Elements of Atomistic Simulations

Garant předmětu:

Antonio Cammarata

Lecturer:

Antonio Cammarata

Tutor:

Antonio Cammarata

Supervisor:

Department of Control Engineering

Synopsis:

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.

Requirements:

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

Syllabus of lectures:

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

Syllabus of tutorials:

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

Study Objective:

Study materials:

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

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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

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomKN:E-26 Cammarata A. 09:15–10:45 (lecture parallel1) Karlovo nám. Laboratoř TŘ2roomKN:E-26 Cammarata A. 11:00–12:30 (lecture parallel1 parallel nr.101) Karlovo nám. Laboratoř TŘ2
Wed
Thu
Fri

The course is a part of the following study plans: