Quantum Molecular Dynamics

Quantum molecular dynamics is the computer simulation of atomic many-body ensembles based on classical, statistical, and quantum mechanics. Such simulations are often the only way to apply quantum mechanics to dynamical many-body systems and thus, are extremely important in theoretical chemistry, nuclear physics, and materials science. In this paper I discuss the subset of molecular dynamics schemes which allow for the study of chemical systems by assuming the separability of nuclear and electronic degrees of freedom. The basic idea of these methods is straightforward: construct a system of many atoms, use quantum mechanics to calculate the force on each atom, integrate Newton\u27s equations of motion for a small time step, and repeat. The first section of this paper discusses the classical n-body problem and introduces the Verlet algorithm for numerical integration. Next, I explain the Hartree-Fock procedure for circumventing the quantum many-bodies problem. Finally, I cover how molecular dynamics can be applied in an umbrella sampling scheme to elucidate the potential energy surface and mechanism of a chemical reaction