Chemistry Reference
In-Depth Information
then the RS energy corrections up to second order in V are as follows:
A
B
0
j
a
0
b
0
i¼
E
0
þ
E
0
E
0
¼hc
0
j
H
0
jc
0
i¼h
a
0
b
0
j
H
0
þ
H
ð
11
:
4
Þ
the unperturbed energy, the energy pertaining to the separate atoms;
E
c
1
¼hc
0
j
H
1
jc
0
i¼h
a
0
b
0
j
V
j
a
0
b
0
i
¼ð
a
0
j
r
1
1
R
¼
E
e
1
ð
11
:
5
Þ
B1
Þþð
b
0
j
r
1
A2
Þþð
a
0
j
b
0
Þþ
the nonexpanded first-order correction, the semiclassical Coulomb inter-
action of the HL theory, said the electrostatic energy; and
2
E
c
2
¼
X
i
X
j
2
h
a
0
b
j
j
V
j
a
0
b
0
i
j
h
a
i
b
0
j
V
j
a
0
b
0
i
j
«
i
«
j
ð
11
:
6
Þ
2
X
i
X
h
a
i
b
j
j
V
j
a
0
b
0
i
«
i
þ«
j
j
the second-order Coulombic energy describing deviations from the rigid
spherical atoms. The first two terms represent the induction (distortion or
polarization) energy involving monoexcitations (top row of Figure 11.2),
a
i
b
j
a
i
b
j
U
B
U
A
ε
i
ε
j
a
0
b
0
a
0
b
0
A
B
A
B
B polarizes A
A polarizes B
a
i
a
i
b
j
b
j
√6
3
μ
i
μ
j
1/
r
12
ε
i
,
μ
i
ε
j
,
μ
j
α
j
ε
i
ε
j
α
i
a
0
b
0
a
0
b
0
A
B
A
B
Mutual polarization of A B
Figure 11.2 Second-order interactions between ground-state H atoms. Top row:
B polarizes A (left) and A polarizes B (right). Bottom row: nonexpanded dispersion
(left) and leading term of the expanded dispersion (right)
