The van der Waals Bond - Models for Bonding in Chemistry - page 164

Here:

¼ a i m B C 6 ð 4 : 64 Þ

is the isotropic coefficient, and:

g 6 ¼ 1 ð 4 : 65 Þ

the anisotropy coefficient for induction. Averaging over angle u , we get for
the isotropic polarization of A by B

ða i ¼ a A Þ

:

a A m B
R 6

D E BA ¼ ð 4 : 66 Þ

We have a similar result for a dipolar molecule A distorting B, so that on
average:

a A m B þ a B m A
R 6

D E ¼ D E BA þD E AB ¼ ð 4 : 67 Þ

and, for identical molecules:

2 am 2
R 6 ¼

C 6
R 6

D E ¼ ð 4 : 68 Þ

Even the leading term of the induction (polarization) energy has an R 6
dependence onRwith an isotropic C 6 ¼ 2 am 2 , but the coefficient depends

now on observable quantities that can be measured by experiment.

This makes an important difference from dispersion coefficients that
should be noted.
Isotropic C 6 dispersion and induction coefficients (in atomic units) for
some homodimers of atoms and molecules taken from the literature are
compared in Table 4.1. We see from the table that the distortion energy is
zero for atoms, which do not have permanent moments, and is always
smaller than the dispersion energy for the molecules considered, with the
only exception of (LiH) 2 . The dispersion energy (London attraction) is
therefore the dominant VdW interaction, 11 the only one for atoms. The
large value for the distortion energy in (LiH) 2 is due to the combined large
values of m and a for LiH,

ða; mÞ

5a 0 , respectively (Bendazzoli 2 : 29ea 0 and 28 :

et al., 2000).

11 Note, however, the importance of the temperature-dependent Keesom effect for dipolar
molecules in the gas phase.