PřF:C9930 Methods of Quantum Chemistry - Course Information

C9930 Methods of Quantum Chemistry

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 1. 3. to Fri 14. 5. Wed 9:00–11:50 B11/206

Prerequisites

C9920 Introduction to QC
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

there are 13 fields of study the course is directly associated with, display

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 interpret outputs of quantum-chemical calculations employing the EHT and HF-SCF methods.

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

recommended literature
• LOWE, John P. Quantum chemistry. 2nd ed. San Diego: Academic Press, 1993, xx, 711. ISBN 0124575552. info
• LEVINE, Ira N. Quantum chemistry. 6th ed. Upper Saddle River, N.J.: Prentice Hall, 2009, x, 751. ISBN 9780132358507. 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

• Enrolment Statistics (Spring 2021, recent)
  
• Permalink: https://is.muni.cz/course/sci/spring2021/C9930