Chemistry Reference
In-Depth Information
C
6
dispersion coefficients for the homodimers of some simple one-electron
and two-electron atomic and molecular systems. It is seen that the
convergence rate of either
a
or C
6
is remarkably slower for the two-
electron systems.
We see fromTable 11.4 that the five-termapproximation gives 82%for
He, 99% for H
2
and 86% for H
2
, showing that convergence is sensibly
worst for the two-electron systems. Table 11.5 shows that the five-term
approximation, yielding practically the exact result for H-H, gives 85%
for He-He andH
2
-H
2
and over 98% for H
2
-- H
2
, confirming the similar
results for polarizabilities.
11.3.3 Other Expanded Interactions
At variance with the dispersion interaction, whose calculation at long
range requires knowledge of N-term pseudospectra of the monomer
molecules, which are not observable quantities, the remaining compo-
nents of the intermolecular interaction, the electrostatic and induction
energies, are instead expressible in terms of physically observable electric
properties of the interactingmolecules, namely the permanent moments
m
and the total polarizabilities
a
of the individual molecules.
(a) As an example, the leading term of the electrostatic interaction
between two dipolar HF(
1
þ
) molecules
7
is given at long range by
the dipole-dipole interaction
8
going as R
3
:
S
2
HF
R
3
E
e
1
¼
m
ð
sin
u
A
sin
u
B
cos
w
2 cos
u
A
cos
u
Þ
ð
11
:
54
Þ
B
which has a minimum for the head-to-tail configuration of the two
molecules:
E
e
1
¼
2
m
2
HF
R
3
ð
11
:
55
Þ
¼
180
, leading to the formation of a collinear H-bond
(H-F
H-F). The next quadrupole-dipole and dipole-quadrupole
u
¼ u
for
A
B
7
Namely, molecules whose first nonzero permanent moment is the dipole moment.
8
Equation 11.54 is just Equation 11.22 weighted in first order with the ground-state wavefunc-
tion when the resulting dipole components are expressed in spherical coordinates.
