Chemistry Reference
In-Depth Information
Table 11.6 Comparison between isotropic C
6
coefficients
ð
E
h
a
0
Þ
for some homo-
dimers of atoms and molecules in the gas phase at T
¼
293 K
Atom-atom Dispersion Molecule-molecule Dispersion
Induction Keesom
He
2
1.46
(H
2
)
2
12.1
0
0
Ne
2
6.35
(N
2
)
2
73.4
0
0
H
2
6.50
(CO)
2
81.4
0.05
0.002
Ar
2
64.9
(NO)
2
69.8
0.08
0.009
Kr
2
129
(N
2
O)
2
184.9
0.19
0.017
Be
2
213
(NH
3
)
2
89.1
9.82
81.3
Xe
2
268
(H
2
O)
2
45.4
10.4
204
Mg
2
686
(HF)
2
19.0
6.3
227
Li
2
1450
(LiH)
2
125
299
8436
contribution comes from attractive dispersion. For dipolar molecules,
induction is usually negligible with respect to dispersion except for
ð
LiH
Þ
2
. The electrostatic energy is not zero when its thermal average is
taken. The corresponding Keesom attractive energies (11.80) are, hence,
the isotropic electrostatic contributions to the interaction energy and are
temperature dependent. A comparison between isotropic C
6
coefficients
for some homodimers at T
¼
293 K is given in Table 11.6. It is seen that
Keesom C
6
ð
T
Þ
is negligible compared with dispersion and induction
coefficients for the homodimers of CO, NO, N
2
O, while for (NH
3
)
2
,
(HF)
2
and (H
2
O)
2
the Keesom dipole orientation forces become increas-
ingly dominant at room temperature, so they cannot be neglected in
assessing collective gas properties such as the equation of state for real
gases and virial coefficients.
Magnasco et al. (2006) recently extended Keesom's calculations up to
the R
10
term, showing that deviations of the Keesom approximation
from the full series expansion are less important than consideration of
the higher order terms in the R
2n
expansion of the intermolecular
potential.
Battezzati and Magnasco (2004) also gave an asymptotic evaluation
|a|
large,
13
of
the Keesom integral
(11.74)
for
obtaining the
formula
exp
ð
2a
Þ
a
2
4
3
2
3a
K
ð
a
Þ
1
ð
11
:
81
Þ
13
This is the case of low temperatures and small distances between the dipoles, as well as the case
of (LiH)
2
, where the interacting dipoles are very large.
