87927 - Computational Material Physics

Academic Year 2024/2025

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics (cod. 9245)

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. Intro: Numerical solution of the Schrödinger (1 particle)

1.1 Direct integration: Shooting method

1.2 Variational approach

1.3 Machine Learning (hints)

2. The many body problem (atoms & molecules)

2.1 The many-body Hamiltonian

2.2 Atoms and molecules

2.3 The Hartree-Fock method

2.4 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. Hands-on Computational Lab

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 5 weeks with approx 5 meetings (4 hours each)

4.0 VASP: basics (input & output)

4.1 Atoms

4.2 Molecules

4.3 Periodic systems: linear chain and graphene

4.4 Solids: carbon allotropes (Band structure and density of states)

Optional projects: band gap beyond DFT, optical properties,surfaces, phonons, machine learning for materials.

Readings/Bibliography

J.M Thijssen, Computational Physics, CAMBRIDGE

Marvin L. Cohen & Steven G. Louie Fundamentals of Condensed Matter Physics, CAMBRIDGE

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

The VASP Manual

VASP Examples

VASP Tutorials

Teaching methods

Front lectures and practical sessions (computational lab). Discussion sessions

Assessment methods

Written project reports on the lab activity and oral exam.

Lab reports: The student should write 4 brief reports (~2 pages) on the 4 main lab activities. It is advisable that the report for one specific lab project should be handed-in before the next lab session (report on lab-day1 handed-in before lab-day2).

Oral exam: typically 3 questions

Alternatively, the student could decide to develop a specific project to present and discuss during the oral exam. In this case the oral exam will involve the discussion of the project and one more question on a topic not related to the project. The final project reports should be delivered 2-3 days before the exam.

The teacher will provide a list of possible projects: advanced application of the VASP code, machine learning projects, implementation of a computer code from scratch, theoretical projects.

Teaching tools

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

Health and safety training modules 1 and 2 must be completed for attending the computational lab.

E' richiesto lo svolgimento dei moduli 1 e 2 di formazione per la sicurezza e salute

Office hours

See the website of Cesare Franchini