Зайцевский А.В. Релятивистская теория электронного строения молекул
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Λ
+
Λ
+
=⇒
e
Λ
+
=
X
u
′
Z
′
|Ψ
u
ihΨ
u
|
e
Λ
+
•
•
•
e
Λ
+
•
Ψ
KRHF
=
1
√
n!
det
Ψ
u
(1)Ψ
u
(2)Ψ
v
(3)Ψ
v
(4)...
,
Ψ
u
Ψ
u
Ψ
u
=
ψ
u
L↑
ψ
u
L↓
ψ
u
S↑
ψ
u
S↓
, Ψ
u
= K
tr
Ψ
u
=
−ψ
u ∗
L↓
ψ
u ∗
L↑
−ψ
u ∗
S↓
ψ
u ∗
S↑
Ψ
u†
Ψ
v
= (Ψ
v†
Ψ
u
)
∗
= Ψ
v†
Ψ
u
Ψ
u†
Ψ
v
= (Ψ
v†
Ψ
u
)
∗
= −Ψ
v†
Ψ
u
.
u = v Ψ
u†
Ψ
u
= Ψ
u†
Ψ
u
Ψ
u†
Ψ
u
= 0
g
12
hΨ
u
Ψ
v
| g
12
|Ψ
u
Ψ
v
i =
D
Ψ
u
Ψ
v
g
12
Ψ
u
Ψ
v
E
= . . . =
D
Ψ
u
Ψ
v
g
12
Ψ
u
Ψ
v
E
,
hΨ
u
Ψ
v
| g
12
|Ψ
v
Ψ
u
i =
D
Ψ
u
Ψ
u
g
12
Ψ
v
Ψ
v
E
= . . . =
D
Ψ
v
Ψ
u
g
12
Ψ
u
Ψ
v
E
.
H
D
hΨ
u
| H
D
|Ψ
u
i = hΨ
u
| H
D
|Ψ
u
i
Ψ
u
′
v
′
uv...
Ψ
HF
Ψ
u
Ψ
v
. . . Ψ
u
′
Ψ
v
′
. . .
Ψ = d
0
Ψ
HF
+
X
u u
′
d
u
′
u
Ψ
u
′
u
+
X
u v u
′
v
′
d
u
′
v
′
uv
Ψ
u
′
v
′
uv
+ . . .
d
0
, d
u
′
u
, d
u
′
v
′
uv
, . . .
•
•
•
SU(2)
•
SU(2)
•
σ/2
H
SC
H
SC
H
SC
H
SC
H
SC
Ψ =
ψ
L
ψ
S
=⇒
c
Ψ =
c
TΨ =
ψ
L
ψ
b
L
ψ
b
L
: ψ
S
=
1
2c
(σ, p)ψ
b
L
H
D
c
T
−1
c
Ψ = E
c
T
−1
c
Ψ;
c
T
−1
c
T
−1
=
1 0
0
1
2c
(σ, p)
.
c
T
−1
(σ, p)(σ, p) = p
2
V
p
2
2
p
2
2
(σ, p)V (σ, p)
4c
2
−
p
2
2
ψ
L
ψ
b
L
= E
1 0
0
p
2
4c
2
ψ
L
ψ
b
L
(σ, p)V (σ, p)
1
4
(σ, p)V (σ, p) = G
SC
+ G
SO
,
G
SC
=
1
8
(∆V ) + p
2
V + V p
2
G
SO
=
1
4
(σ, (∇V ) × p)
(
c
H
SC
+
c
H
SO
)
c
Ψ = E
b
S
c
Ψ,
c
H
SC
=
V
p
2
2
p
2
2
−
p
2
2
+
1
c
2
G
SC
,
c
H
SO
=
0 0
0
1
c
2
G
SO
,
b
S =
c
T
−2
=
1 0
0
p
2
4c
2
.
c
H
SO
1/c
2
c
H
SC
c
Ψ = E
b
S
c
Ψ,
ψ
b
L
ψ
L
c
H
SC
b
S
c
H
SC
b
S
1/c
2
λ = 1/c
2
E = E
0
+ λE
1
+ . . .
E
1
g
12
c
T
g
12
=⇒
b
g
12
=
c
T
−1
1
c
T
−1
2
g
12
c
T
−1
2
c
T
−1
1
b
g
12
ψ
L
= ψ
LL...L
ψ
L
P
L
=
1
2
Y
i
(β
i
+ 1)
P
L
Ψ = ψ
L
P
R
= 1 − P
L
P
R
Ψ = ψ
R
ψ
R
=
0
ψ
LL...S
. . .
ψ
SS...S
.
H
H =
H
LL
H
LR
H
RL
H
RR
,
H
LL
= P
L
HP
L
H
LR
= P
L
HP
R
Ψ =
ψ
L
ψ
R
H
LL
ψ
L
+ H
LR
ψ
R
= Eψ
L
H
RL
ψ
L
+ H
RR
ψ
R
= Eψ
R
,
ψ
R
ψ
R
= (E −H
RR
)
−1
H
RL
ψ
L
h
H
LL
+ H
LR
(E − H
RR
)
−1
H
RL
i
|
{z }
ψ
L
= Eψ
L
H
eff
H
eff
•
• Ω
H
eff
Ω
Ω : Ωψ
L
= Ψ
Ω = P
L
+ (E − H
RR
)
−1
H
RL
.
H
eff
Ω
U : ψ → ψ
′′
= Uψ H
eff
H
′′
eff
= UH
eff
U
−1
,
ΩU
−1
ΩH
eff
P
L
= HΩP
L
,
P
L