Chemistry Reference
In-Depth Information
Figure 3.19
Cubic control volume considered away from any physical boundaries.
an example of a molecular dynamic simulation to demonstrate the operation of
the developed model. For this, the example considered will be a cubic volume
of methane molecules suspended away from any boundaries to allow the use of
periodic boundary conditions in all three dimensions (Figure 3.19).
The 512 methane molecules (CH
4
) used in this example interact via the soft
sphere Lennard-Jones 6-12 potential and move according to Newton's law via the
Verlet algorithm as described above. Although this is a simple steady state system,
this example can demonstrate the application of molecular dynamic simulations.
To start the simulation, the number of molecules and their properties are input
into the initialization stage of the simulation. This allows a lattice of molecules
to be created to fill the domain with the given number in order to generate the
required density. The set temperature is then used to apply random velocities to
the molecules according to the Boltzmann distribution.
The next part of the simulation is to equilibrate, or settle, the molecules, as
the initial lattice is not a stable maintainable state, but a lattice makes for easy
initial placement. During the breakout of this lattice, there is also large variations
in molecular properties.
Figure 3.20 displays what happens when the molecules in the lattice are re-
laxed. Here, potential (PE), kinetic (KE) and total energies (E total) are plot-
ted from
t
1 ps. During the equilibration period, the kinetic energy
(and hence the temperature) is kept constant. This is because while the molecules
are settling down they can be exposed to unphysical and high interaction forces,
which can cause the energy of the system to become out of control. For this, sim-
ple velocity scaling is used.
Velocity scaling is a crude method of temperature control in molecular sys-
tems, where the kinetic energy of the molecules calculated using
=
0to
t
=
1
2
m
2
E
KE
,
t
=
v
(3.81)
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