Scheda insegnamento
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Docente Cesare Franchini
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Crediti formativi 6
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SSD FIS/03
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Modalità didattica Convenzionale - Lezioni in presenza
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Lingua di insegnamento Inglese
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Campus di Bologna
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Corso Laurea Magistrale in Physics (cod. 9245)
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Orario delle lezioni dal 28/09/2022 al 23/12/2022
Anno Accademico 2022/2023
Conoscenze e abilità da conseguire
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.
Contenuti
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 Variational approach
1.3 Machine Learning
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. 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 4 weeks with 4 meetings (4 hours each)
4.0 VASP: basics (input & output)
4.1 Atoms, molecules and solids
4.2 The band gap problem: metal, insulator, semimetal
Band structure and density of states
4.4 Optional (1). Magnetism: long-range ordering and exchange interactions
4.5 Optional (2). Optical, dielectric and phonon properties
Testi/Bibliografia
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
Metodi didattici
Front lectures, practical sessions (computational lab), exrecises
In considerazione della tipologia di attività e dei metodi didattici adottati, la frequenza di questa attività formativa richiede la preventiva partecipazione di tutti gli studenti ai moduli 1 e 2 di formazione sulla sicurezza nei luoghi di studio, [https://elearning-sicurezza.unibo.it/] in modalità e-learning
Modalità di verifica e valutazione dell'apprendimento
Written project reports on the lab activity and oral exam.
Oral exam: typically 3 questions on the three different part of the program
Lab reports: The student should write 4 brief reports (~2 pages) on the 4 lab activities. 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).
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.
Strumenti a supporto della didattica
Blackboard, Slides, Llive computational examples (laptop), computational lab.
Orario di ricevimento
Consulta il sito web di Cesare Franchini