Introduction to Energy Models

Introduction to Energy Models

(Parte 1 de 7)

MAE 715 –Atomistic Modeling of Materials

N. Zabaras (3/25/2009) 1

Material for these lecture notes was compiled from the references below

9MIT’s 3.320 course notes (Prof. G. Ceder)

9Physics 460, Solid State Physics (Prof. R. Martin)

9C. Kittel, Introduction to Solid State Physics

9N.W. Ashcroft and N.D. Mermin, Solid State Physics

9A. Leach, Molecular Modelling: Principles and Applications (chapter 4and chapter 6Aand 6B)

9Empirical potentials in Chemistry

9Database of published interatomicparameters (exportable to GULP)

9Daw, M. S., Foiles, S. M. & Baskes, M. I. The EAM: a review of theory and applications Materials Science Reports 9, 251 (1993).

9Collection of papers on empirical potentials for Silicon

9Example of the Clementiand RoettiTables

9L. Girifalcoand V. Weizer, Applications of the Morse potential to metals, Phy Rev 114 (1959) 687.

Introduction to Energy Models

MAE 715 –Atomistic Modeling of Materials

N. Zabaras (3/25/2009) 2

Energy Models

¾We need to have an adequate energetic description of materials for reliable simulations.

¾We distinguish these models in (a) empirical energy, (b) semi-empiricaland (c) ab-initio or quantum mechanical models (in order of increased transferability and computational cost)

Empirical models

(functional form with parameters fitted to data)

Pair potentials

Multi body potentials Effective Medium Theories

Semi-empirical models

Tight binding MINDO/NINDO

Quantum mechanical models

(start from the many body Schrödinger equation and make approximations)

Hartree Fock

Density Functional Theory Quantum Monte Carlo

Energy only

Energy and electronic structure

MAE 715 –Atomistic Modeling of Materials

N. Zabaras (3/25/2009) 3

Energy Models

¾In empirical models, we take some form for the energy and fit it to any data we may have.

Data can be: experimental, theoretical or computational

¾In quantum mechanical models, there is no fitting aside --you just solve the Schrödinger equation.

¾Semi-empirical methods are in between: quantum mechanically informed but empirical in the parameters.

•Example of this is Tight binding(the chemists often use MINDO and NINDO).

Here we have parameterized Schrödinger equations, where the `overalp integrals’ between wave functions are not computed but are parameterized.

You save a lot of time with these approaches at the expense of accuracy.

MAE 715 –Atomistic Modeling of Materials

N. Zabaras (3/25/2009) 4

Energy Models

¾More and more people do ab-initio these days.

¾The reason we spent a few lectures on empirical models is because they are useful for making general predictions about large systems.

¾If you work with potentials, you have no information about electrons. You just have energies as a function of position.

¾If you work with semi-empirical or quantum mechanics methods, you know something about the electronic structure of the material.

MAE 715 –Atomistic Modeling of Materials

(Parte 1 de 7)