Computer-Modelling-for-Lennard-Jones

Lennard Jones Interaction Potential

Considering a model system interacting through the Lennard-Jones potential, a model for weakly-interacting neutral systems. Its attractive part is the leading $o (r^{-6})$ term of van der Waals interactions. The repulsive $o (r^{-12})$ term is a numerically simple way to model core-core repulsion. The potential energy of two particles at $\mathbf{r}_1$ and $\mathbf{r}_2$ may be written as：

$$U(\mathbf{r}_1,\mathbf{r}_2) = 4\epsilon [(\frac{\sigma}{r})^{12}-(\frac{\sigma}{r})^{6}]$$

where $r=|\mathbf{r}_1-\mathbf{r}_2|$. $\epsilon$ is the classical binding energy.

Files included:

cal_module.py: the python file for simulating LJ potential, including all of the functions needed for the experiment particle3D.py: the python file defining the Particle3D class li_utils.py, plot_xyz.py, test_basic_functions_lj.py : The provided python files

solid.xyz: XYZ trajectory file for representing simulation run of solid material solid.gif: 3d display of solid.xyz gas.xyz: XYZ trajectory file for representing simulation run of gas material gas.gif: 3d display of gas.xyz out.xyz: XYZ trajectory file for basic test, showing two particles out.gif: 3d display of out.xyz

How to run my code:

input: parameters output: time.npy, kinetic.npy, potential.npy, total.npy and MSD.npy xxx.xyz(trajectory file), 1、Solid Argon:Run the code with 32 particles, ρ = 1.0, T = 0.1, dt = 0.01 (in reduced units) for 1000 steps. for simulation, use the following command:

python cal_module.py -n 32 -d 1.0 -t 0.1 --dt 0.01 -Nstep 1000 -o solid.xyz

in this case, input of the python file is the parameters, -n indicates number of particles, -d is the density, -t is the temperature, --dt and -Nstep is the simulation parameter, the time step and number of simulation steps. -o is the name of output file, which is solid.xyz

2、Gaseous Argon:Run the code with 30 particles, ρ = 0.05, T = 1.0, dt = 0.005 (in reduced units) for 2000 steps. for simulation, use the following command:

python cal_module.py -n 30 -d 0.05 -t 1.0 --dt 0.005 -Nstep 2000 -o gas.xyz

in this case, input of the python file is the parameters, -n indicates number of particles, -d is the density, -t is the temperature, --dt and -Nstep is the simulation parameter, the time step and number of simulation steps -o is the name of output file, which is gas.xyz

3、for observable : when run cal_module.py, other quantities such as kinetic, potential, total energies and MSD are saved as kinetic.npy, potential.npy, total.npy and MSD.npy separately.

4、for visualization you can run plot_xyz.py to generate 3d animation of particles using the following command:

python .\plot_xyz.py .\gas.xyz --3d -o gas.gif

in this case, the filename after python .\plot_xyz.py is the input file, --3d means plot in 3D, -o is the name of output file, which is gas.gif. In addition, you can also use -s to denote number of steps per frame of the animation