Potential_Part_1

# Potential_Part_1 - Introduction to interatomic potentials(I...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei In order to use Molecular Dynamics or Monte Carlo methods we have to define the rules that are governing interaction of atoms in the system. In classical and semi-classical simulations these rules are often expressed in terms of potential functions. The potential function U( r 1 , r 2 , …, r N ) describes how the potential energy of a system of N atoms depends on the coordinates of the atoms, r 1 , r 2 , …, r N . It is assumed the electrons adjust to new atomic positions much faster than the motion of the atomic nuclei (Born-Oppenheimer approximation). The forces in MD simulation are defined by the potential, How to obtain the potential function for a particular system? Introduction to interatomic potentials (I) 1. One can assume a functional form for the potential function and then choose the parameters to reproduce a set of experimental data. This gives so-called empirical potential functions (e.g. Lennard-Jones, Morse, Born-Mayer). 2. One can calculate the electronic wavefunction for fixed atomic positions. This is difficult for a system of many atoms. Different approximations are used and analytic semi- empirical potentials are derived from quantum-mechanical arguments (e.g. Embedded Atom Method (EAM) by Foiles, Baskes, and Daw, Glue Model by Ercolessi et al., bond- order potentials by Tersoff and Brenner, etc.). 3. One can perform direct electronic-structure (quantum-mechanics-based) calculations of forces during so-called ab-initio MD simulation (e.g., Car-Parrinello method using plane- wave psuedopotentials). ) r ,..., r , r ( U F N 2 1 i r i r r r r r =

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Going from QM to classical mechanics through the Born-Oppenheimer approximation In Molecular Dynamics or Monte Carlo methods we use potential function U to describe interaction among atoms. But we know that in real materials the dynamics of atoms is controlled by the laws of quantum mechanics and the bonding is defined by the electrons that are not present in classical MD/MC. Is the use of the potential functions justified?
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Potential_Part_1 - Introduction to interatomic potentials(I...

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