
2
1
x
(S
z
=
0)
=
cx
·
yy [(
αβ
−
βα
)
K(c
,
x
∗
)
+
K
(c
,
y
∗
)
The singlet-triplet (ST) or EX splitting is given by
ST
=
=
2 K(c
,
x
∗
), where K(c,x
∗
) is the exchange interaction energy between 1
σ
u
and
1
π
gx
. Only one 1
σ
u
→
1
π
g
excited-state (
3
u
) is observed in the lowest excitation
energy region, which is similar to the case of N
2
.
In the higher energy region, X-ray absorption of the O
2
molecules results in
the excitation from the neutral triplet ground state with two unpaired electrons to
the two triplet core-excited states with four unpaired electrons involving a pro-
motion to a Rydberg orbital. They can be regarded as triplet coupled states of the
Rydberg electron with the quartet (Q) and doublet (D) core-ionized states with
three unpaired electrons [23], where the ionized state Q is lower by 1.1 eV than
the ionized state D and the Rydberg series is converging to one of them.
Two dipole-allowed triplet 1
σ
g
→
3
σ
u
(
3
u
) excited states with the same elec-
tron configuration (1
σ
g
)
1
(1
π
gx
)
1
(1
π
gy
)
1
(3
σ
u
)
1
should also be observed below the
two ionization thresholds, because no resonance is experimentally observed above
the thresholds, as shown in Fig. 12. In general, the wave functions for the lower
and higher triplet 1s
excited-states
σ
∗
(L) and
σ
∗
(H) are described with the
mixing between the triplet configuration state functions
(Q) and
(D) as follows:
→
σ
∗
σ
∗
(L)
=
a
·
(Q)
+
b
·
(D)
σ
∗
(H)
=
b
·
(Q)
−
a
·
(D)
[3
βααα
−
α
(
βαα
+
αβα
+
ααβ
)]
/
√
12
(Q)
=
·
