# Introduction to First Principle Molecular Dynamics (FPMD) Methods

In a traditional MD simulation of a system of molecules, force fields (pair potential for example) are parameterized either based on experiments or electronic structure calculations. The molecules are then evolved with Newtonian equations of motion with an integrator (Velocity Verlet for example) and environmental constraints are imposed with a thermostat and a barostat. In FPMD, the force field approximation is lifted by performing an on-the-fly electronic structure calculation. Everything else is usually kept the same.

# CMD

Centroid molecular dynamics is based on Feynman’s path integral formulation of quantum mechanics detailed by Cao and Voth in a series of JCP papers starting with this one.

# BOMD

A converged DFT calculation at each MD step.

# CPMD

Dynamic simulated annealing, with MD and DFT evolved together at every step.

# PIMD

Exploit the isomorphism between classical ions and ring polymers.

Core Concepts:

1. Pair-Potential Molecular Dynamics
2. Density Functional Theory
3. Born-Oppenheimer Molecular Dynamics
4. Simulated Annealing
5. Car-Parrinello Molecular Dynamics
6. Thermo Density Matrix