A simple computational code to compute the basic behaviour of a system of particles and determine its consistency under the Lennard Jones Potential Curve.
One of the most widely used intermolecular potentials in classical many-body simulations, is the so-called Lennard-Jones 12-6 potential,
$\displaystyle V(r) = 4 \epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]$
Also expressed as,
$\displaystyle V(r) = \left(\frac{A}{r^{12}}\right) - \left(\frac{B}{r^{6}}\right)$ \
where,
-
$V$ is the intermolecular potential between the two atoms or molecules. -
$\epsilon$ is the well depth and a measure of how strongly the two particles attract each other. -
$\sigma$ is the distance at which the intermolecular potential between the two particles is zero (Figure 1).$\sigma$ gives a measurement of how close two non-bonding particles can get and is thus referred to as the van der Waals radius. It is equal to one-half of the internuclear distance between nonbonding particles. -
$r$ is the distance of separation between both particles (measured from the center of one particle to the center of the other particle). -
$A = 4 \epsilon \sigma^{12}$ ,$B = 4 \epsilon \sigma^{6}$ - Minimum value of
$\Phi(r)$ at$r=r_{min}$ .
Lennard-Jones-type
The code exists in two variants, C++ and Python. Execution of each variant does not require additional installation other than the basic language compilers.
- C++
cd /Home/User/File_Location
g++ Molecular_Dynamics.cpp
./a.out
- Python
cd /Home/User/File_Location
python3 Translated_MD.cpp
python3 Plot_part.py