Lennard-Jones (6-12) was a widely adopted model used in early MD simulations which is considered a reasonable description of van der Waals interactions for noble gas elements with class-shell atoms.
Morse Potential
Ionic Potentials
Coulomb Potential. The long-range electrostatic interactions must be treated differently from short-ranged interactions because it involves computation between all ionic pairs. This computation in the O(N2)
Ewald Summation. The Ewald simmation decomposes the electrostatic inteaction into a short-ranged component, plus a long-ranged component, which can be efficiently summed in the reciprocal space to reduce the computation time to order O(N3/2)
Transferability. No one single physical property that can determine the entire potential function. Using different data to fix the model parameters of the same potential form can lead to different simulations, making quantitative comparison ambiguous. To validate a model, calculate an observable property not used in fitting a compare with an experimental or ab-initio data. This provides a test for transferability, which is a key measure of robustness of a model
Simulation Systems
Supercell. A simulation system is typically a parallelepiped supercell in which particular are either placed in a very regular manner, as in a crystal lattice, or in some random manner as in modeling a gas or liquid.
Periodic Boundary Conditions. For the simulation of bulk properties is conventional to use periodic boundary conditions. When a particle moves out of the boundary of the simulations cell, an image particle enters on the opposite side. The effect is that particles cannot be lost or created. If the particle number is conserved and the simulation cell volume does not change, the system density remains constant. [add discription of image cell, and image particles].
Minimum Image Convention. The minimum image convention is a procedure in which one takes the nearest neighbor to an actual particle as the interaction partner, regardless of whether this neighbor is an actual particle or an image particle (that is a particle that exists outside the simulation cell and interacts).
Neighbor Lists. Keeps track of who are the nearest, second nearest, ..., nth structure of each particle. This saves time for checking each particle in the system when forces are calculated at each time step.
Cai W., Li J., and Yip S. (2012) Molecular Dynamics. In: Konings R.J.M., (ed.) Comprehensive Nuclear Materials, volume 1, pp. 249-265 Amsterdam: Elsevier. Link
Allen, M.P, and Tildesley, M.P. Computer Simulations of Liquids. Oxford: Oxford Science Publications.
Ewald, Paul Peter. "Die Berechnung optischer und elektrostatischer Gitterpotentiale." Annalen der Physik 369.3 (1921): 253-287.