Popis předmětu - BE0M35EAS

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BE0M35EAS Elements of Atomistic Simulations
Role:  Rozsah výuky:2P+2L
Katedra:13135 Jazyk výuky:EN
Garanti:Cammarata A. Zakončení:Z,ZK
Přednášející:Cammarata A. Kreditů:4
Cvičící:Cammarata A. Semestr:Z,L

Anotace:

The final goal of the course is to acquire basic knowledge of Classical and Quantum Mechanics to design in-silico experiments within the Materials Science field. At the end of the course, the students will know: - how the fundamental equations of thermodynamics, newtonian and statistical mechanics are implemented in simulative softwares with the aim to calculate thermodynamical properties; - how the Schrödinger equation is setup and numerically solved in order to calculate physical quantities; - how to combine both classical and quantum mechanics to model experimental results; and - a general protocol for the design of new materials at the atomic scale with target properties. By means of simulation laboratory experience, the students will eventually learn how to setup and run simulations, and how to analyse and present the results by using post-processing softwares.

Obsah:

The aim of this course is to give a basic knowledge of the principles and techniques of computational materials science. At the end of the course, the student will be able to setup simple simulations to study atomic-scale material properties and to lay the foundations of a material design project; eventually, the students will gain the proper background to extend their academic formation with higher degree courses (e.g. PhD in Applied Physics, Materials Science or equivalent). The course covers the physical understanding of matter from an atomic point of view. Topics covered include static and dynamical description of matter at the atomic level. The course is tailored for master degree students with basic knowledge of laws of thermodynamics and Newton's laws. Fundamental theories in solid state physics are introduced together with their software implementation, showing how to use them in current-day technology, industry, and research. The course has a theoretical lecture component and laboratory experiences, making extensive use of examples and exercises to illustrate the subject.

Osnovy přednášek:

1. Introduction to the course: lessons outline, introduction to the computational environment (e.g. bash shell, code compilation) and to the use of High Performance Computing facilities (ssh, rsync, SLURM, parallelism)
2. Fundaments of thermodynamics and statistical mechanics (state variables, laws of thermodynamics, phase space, partition functions, ensembles, ...)
3. Units & dimensions, periodic boundaries conditions, integrators (e.g. Verlet, Leapfrog)
4. Classical force fields, potential energy surfaces, types of interaction, calculation techniques
5. Non-Hamiltonian dynamics, thermostats & barostats (e.g. Berendsen, Nose-Hoover/Rahman-Parrinello)
6. Non-equilibrium MD simulations, external forces, constraints
7. Introduction to quantum mechanics: the postulates of quantum mechanics, the uncertainty principle, time dependent and time independent Schrödinger equation, Hamiltonian, observable quantities and expectation values
8. The hydrogen atom and the hydrogen-like orbitals; Molecular Orbitals, Roothan-Hall Self Consistent Field procedure, Density Functional Theory
9. Crystal structures and reciprocal lattice, the Born-Oppenheimer approximation, the Hellmann-Feynman theorem
10. Free electron model, the Bloch's theorem, energy bands
11. Phonon description of atomic motions
12. Phonon description of thermal properties, anharmonic interactions
13. The Franck-Condon principle, the Jablonski Diagram, Electron-Phonon coupling
14. Atomic-scale design of new materials

Osnovy cvičení:

1. Introduction to LAMMPS, preparing an input script for energy minimization, introduction to VMD
2. NVE molecular dynamics simulations, case study
3. NpT molecular dynamics simulations, case study
4. Steered MD simulations, case study: sliding of a MoS2 flake on a substrate
5. Introduction to parallel environment in MD simulations
6. Individual student projects on MD simulations and remarks
7. Introduction to ABINIT, preparing an input script for electronic energy minimization, introduction to visualization software for solid state physics (e.g. VESTA)
8. Visualization of hydrogen orbitals and relative energies, analysis of electronic charge density of molecular systems (e.g. electronic charge differences, Electron Localization Function, Bader analysis, Orbital Population)
9. Construction of crystal unit cells, application of the Hellmann-Feynmann theorem: optimization of atomic geometries
10. Electron Density of States, bond covalency analysis
11. Calculation and visualization of phonon modes, phonon Density of States
12. Calculation and analysis of thermal properties from phonon modes
13. Simple example of electron-phonon coupling
14. Materials design, case study: layer shift in MX2 transition metal dichalcogenides

Literatura:

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics, 3rd edition, Oxford University Press, ISBN 0-19-855947-X
Charles Kittel, Introduction to Solid State Physics, 8th edition, Wiley IPL, ISBN-13: 9788126535187 ------------------------------------------------------------------------------ Peter Atkins, Julio de Paula, Physical Chemistry, 9th Edition, Oxford University Press, ISBN-13: 9780199543373 Daan Frenkel, Berend Smit, Understanding Molecular Simulation, 2nd Edition, Academic Press, ISBN-13: 9780122673511
H. Goldstein, C. P. Poole and John Safko, Classical Mechanics, 3rd edition, Pearson Education, ISBN-13: 9788131758915
C. Cohen-Tannoudji, B. Diu and Frank Laloe, Quantum Mechanics Vol.1, 1st edition, Wiley, ISBN-13: 9780471164333

Požadavky:

Derivative of a function, definite and indefinite integral, Newton‘s equations, laws of thermodynamics, basic usage of a computer.

Předmět je zahrnut do těchto studijních plánů:

Plán Obor Role Dop. semestr


Stránka vytvořena 23.4.2024 17:50:37, semestry: Z,L/2023-4, Z/2024-5, připomínky k informační náplni zasílejte správci studijních plánů Návrh a realizace: I. Halaška (K336), J. Novák (K336)