Quantum Chemistry: Density functional theory

Objectives:
The students will obtain fundamental knowledge on density functional theory (DFT). The students will learn to prepare, run and analyse simple DFT simulations. They will use freely available program packages and tools, such as Quantum Espresso, GAMESS and GPAW and the scripting environment ASE and Python. The students will learn about molecular and periodic system, the differences in approach and the limitations.
During the tutorial, a practical example of modelling the diffusion barrier on a surface will be given.

General competencies:
• The students will know the research methods for quantum chemical modelling
• The students will be able to use quantum chemical modelling in their line of research
• The students will develop communication skills to present their results in a written and oral form
• The students will be able to work independently
• The students will learn to work in international teams

Course-specific competencies:
• The students will understand the methods for quantum chemical modelling and their limitations
• The students will understand electron correlation and different ways of approximating it
• The students will understand the difference between modern functionals (hybrid, GGA) and earlier ones (LDA)
• The students will able to prepare quantum chemical simulation and run them
• The students will be able to prepare a model that corresponds to a real problem
• The students will be capable of critically analyzing the data from quantum chemical simulations
• The students will understand when DFT is not the most suitable method

Completed Bologna second level study programme or an equivalent pre-Bologna university study programme.

1. Introduction to the density functional theory, wave function, the Schrödinger equation, operators
2. Hohenberg-Kohn theorems, Kohn-Sham formalism, electron correlation
3. Basis sets and pseudopotentials
4. Functionals: LDA, GGA, hybrid; the problem of van der Waals interactions
5. Periodic systems and supercells: Bloch theorem, reciprocal space, Brillouin zone
6. Density of state, band structure, Fermi energy: differences between metals and nonmetals, semiconductors
7. Structure optimization, vibrational analysis
8. Born-Oppenheimer and Car-Parrinello molecular dynamics
9. Energy differences: bond strength, reaction energy, adsorption energy
10. Surfaces: surface energy, work function
11. Electron density: molecular orbitals, charge density difference, projected density of states, charge donation and backdonation
12. Chemical reactions: transition state theory, collision theory, transition states search, activation energy
13. Application to catalysis; homogeneous and heterogeneous catalysis, solvent effects, differences when describing electrocatalysis and photocatalysis
14. The effect of electric fields; charged systems, solvation.
15. Tutorial: diffusion of hydrogen and oxygen on a surface.

The students will have obtained an overview of quantum chemical methods and techniques.

The students will have obtained a broad understanding of the DFT approaches.

The students will have a functional knowledge required to bootstrap a quantum chemical simulation.

The students will be able to analyze and interpret the results of quantum chemical simulations.

The student will be able to use the quantum chemical modelling in their line of research.

Books: * Giustino, Feliciano. Materials modelling using Density Functional Theory: Properties and Predictions, Oxford University Press, Oxford, 2014. Catalogue E-version * David S. Sholl, Janice A. Steckel. Density Functional Theory: A Practical Introduction. John Wiley & Sons, 2011. E-version * Koch, Wolfram; Holthausen, Max C. A chemist's guide to density functional theory, 2. ed.: Weinheim: Wiley-VCH, cop. 2001 E-version * Szabo, Attila; Ostlund, Neil S. Modern quantum chemistry: introduction to advanced electronic structure theory 1. ed., rev.: Mineola, N.Y.: Dover, 1996 E-version * Roald Hoffmann. Solids and surfaces: A chemist’s view of bonding in extended structures, Wiley-VCH, New York, 1988.Catalogue E-version

Articles: * Z. W. Chen, L. X. Chen, Z. Wen, Q. Jian. Understanding electro-catalysis by using density functional theory, 21 (2019), 23782–23802. https://doi.org/10.1039/C9CP04430B * S. Ghosh et al. Combining Wave Function Methods with Density Functional Theory for Excited States, Chemical Reviews, 118 (2018), 7249–7292. https://doi.org/10.1021/acs.chemrev.8b00193 E-version * N. Mardirossian, M.-H. Gordon. Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals, Molecular Physics, Vol. 115 (2017), 2315–2372. https://doi.org/10.1080/00268976.2017.1333644 E-version * Jain, Y. Shain, K. A. Persson, Computational predictions of energy materials using density functional theory, Nature Reviews Materials, Vol. 1 (2016), 15004 https://doi.org/10.1038/natrevmats.2015.4 E-version * R. O. Jones, Density functional theory: Its origins, rise to prominence, and future, Reviews of Modern Physics, Vol. 87 (2015), 897–923 https://doi.org/10.1103/RevModPhys.87.897 E-version * Hammer, J. K. Norskov, Theoretical surface science and catalysis –Calculations and concepts, Advances in Catalysis, 45 (2000), 71–129 https://doi.org/10.1016/S0360-0564(02)45013-4

Oral exam, Term paper, Oral defense of the term paper

1. HOČEVAR, Brigita, PRAŠNIKAR, Anže, HUŠ, Matej, GRILC, Miha, LIKOZAR, Blaž. H2−free Re-based catalytic dehydroxylation of aldaric acid to muconic and adipic acid esters. Angewandte Chemie : International edition. 18 Jan. 2021, vol. 60, iss. 3, str. 1244-1253. ISSN 1433-7851
   IF: 12.96.

2. HUŠ, Matej, KOPAČ, Drejc, BAJEC, David, LIKOZAR, Blaž. Effect of surface oxidation on oxidative propane dehydrogenation over chromia: an ab initio multiscale kinetic study. ACS catalysis. 2021, 11, 17, str. 11233-11247, ilustr. ISSN 2155-5435.
   IF: 12.35

3. KOPAČ, Drejc, LIKOZAR, Blaž, HUŠ, Matej. How size matters: electronic, cooperative, and geometric effect in perovskite-supported copper catalysts for CO2 reduction. ACS catalysis. 3. Apr. 2020, vol. 10, iss. 7, str. 4092-4102, ilustr. ISSN 2155-5435.
   IF: 12.35

4. KOPAČ, Drejc, LAŠIČ JURKOVIĆ, Damjan, LIKOZAR, Blaž, HUŠ, Matej. First-principles-based multiscale modelling of nonoxidative butane dehydrogenation on Cr2O3(0001). ACS catalysis. 2020, vol. 10, iss. , str. 14732-14746, ilustr. ISSN 2155-5435.
   IF: 12.35

5. HUŠ, Matej, DASIREDDY, Venkata D. B. C., STRAH ŠTEFANČIČ, Neja, LIKOZAR, Blaž. Mechanism, kinetics and thermodynamics of carbon dioxide hydrogenation to methanol on Cu/ZnAl2O4spinel-type heterogeneous catalysts. Applied catalysis. B, Environmental, ISSN 0926-3373, Jun. 2017, vol. 207, 267-278.
   IF: 9.45.