Chemistry Reference
In-Depth Information
For the transition integral involving the biexcitations we obtain
*
+
1
r
B1
1
r
A2
þ
1
r
12
þ
1
R
h
a
i
b
j
j
V
j
a
0
b
0
i¼
a
i
b
j
a
0
b
0
ð
11
:
11
Þ
*
+
1
r
12
¼
a
i
b
j
a
0
b
0
¼ð
a
0
a
i
j
b
0
b
j
Þ
the interaction between the two transition densities
½
a
0
ð
r
1
Þ
a
i
ð
r
1
Þ
onAand
½
b
0
ð
r
2
Þ
b
j
ð
r
2
Þ
on B.
The first few orders of nonexpanded RS perturbation theory for the
H-H interaction are then
exp
ð
2R
Þ
R
5
8
R
3
1
E
c
1
¼
E
e
1
¼
4
R
2
6
R
3
1
þ
ð
11
:
12
Þ
the first-order electrostatic energy, with its explicit dependence on the
internuclear distance R, showing the charge-overlap nature of the inter-
action between neutral H atoms.
For the second-order energy:
ind
;
A
ind
;
B
disp
2
E
2
¼
E
þ
E
þ
E
ð
11
:
13
Þ
2
2
where
2
¼
X
i
ð
a
0
a
i
j
U
B
Þ
ind
;
A
E
ð
11
:
14
Þ
2
«
i
is the polarization energy of A by B (B distorts A from its spherical
symmetry),
2
¼
X
j
ð
b
0
b
j
j
U
A
Þ
ind
;
B
E
ð
11
:
15
Þ
2
«
j
is the polarization energy of B by A (A distorts B from its spherical
symmetry) and
2
¼
X
i
X
ð
a
0
a
i
j
b
0
b
j
Þ
disp
2
E
ð
11
:
16
Þ
«
i
þ«
j
j
