Biomedical Engineering Reference
In-Depth Information
A study of the effect of variations in the interatomic potential of argon on the calculated
properties of the dilute gas has led to a numerically tabulated potential which satisfactorily
agrees with all available equilibrium and transport data. This potential differs significantly
from previously used pair potentials.
Their approach makes use of the second virial coefficient mentioned above.
2.13 Site-Site Potentials
The L-J potential has played an important role in the history of molecular modelling. Early
work focused on atoms, but, as I explained, there were many ambitions attempts to model
simple molecules as if they were in some way L-J atoms, and the parameters have to be
interpreted as applying to some kind of average over molecular rotations (and presumably
vibrations).
Suppose now that we want to try and understand the interaction between two dinitrogen
molecules in more depth. In view of our discussion above, the instantaneous interaction
energy will clearly depend on the separation of the two diatoms, together with their mutual
angular arrangement in space.
Figure 2.7 shows two such dinitrogens, oriented arbitrarily in space with respect to each
other. NitrogenA and nitrogen B make up a stable diatom, as do atoms C and D. We ignore
the fact that the molecules have vibrational energy, and the two diatoms are taken to be
rigid. As a first approximation, the mutual potential energy of the pair of diatoms could be
calculated by adding together the appropriate L-J parameters. If I write as shorthand the
L-J interaction between atoms A and C as
4ε
σ
R
AC
6
12
σ
R
AC
U
L
−
J
(A, C)
=
−
then the total interaction between the two diatomics is taken as
U
L
−
J
=
U
L
−
J
(A, C)
+
U
L
−
J
(A, D)
+
U
L
−
J
(B, C)
+
U
L
−
J
(B, D)
(2.29)
Such a potential is called a
site-site potential
. We will meet such potentials later in the text.
B
A
C
D
Figure 2.7
Two dinitrogen molecules, arbitrarily oriented
