Both methods model the time evolution of the atom–atom interactions and help extract the dynamic, thermodynamic, and structural properties of the materials. MD simulations typically consist of a data file of the initial coordinates of the atoms of interest, and a method or force field for characterizing the atom–atom interactions. The accuracy of the simulation results, typically defined by the user, depends on the approximations used in calculating the trajectories of the atoms. The trajectories are generated by numerically integrating Newton’s equations of motion and the atom–atom interactions are characterized by interatomic ‘‘potentials’’ (also known as force fields). These potentials are typically fitted to experimental data or high-level AIMD simulation results.

A shortcoming of the MD simulations is the limited transferability to various regions of the materials phase diagram. This is because the potentials used in the simulations are typically not fitted to the experimental data in all these regions. In addition, MD simulations do not accurately model the changes in the chemical bonding because of neglecting the effects of quantum chemical electronic polarization. When the materials undergo transformations to other polymorphs, the empirically derived potentials may not perform well. Another limitation of the MD simulations is when incorporating several materials into a single model or including many-body effects. Both of these cases would increase the computational time and hardware requirements, impeding the chance to obtain acceptable results in a reasonable time-frame.

cited from On force fields for molecular dynamics simulations of crystalline silica

Classical Mechanics means Newtonian physics, up to 100 thousands of atoms. Ab initio ("from the beginning") means quantum physics, another world. You can only tackle a few atoms in this case but can make and break bonds, transfer electrons, etc: you model the particles as nuclei and electrons employing approached solutions to the Schrodinger equation, while classical MD employes force fields which subtitutes atoms and bonds by spheres and spring, and make the use of empirical parameters (doesn't calculate anything "real")

Classical molecular dynamics

1)Interactions are approximated by classical model potentials constructed by comparison with experiment (empirical potentials) 2)Leads to simulation of purely classical many-particle problem 3)Works well for simple particles (such as noble gases) that interact via isotropic pair potentials

4)Poor for covalent atoms (directional bonding) and metals (electrons form Fermi gas)

5)Simulations fast, permit large particle numbers

Ab-initio molecular dynamics

1)Performs a full quantum calculation of the electronic structure at every time step (for every configuration of the atomic nuclei), Ab-initio = from first principles

2)Forces are found the dependence of the energy on the particle positions

3)Much higher accuracy than classical MD, but much higher numerical effort (restricts number of particles and simulation time)

Spatial and timescales that can be explored by means of molecular simulations as well as a comparison with experimental data.

cited from Neutron scattering, a powerful tool to study clay minerals