Chemistry Reference
In-Depth Information
[2
αβαα
−
αα
(
αβ
+
βα
)]
/
√
6
(D)
=
·
=
σ
∗
·
·
σ
∗
xy
cxy
or
c
where Q
[3
βααα
−
α
(
βαα
+
αβα
+
ααβ
)] consists of the quartet spin couplings
[
ααα
](S
z
=
=
1
/
2) among the second to fourth
orbitals (cxy or Vxy) in the orbital product
, and D
3
/
2) and [
βαα
+
αβα
+
ααβ
](S
z
=
[2
αβαα
−
αα
(
αβ
+
βα
)]
consists of the doublet spin coupling [2
βαα
−
α
(
αβ
+
βα
)] (S
z
=
=
1
/
2). For con-
venience,
σ
∗
(D) and c(D) describe
=
σ
∗
σ
∗
xy coupled with
·
cxy and c
·
[2
αβαα
−
αα
(
αβ
+
βα
)]
/
√
6, respectively. The transition intensity ratios
from the ground-state
3
G
to
(Q) and
(D) are approximately given as follows:
D
=
3
G
|
2
/
|
3
G
|
2
I
Q
/I
D
(
)
=|
r
|
(Q)
|
r
|
(D)
|
=
2
indicating that the Q-dominant state is always stronger in the transition intensity
than the D-dominant state, irrespective of
=
σ
∗
·
·
σ
∗
xy [23, 83]. In
other words, we cannot distinguish from the observation which is the better de-
scription,
σ
∗
(Q) and
σ
∗
(D) or c(Q) and c(D); namely, which is more strongly spin
coupled with the
π
∗
valence electrons, the core or
σ
∗
valence electron. To describe
σ
∗
(L) and
σ
∗
(H) more accurately,
σ
∗
(Q) and
σ
∗
(D) should be mixed through
the configuration interaction, which give the same solution as started from c(Q)
and c(D).
cxy or c
2. Comparison with S
2
and Se
2
As shown in [83], we can get a phase diagram for the most dominant character
in the lower and higher 1s
→
σ
∗
excited state
σ
∗
(L) and
σ
∗
(H) among the four
combinations of the orbital parts
σ
∗
·
·
σ
∗
xy with the two triplet spin
couplings Q and D. There are two cases A and B for K(
σ
∗
,π
∗
)
>
K(
σ
∗
,c
)
>
K(
c, π
∗
). In Case A, K(
σ
∗
,π
∗
)
cxy and c
K(
σ
∗
,c
)
>
K(
c, π
∗
); then,
σ
∗
(Q) and
σ
∗
(D)
are the better description and the core and
π
∗
electrons are well coupled with the
quartet (Q) and doublet (D) spins, but the D-dominant state is lower in energy than
the Q-dominant state [83]. On the other hand, in Case B, K(
σ
∗
,π
∗
)
≈
K(
σ
∗
,
c)
>
K(c
,π
∗
); then, c(Q) and c(D) are the better description and the
σ
∗
and
π
∗
electrons
are coupled with the Q and D spins. In summary,
K(
σ
∗
,π
∗
)
K(
σ
∗
,c
)
>
K(
c, π
∗
)
σ
∗
(L)
Case A
≈
≈
σ
∗
(D)
σ
∗
(H)
≈
σ
∗
(Q)
K(
σ
∗
,π
∗
)
K(
σ
∗
,
c)
>
K(c
,π
∗
)
σ
∗
(L)
Case B
≈
c(Q)
σ
∗
(H)
≈
c(D)
In O
2
, the exchange interactions involving the
σ
∗
electron, K(
σ
∗
,π
∗
) and K(
σ
∗
,c
),
are comparable; then, the 1s
→
σ
∗
excitation in O
2
belongs to Case A. On the other
