Chemistry Reference
In-Depth Information
Figure 4.2
The five angles specifying in general the relative orientation of two
polyatomic molecules. Reprinted from Magnasco, V., Methods of Molecular Quan-
tumMechanics: An Introduction to ElectronicMolecular Structure. Copyright (2009)
with permission from John Wiley and Sons
multipoles
6
. Since atoms have no permanent electric moments, their elec-
trostatic interaction at long range is zero. The values of the first three electric
moments at their equilibrium distances for a few molecules are given in
Table 5.2 of the next chapter, while Section 5.2.1 gives the explicit expres-
sions of the angular dependence of the first three terms of the expanded
electrostatic interaction beteween two hydrogen fluoride molecules.
The two papers cited above also give explicit expressions for the
polarization (induction) energies between polar molecules. They are
expressed in terms of permanent moments and static polarizabilities of
the interacting molecules. Both are observable quantities that can be
measured by experiment.
In what follows, we shall limit ourselves mostly to consideration of the
long-range dispersion interaction between: (i) two atoms; (ii) two linear
molecules A and B; and (iii) an atomA, at the origin of the intermolecular
coordinate system, and a linear molecule B, whose orientation with
respect to the z axis is specified by the single angle
u
(Figure 5.3 in the
next chapter).
The expanded dispersion energy involves the interaction between
induced moments on two atoms, the leading term describing the inter-
action between induced dipoles on A and B being:
4
X
i
X
«
i
«
j
«
i
þ«
j
¼
C
6
R
6
¼
6
R
6
1
6
R
6
C
11
E
disp
2
a
i
a
j
ð
6
Þ¼
ð
4
:
18
Þ
j
6
An electric multipole is specified by its value of l as 2
l
pole
ð
l
¼
1 dipole, l
¼
2 quadrupole,
. Hence, the electrostatic interaction is between 2
l
2
l
0
poles, the leading
l
¼
3 octupole
;
etc
:Þ
term for two dipolar molecules
ð
l
¼
l
0
¼
1
Þ
being the dipole-dipole interaction.
