C9930 Methods of Quantum Chemistry

Faculty of Science
Spring 2019
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Markéta Munzarová, Dr. rer. nat. (lecturer)
Guaranteed by
doc. Mgr. Markéta Munzarová, Dr. rer. nat.
Department of Chemistry – Chemistry Section – Faculty of Science
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Wed 10:00–11:50 C12/311
Prerequisites
C9920 Quantum Chemistry Introduction
Successful completion of the course C9920.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The goal of the course C9930 is to explain the basic foundations of quantum chemical methods on the level employing mathematical and physical background accessible to students of chemistry and biochemistry. The second goal is a continuous builiding-up of abstraction necessary for the understanding of molecular electronic structure.
Learning outcomes
At the end of the course the students will be able to understand the basic principles of QCH methods and the strategies of computing molecular properties. Further, they will be able to interpretation of the results.
Syllabus
  • 1] Extended Hueckel method. 2) Hartree method of self-consistent field for atoms. Approximation of non-interacting electrons, approximation of STOs with fixed shielding, approximation of STOs with optimized shielding, approximation of a general product. Potential energy operator, Coulomb operator, Hartree equations, self-consistent-field method. Energy of an atom in the Hartree approximation, Coulomb integral. 2) Hartree-Fock (HF) method. Fundamental problem of the Hartree product. Antisymmetry of the wavefunction. Slater determinant. Fock operator, Coulomb and exchange operator, Hartree-Fock equations. Energy of an atom in the Hartree-Fock approximation, Coulomb and exchange integrals. HF calculation of the H2O molecule in a minimal basis. Symmetry basis functions, shapes of MOs, total wavefunction. 3) Bases in ab initio calculations. The principle of MO searching as linear combinations of atomic orbitals. Slater-type and Gauss-type orbitals. Terminologies of STO and GTO bases. 4) An example of an input and an output for the program Gaussian. The structure of input and output, keywords, means of geometry specification, output analysis. 5) Variational method. The proof of the variational theorem. The principle of the variational method. Variational calculation of H atom polarizability. 6) Perturbation theory. Principle. Taylor expansion. Basic equations of the non-degenerate case: first-order correction for the energy and wavefunction, second-order correction for energy. PT calculation of ground-state energy for two-electron systems H-, He, Li+. Application of perturbation theory in qualitative MO theory. 7) Post-Hartree-Fock methods: Configuration interaction (CI). Electron correlation. General form of the wavefunction. Excited determinants. Configuration interaction (CI). CI-secular equation. Configuration state functions, Slater-Condon rules, Brillouin's theorem. Size of the CI matrix. Truncated CI methods. 8) Illustration how CI accounts for electron correlation. Structure of the full CI matrix for the H2 molecule, symmetry consequences, form of CI wavefunction, RHF description shortcomings, RHF dissociation problem, UHF description, spin contamination. Variationality and size consistency. Current status of the CI method. 9) MP a CC methods. Moeller-Plesset perturbation theory. Energy to the first and the second order. Typical convergence behavior of the MP methods. Variationality and size consistency. Methods of coupled pairs and coupled clusters: principle, advantages of the CC methods, computational feasibility. 10) Density Functional Theory (DFT) I: Principle. Wavefunction as the foundation in traditional post-HF methods. Electron density as the fundamental property in DFT. 1st Hohenberg-Kohn theorem, proof. Searching for the electron density of the ground state. 2nd Hohenberg-Kohn theorem. 11) Density Functional Theory II: Model performance and practical aspects. Kohn-Sham (KS) approach in principle and in praxis. KS potential, local density approximation (LDA). GGA approximations and hybrid functionals. Comparison of results for individual functionals and properties. 12) Wavefunction and electron density: analysis. Interpretation of MO energies and shapes. Mulliken population analysis, the “Natural Bond Orbitals” (NBO) concept.
Literature
  • LEVINE, Ira N. Quantum chemistry. 6th ed. Upper Saddle River, N.J.: Prentice Hall, 2009, x, 751. ISBN 9780132358507. info
  • LOWE, John P. Quantum chemistry. 2nd ed. San Diego: Academic Press, 1993, xx, 711. ISBN 0124575552. info
  • PILAR, Frank L. Elementary quantum chemistry. 2nd ed. New York: McGraw-Hill Publishing Company, 1990, xvi, 599 s. ISBN 0-07-050093-2. info
  • KOCH, Wolfram and Max C. HOLTHAUSEN. A chemist's guide to density functional theory. 2nd ed. Weinheim: Wiley-VCH, 2001, xiii, 300. ISBN 3527304223. info
Teaching methods
Lectures incl. discussion, exercises, consultations.
Assessment methods
Written test with a follow-up discussion.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2019, recent)
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