Chemistry Reference
In-Depth Information
of additional parameters for unlike atoms. Thus, many combining rules have been
proposed, which are empirical or based on mathematical and physical intuition
[
26
-
31
]. Most of the combining rules for the LJ potential parameters rely on
pure component data alone. However, some combining rules incorporate additional
molecular information like polarizability, ionization potential, or diamagnetic sus-
ceptibility. A review and detailed description of LJ combining rules can be found,
e.g., in [
32
-
34
].
Some force fields use the geometric mean (Berthelot rule) for both LJ parameters:
s
i
s
p
;
s
ij
¼
e
i
e
p
:
e
ij
¼
(11)
However, by far the most commonly employed LJ combining rule is that of
Lorentz [
35
] and Berthelot [
36
]:
1
2
ðs
i
þ s
j
Þ;
s
ij
¼
p
e
i
e
j
e
ij
¼
:
(12)
The use of the arithmetic mean for the unlike size parameter was proposed by
Lorentz motivated by the collision of hard spheres; on the other hand, the geometric
mean for the unlike energy parameter was proposed with little physical argument by
Berthelot. Therefore, it is not surprising that this combining rule often leads to
inaccurate mixture properties [
34
,
37
,
38
].
An effective approach is to provide the Lorentz-Berthelot combining rule with
at least one extra parameter that can be adjusted to some experimental data of
the mixture. A modification that is adequate for the description for the unlike LJ
parameters for vapor-liquid equilibria [
34
]is
1
2
ðs
i
þ s
j
Þ;
e
ij
¼ x
s
ij
¼
p
e
i
e
j
:
(13)
This modified rule was successfully applied to vapor-liquid equilibria of numerous
mixtures [
39
-
41
]. Here, the binary parameter
was adjusted to one experimental data
point for vapor pressure or Henry's law constant of the studied binary mixture.
x
2.1.3 Electrostatic Interactions
The electrostatic interactions of ionic and polar molecules in the form of charges or
multipoles contribute significantly to the potential energy. For an exact description of
a typical charge distribution, a large set of electric moments is required [
42
]. However,
often just dipoles and quadrupoles are taken into account, since they are usually the
most significant [
19
]. Because the multipole expansion at one site converges slowly,
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