NANOSCALE DEVICES: APPLICATIONS AND MODELING - Bio-Inspired and Nanoscale Integrated Computing - page 57

Potential energy

Equilibrium point

d

Interatomic distance

Figure 2.15. A simple representation of the interaction potential energy of two
atoms.

the two atoms are a distance d apart, they are in equilibrium. If they are pushed
closer, the force between them will be repulsive. If they are pulled farther, the force
between them will be attractive. Both cases would lead to the atoms going back to
their equilibrium distance.
Here is how molecular dynamics works in principle: consider a system of a
number of atoms. We place them in close proximity and would like to find what
the equilibrium position of each atom in the ''relaxed'' structure would be. We can
start by calculating the force on each atom resulting from the rest of the atoms,
using curves such as the one in Figure 2.15. Then, using Newton's equation of
motion F=ma, we can calculate the acceleration on each atom due to this force.
Now we let all the atoms move under these accelerations for a very small duration
of time—a duration short enough that we can assume the force (and, as a result,
acceleration) on each atom does not change significantly during that time. After
this very short time, we have the new locations of the atoms and their new
velocities. From the new locations we can calculate the new accelerations each will
be feeling, and then move in time one more short step. If we repeat this process for
a large enough number of time steps, at some point we will see that the atoms will
not move significantly any longer as time passes. This will be the equilibrium or
relaxed configuration of the system. One way to see this is to plot the total
potential energy (the sum of all atom-atom interactions) of the system as a
function of time. Eventually, this curve will saturate and asymptotically go toward
the relaxed energy of the system.
One important issue to consider is that the system could converge to the
metastable state closest to where we started from (in terms of initial choice of
atomic positions). Therefore, in order to find the global minimum energy
configuration of the structure, one may need to repeat the simulation with various
choices of initial configurations and compare the end results in terms of total
energy, or incorporate mechanisms to ''kick'' the system out of metastable
configurations (using parameters such as thermal energy) with the hope that it
will find its global minimum. Many variations of molecular dynamics are in use
today and they can handle systems of relatively large numbers of atoms
(thousands or tens of thousands of atoms) in reasonable time on present day