PřF:C9930 Methods of Quantum Chemistry - Course Information

C9930 Methods of Quantum Chemistry

Extent and Intensity

2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Teacher(s)

doc. Mgr. Markéta Munzarová, Dr. rer. nat. (lecturer)

Guaranteed by

doc. Mgr. Markéta Munzarová, Dr. rer. nat.
National Centre for Biomolecular Research – Faculty of Science
Supplier department: National Centre for Biomolecular Research – Faculty of Science

Timetable

Mon 11:00–12:50 C04/211

Prerequisites

absolving of the couse 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

• Chemoinformatics and Bioinformatics (programme PřF, B-BCH)

Course objectives

This course, in continuation of the C9920 course, completes and elaborates the foundations of quantum chemistry methods. Further, it focuses on the strategies of analysing the results of quantum chemical calculations. An emphasis is put on various approaches towards the analysis of electron density distribution in the framework of one-electron approaches (canonical MO, NBO). Additionally, geometry optimization techniques as well as the inclusion of dynamics and solvation will be presented. At the end of the course students should be able to understand of QCH methods and the strategies of computing molecular properties, and also to understand the interpretation of the results.

Syllabus

• 1) 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 vartiational 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 matirx. Truncated CI methods. 8) Illustration how CI accounts for electron correlation. Structure of the full CI matrix for the H2 molecule, symmetry consequencies, 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 fundametal 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, consultations.

Assessment methods

Teaching methods used: lectures, class discussion, presentation of lecturer's scientific results and corresponding discussion, homeworks, reading from recommended literature. Finalization demands: Written exam.

Language of instruction

Czech

Further Comments

Study Materials

• Enrolment Statistics (Spring 2012, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2012/C9930