Chemistry Reference
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where
is a measure of
the magnitude of the repulsive interaction. The square-well (SW) potential is the
simplest model that considers both repulsion and attraction:
n
is a parameter usually chosen to be an integer number and
z
8
<
1
r
ij
s;
es<
u
SW
r
ij
ls;
ð
r
ij
Þ¼
(3)
:
0
r
ij
> ls;
where
e
is a measure of the attractive interaction and
l
is some multiple of the hard-
sphere diameter. Another simple potential that includes a physical description of
dispersion is the Sutherland potential:
1
r
ij
s;
u
Su
ð
r
ij
Þ¼
(4)
6
eðs=
r
ij
Þ
r
ij
> s:
The HS, SS, SW, and Sutherland potentials are highly idealized approximations
that are nowadays rather used for the development of liquid state theories.
The most popular effective pair potential representing the Van der Waals inter-
actions is the Lennard-Jones (LJ) potential, which was given in a general form by
Mie [
14
]:
n
m
1
n
n
m
m
e
r
ij
r
ij
n
m
u
Mie
ð
r
ij
Þ¼
;
(5)
n
m
where
are the size parameter and the energy well-depth, respectively. For
the dispersive term,
m
s
and
e
6 is specified because of its physical significance. For the
repulsive term, with little theoretical justification,
n
¼
¼
9···16 is usually employed.
The most common form is the LJ 12-6 potential (
n
¼
12,
m
¼
6):
"
#
12
6
r
ij
r
ij
u
LJ
ð
r
ij
Þ¼
4
e
:
(6)
The choice of the exponent
n
¼
12 has rather computational than physical
reasons, because it is simply the square of the dispersion term.
There are also many variations of the LJ 12-6 potential. One example is the
computationally inexpensive truncated and shifted Lennard-Jones potential (TSLJ),
which is commonly used for molecular simulation studies in which large molecular
ensembles are regarded, e.g., for investigating condensation processes [
15
,
16
].
Another version of the LJ potential is the Kihara potential [
17
], which is a non-
spherical generalization of the LJ model.
One weakness of the LJ potential is the lack of a realistic description of repul-
sion, which originates from the Pauli exclusion principle. The Buckingham expo-
nential-6 potential takes the actual exponential decay into account [
18
]:
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