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Lecturer(s)
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Futera Zdeněk, RNDr. Ph.D.
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Course content
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1. Quantum mechanics, wave function, electron density 2. Hartree-Fock equations and methods how to solve them 3. Hohenberg-Kohn theorems, N- a v-representability 4. Kohn-Sham equations and methods how to solve them 5. Density functionals (LDA, GGA, hybrid, range - separated, meta-GGA) 6. Description of molecular systems, localized basis sets 7. Description of solid-state materials and surfaces, plane-wave basis sets 8. Pseudopotetials, their types and applications 9. Energy, forces, ionization potentials and other properties 10. Geometry optimization, description of chemical reactions, vibrational spectra 11. Born-Oppenheimer and Car-Parrinello molecular dynamics 12. Time-dependent description (TDDFT), excited states, optical spectra 13. Limits of DFT, multireference and many-body approaches Besides the theoretical lectures, practical tutorials are part of this course where the available DFT software is presented and students learn to perform basic simulation techniques based on DFT (computing of electronic properties, band gap, ionization potentials, geometry optimization, molecular dynamics, vibration and optical spectra calculations).
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Practical training
- Class attendance
- 39 hours per semester
- Preparation for exam
- 24 hours per semester
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Learning outcomes
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Density functional theory (DFT) is currently the most popular theoretical and computational approach to describe molecular systems, solid state materials as well as their surfaces and various interfaces. In this course theoretical background of DFT is presented together with practical techniques often used in DFT simulations.
The theoretical background of DFT is presented together with practical techniques often used in DFT simulations. Absolvent of the course should be able to perform elementary calculations of molecular-system properties by using available software and understand the output of such specialized programs.
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Prerequisites
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Basic knowledge of theoretical mechanics (Lagrange and Hamilton formalism for the description of physical systems), non-relativistic quantum mechanics (postulates, Schrodinger equation and its solutions for linear harmonic oscillator and hydrogen atom), and mathematics for physicists (linear algebra and differential calculus)
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Assessment methods and criteria
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Oral examination
Active attendance of the tutorials (max. 2 absences, work on the assigned tasks) is required to obtain the credit. Attendants need to prove at least a general understanding of the presented theory (i.e., knowledge of basic assumptions, principles, and applicability of DFT) by answering more than 70% of questions to pass the exam successfully.
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Recommended literature
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Burke, K. The ABC of DFT, Uni. of California, 2007. 2007.
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Flolhais, C., Nogueira, F., Marques, M. A. L. A primer in Density Functional Theory, Springer, 2003. 2003.
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Martin, R. M. Electronic Structure: Basic Theory and Practical Methods, Cambridge Uni. Press, 2008. 2008.
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Marx, D., Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge Uni. Press, 2009. 2009.
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Parr, Robert G.; Yang, Weitao. Density-functional theory of atoms and molecules. 1st pub. Oxford : Oxford University Press, 1989. ISBN 0-19-509276-7.
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