swetanjal/lennard-jones-system

Simulating the trajectory of Argon atoms in a box using Lennard Jones Potential to model the interaction between particles and Velocity Verlet algorithm to solve the equations of motion

Lennard Jones System

Link to repo: https://github.com/swetanjal/Lennard-Jones-System

Specification of the system:

• Number of partciles (N) = 108
• Dimensions of box along X axis(Lx) = 18.0 A
• Dimensions of box along Y axis(Ly) = 18.0 A
• Dimensions of box along Z axis(Lz) = 18.0 A
• epsilon = 0.238 kcal/mol
• sigma = 3.4 A
• Initial constraint rij >= 3.4 A

Problem Statement:

1. Generation of initial configuration
2. Calculating the negative gradient of the total potential energy function
3. Total potential energy minimization
4. Sample initial velocities from the Maxwell-Boltzmann velocity distribution
5. Solve the Hamilton's equations of motion and generate trajectories of atomic coordinates and velocities
6. Calculate mean square displacement, velocity correlation function, van Hove correlation function, and dynamic structure factor

Instructions to run code:

# Changing into the src directory
cd src

python3 main.py [--minimize-potential] [--initial-config filename] [--initial-velocity filename] [--frames n_frames] [--temperature value_in_K]

# Example Usage
python3 main.py --minimize-potential --frames 250

When option minimize-potential is set to True, step 3 i.e total potential energy minimization step takes place and the configuration is saved after that in corresponding pdb files.

Use initial-config flag to load coordinates of particles from pdb file.

Use initial-velocity flag to load velocity of particles from pdb file.

Instructions to generate mean square displacement plot:

python3 msd.py ../outputs/argon_coordinates.pdb

Instructions to generate velocity autocorrelation plot:

python3 velocity_corr.py ../outputs/argon_velocities.pdb

Instructions to generate Vann Hove correlation plot:

python3 vann_hove.py ../outputs/argon_coordinates.pdb

Instructions to generate Dynamic Structure Factor

# Please change the number of frames to average in sample_s_k_full.in

./computeStructureFactor -i sample_s_k_full.in

python3 plot_structure_factor.py ../outputs/traj_out.txt

Instructions to generate Dynamic Structure Factor(Double Fourier Transform of Van Hove Correlation Fn.)

python3 structure_factor.py ../outputs/argon_coordinates.pdb no_of_frames

Description of files generated in outputs:

1. argon_coordinates.pdb : A PDB file containing the coordinates of trajectory of all N atoms.
2. argon_velocities.pdb : A PDB file containing the velocity trajectories of all N atoms.
3. initial_config_coords.xyz : A file in xyz format which contains coordinates of N atoms, generated randomly adhering to the constraints given in the problem statement. This generated file can be used to load initial coordinate configuration into the system.
4. initial_config_velocities.xyz: A file in xyz format which contains initial velocities of each of the N atoms sampled from Maxwell Boltzmann Velocity Distribution. This file can be used to load the inititial velocity configuration into the system.
5. minimized_config_coords.xyz : A file in xyz format which contains the coordinates of N atoms after the Potential Energy Minimization step.
6. traj.xyz : A file in xyz format which contains the coordinate trajectory of each of the N atoms.

README: https://docs.google.com/document/d/1Ktl6CnwiAqsZnHV3XtD3a-qb3JYfnMJgpoVlE54ZoxU/edit?usp=sharing