Chemistry Reference
In-Depth Information
While the polarizability of the atom is isotropic, the linear molecule has
two dipole polarizabilities,
a
jj
, the parallel or longitudinal component
directed along the intermolecular axis, and
a
?
, the perpendicular or
transverse component perpendicular to the intermolecular axis (McLean
and Yoshimine, 1967). The molecular isotropic polarizability can be
compared to that of atoms, and is defined as:
a
jj
þ
2
a
?
3
a ¼
ð
4
:
25
Þ
while:
Da ¼ a
jj
a
?
ð
:
Þ
4
26
is the polarizability anisotropy, which is zero for
a
?
¼ a
jj
.
The composite system of two different linear molecules has hence four
independent elementary dipole dispersion constants, which in London
form can be written as:
<
4
X
i
X
4
X
i
X
e
i
jj
e
j
jj
e
i
jj
e
1
1
j
?
A
¼
a
i
jj
a
j
jj
jj
;
B
¼
a
i
jj
a
j
?
?
;
e
jj
þ e
e
jj
þe
i
j
i
j
j
j
ð
4
:
27
Þ
4
X
i
X
4
X
i
X
:
e
?
e
1
1
e
i
?
e
j
?
i
j
jj
C
¼
a
i
?
a
j
jj
jj
;
D
¼
a
i
?
a
j
?
e
?
þe
e
?
þe
i
j
i
j
?
j
j
For two identical linear molecules, there are three independent disper-
sion constants since C
B.
It has been shown elsewhere (Wormer, 1975; Magnasco and Ottonelli,
1999) that the leading (dipole-dipole) term of the long-range dispersion
interaction between two linear molecules has the form:
¼
E
disp
2
R
6
C
6
¼
ðu
A
; u
B
; wÞ
ð
4
:
28
Þ
ðu
A
; u
B
; wÞ
C
6
being an angle-dependent dipole dispersion coefficient,
which can be expressed (Meyer, 1976) in terms of associated Legendre
polynomials on A and B as:
C
6
X
L
A
L
B
M
6
P
L
A
ð
P
L
B
ð
C
6
ðu
A
; u
B
; wÞ¼
L
A
L
B
M
g
cos
u
A
Þ
cos
u
B
Þ
ð
4
:
29
Þ
where L
A
;
L
B
¼
0
;
2 and M
¼j
M
j¼
0
;
1
;
2. In Equation (4.29), C
6
is the
isotropic coefficient and
g
6
is an anisotropy coefficient defined as:
C
L
A
L
B
M
6
C
6
L
A
L
B
M
6
g
¼
ð
4
:
30
Þ
