Intro to Molecular Dynamics: Coding MD From Scratch

This is a brief introduction to how MD simulations work: essentially numerically solving Newton’s equations for a bunch of interacting objects. It is a bit different from my usual videos because it is just something I was screwing around with for fun and thought it might be interesting to post. If you notice any issues with the code or the math please let me know. As I said, I was just screwing around so it’s not as extensively checked as publication-quality research.

Correction: When running the water simulations, there was an error in the epsilon values I was using. The videos I included are not too far off but I thought I should mention it.

Correction: As pointed out by MCMC271, simply rescaling the velocities like I did does not produce the correct probability distributions for the NVT ensemble and is thus not a good way to keep the temperature constant. I should have stated this in the video and pointed the viewer to better thermostats.

References:
Ovito: https://www.ovito.org
LJ parameters for hydrogen: https://citeseerx.ist.psu.edu/viewdoc...
H2O parameters (bonds/LJ parameters): http://dx.doi.org/10.1016/j.fluid.200...
Code: https://github.com/PolymerTheory/MDFr...
(Still not sure if to include the code so it may or may not be public)

In case I do not get around to making a video on using available MD software, I recommend looking into LAMMPS, NAMD or GROMACS:
LAMMPS:
Download from: https://docs.lammps.org/Install.html
Tutorial page: https://www.lammps.org/tutorials.html
I particularly recommend the .pdf files numbered SoR 01, 05 and 11
NAMD:
Tutorial: http://www.ks.uiuc.edu/Training/Tutor...
GROMACS:
https://www.gromacs.org
If you feel like paying for software, you should also check out Materials Studio and/or COMSOL.

Chapters:
0:00 Hello
0:39 Newton's equations
1:21 Code
2:30 Visualization (matplotlib)
3:10 Boundary conditions (periodic)
4:35 BCs (reflecting)
5:55 Visualization (OVITO)
7:45 Lennard-Jones interactions
13:14 Periodic BC interaction discussion
14:48 Particle types
15:12 Microcanonical (NVE) ensemble
16:33 Canonical ensemble (fixing T)
19:26 Bond potentials
22:17 Bond angles
26:32 Dihedral angles
27:11 Electrostatics
28:28 Combining potentials
29:33 Polymers
30:08 Potential cutoff
30:53 Gravity
31:28 Summary