87927 - COMPUTATIONAL MATERIAL PHYSICS

Learning outcomes

At the end of the course the student will become familiar with different computational methodologies used to model and understand the properties of materials, with emphasis on first principles methods. The content of the course includes: basic ideas and concepts of numerical simulations; introduction to numerical solution of the one-body and many-body Schrödinger equation; Hartree-Fock and density-functional theory; electronic structure methods. Selected examples of properties of materials predicted from electronic structure schemes will be presented and discussed theoretically, but also through practical computational exercises. The student will be able to test the applicability of the various computational tools to diverse problems through the implementation and execution of model computer programs.

Course contents

0. Introduction

Brief introduction to numerical simulations and basic principles of quantum mechanics necessary for the solution of the Schrödinger equation for a system of many electrons.

1. Numerical solution of the Schrödinger (1 particle)

1.1 Direct integration: Shooting method

1.2 Matrix approach (Lanczos)

1.3 Variational approach

2. The many body problem (atoms & molecules)

2.1 The many-body Hamiltonian

2.2 The Hartree-Fock method

2.3 The Density Functional Theory

3. Electrons in a periodic potential: electronic structure schemes

3.1 Kronig-Penney model

3.2 The tight-binding method

3.3 The Augmented plane wave method

3.4 The pseudopotential method

4. Materials & Hands-on

Application of electronic structure methods for the calculation of properties of materials: theory and practical calculations.

Computational lab using the Vienna Ab Initio Simulation Package (VASP). This part of the course will be developed in the last 2 weeks (~4 meetings).

4.0 VASP: basics (input & output)

4.1 Structure: 1D, 2D & 3D

4.2 The band gap problem: metal, insulator, semimetal

       Band structure and density of states

4.4 Magnetism: long-range ordering and exchange interactions

4.5 Optional:  Optical, dielectric and phonon properties

Readings/Bibliography

J.M Thijssen, Computational Physics, CAMBRIDGE

R.M. Martin, Electronic Structure: Basic Theory and Practical Methods, CAMBRIDGE

E. Kaxiras, Atomic and Electronic Structure of solids, CAMBRIDGE

R.M. Martin, L. Reining, and D.M. Ceperley, Interacting Electrons: Theory and Computational Approaches, CAMBRIDGE

F. Giustino, Materials Modelling using Density Functional Theory: Properties and Predictions, OXFORD

VASP Manual

Teaching methods

Front lectures, practical sessions (computational lab), group discussions

Assessment methods

Written project report (optional but recommended) and oral exam.

The teacher will provide a list of possible projects.  Most of the projects will focus on advanced applications of the VASP but the student could also decide to choose purely theoretical projects (elaborations of a specific theories or specific equations relevant to the field of computational materials science) or the implementation of a computer code.

Teaching tools

Blackboard, Slides, Llive computational examples (laptop), computational lab.

Office hours

See the website of Cesare Franchini