Elements of Atomistic Simulations
Code  Completion  Credits  Range  Language 

BE0M35EAS  Z,ZK  4  2P+2L  English 
 Course guarantor:
 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 insilico 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 postprocessing 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. NonHamiltonian dynamics, thermostats & barostats (e.g. Berendsen, NoseHoover/RahmanParrinello)
6. Nonequilibrium 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 hydrogenlike orbitals; Molecular Orbitals, RoothanHall Self Consistent Field procedure, Density Functional Theory
9. Crystal structures and reciprocal lattice, the BornOppenheimer approximation, the HellmannFeynman 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 FranckCondon principle, the Jablonski Diagram, ElectronPhonon coupling
14. Atomicscale 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 HellmannFeynmann 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 electronphonon 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 019855947X
Charles Kittel, Introduction to Solid State Physics, 8th edition, Wiley IPL, ISBN13: 9788126535187

Peter Atkins, Julio de Paula, Physical Chemistry, 9th Edition, Oxford University Press, ISBN13: 9780199543373
Daan Frenkel, Berend Smit, Understanding Molecular Simulation, 2nd Edition, Academic Press, ISBN13: 9780122673511
H. Goldstein, C. P. Poole and John Safko, Classical Mechanics, 3rd edition, Pearson Education, ISBN13: 9788131758915
C. CohenTannoudji, B. Diu and Frank Laloe, Quantum Mechanics Vol.1, 1st edition, Wiley, ISBN13: 9780471164333
 Note:
 Timetable for winter semester 2024/2025:

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 Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: