Chemistry Reference
In-Depth Information
Then, with such an expanded V, it is easily seen that
E
c
1
¼
E
e
1
¼
0
ð
11
:
23
Þ
ind
;
A
ind
;
B
E
¼
E
¼
0
ð
11
:
24
Þ
2
2
so that the only surviving term at long range is the London dispersion
attraction:
R
6
X
i
X
2
1
jh
a
i
b
j
j
x
1
x
2
þ
y
1
y
2
2z
1
z
2
j
a
0
b
0
ij
disp
2
E
¼
«
i
þ«
j
j
ð
11
:
25
Þ
R
6
X
i
X
2
2
6
jð
a
0
a
i
j
z
1
Þj
jð
b
0
b
j
j
z
2
Þj
¼
«
i
þ«
j
j
where we have taken into account the spherical symmetry of atoms A and
B, giving
(
ð
a
0
a
i
j
x
1
Þ¼ð
a
0
a
i
j
y
1
Þ¼ð
a
0
a
i
j
z
1
Þ
on A
ð
11
:
26
Þ
ð
b
0
b
j
j
x
2
Þ¼ð
b
0
b
j
j
y
2
Þ¼ð
b
0
b
j
j
z
2
Þ
on B
Since
¼
X
2
2
i
i
¼
2
jð
a
0
a
i
j
z
1
Þj
¼
2
m
A
A
A
i
a
«
i
; a
i
a
ð
11
:
27
Þ
«
i
A
, the dipole polarizability of atom
is the ith pseudostate contribution to
a
A, and
¼
X
2
¼
2
m
2
j
«
j
; a
j
¼
2
jð
b
0
b
j
j
z
2
Þj
B
B
B
j
a
j
a
ð
11
:
28
Þ
«
j
B
, the dipole polarizability of atom
B, the formula for the leading term of the expanded dispersion can be
written in the so-called London form:
is the jth pseudostate contribution to
a
!
2
!
«
i
«
j
«
i
þ«
j
R
6
X
i
X
4
X
i
X
2
j
«
i
þ«
j
¼
2
2
j
m
i
m
2
i
m
6
6
R
6
1
2
m
disp
2
E
¼
«
i
«
j
j
j
4
X
i
X
6
R
6
1
j
a
i
a
j
«
i
«
j
6
R
6
C
11
¼
«
i
þ«
j
¼
ð
11
:
29
Þ
