Chemistry Reference
In-Depth Information
the MEP of B; that
¼
X
j
2
¼
X
j
2
jð
B
0
B
j
j
U
A
jh
A
0
B
j
j
A
0
B
0
ij
Þj
ind
;
B
E
ð
11
:
37
Þ
2
«
j
«
j
is the polarization (distortion) of B by the static field of A, described by the
MEP U
A
; and that
D
A
0
B
0
E
A
i
B
j
P
i
0
<
j
0
r
i
0
j
0
1
2
2
¼
X
i
X
¼
X
i
X
h
A
i
B
j
j
V
j
A
0
B
0
i
disp
2
E
«
i
þ«
j
«
i
þ«
j
j
j
ð
11
:
38
Þ
is the dispersion interaction, a purely electronic term arising from the
density fluctuations of the electrons onAandBwhich are coupled together
through the intermolecular electron repulsion operator r
1
12
(1 on A, 2
on B).
Generalization of the previous H-H results to molecules is possible in terms
of the charge-density operator (Longuet-Higgins, 1956) and of static and
transition electron densities, P
A
r
1
Þ
and P
B
r
2
Þ
, P
A
ð
00
j
r
1
;
ð
00
j
r
2
;
ð
0i
j
r
1
;
r
1
Þ
and
P
B
r
2
Þ
respectively on A and B. The nonexpanded dispersion energy
between molecules A and B then takes the simple integral form
ð
0j
j
r
2
;
2
ÐÐ
dr
1
dr
2
P
A
r
1
Þ
P
B
ð
0i
j
r
1
;
ð
0j
j
r
2
;
r
2
Þ
2
¼
X
i
X
r
12
disp
E
ð
11
:
39
Þ
«
i
þ«
j
j
which canbe comparedwith the corresponding integral expression (11.16)
found for the H-H interaction, where P
A
r
1
Þ¼
a
0
ð
r
1
Þ
a
i
ð
r
1
Þ
and
ð
0i
j
r
1
;
P
B
r
2
Þ¼
b
0
ð
r
2
Þ
b
j
ð
r
2
Þ
.
ð
0j
j
r
2
;
11.3.2 Expanded Energy Corrections up to Second Order
In molecules, the interaction depends on the distance R between their
centres of mass as well as on the relative orientation of the interacting
partners, which can be specified in terms of the five independent angles
5
5
These angles are simply related to the Euler angles describing the rotation of a rigid body (Brink
and Satchler, 1993).
