C9920 Introduction to Quantum Chemistry

Faculty of Science
Autumn 2023
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)
Mgr. Hugo Semrád, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Markéta Munzarová, Dr. rer. nat.
Department of Chemistry – Chemistry Section – Faculty of Science
Contact Person: doc. Mgr. Markéta Munzarová, Dr. rer. nat.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science
Timetable
Thu 12:00–13:50 B11/305
  • Timetable of Seminar Groups:
C9920/01: Tue 16:00–16:50 A08/309, H. Semrád
C9920/02: Tue 17:00–17:50 A08/309, H. Semrád
Prerequisites
Any of the university introductory classes on mathematics. Sufficient is any of mathematics courses for students of chemistry, biochemistry, or chemistry with teaching specialization.
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 course represents a one-semestre introduction into the foundations of quantum chemistry and its applications to the reproduction, interpretation, and prediction of experimental data for systems of chemical interest. The course is intended for putting a theoretical foundation needed by students, who consider using methods of quantum chemistry in their own scientific work or those who already started doing so. The mathematical formalism used is reduced to a minimum, and the basic quantum-mechanics concepts are introduced within the course using given examples. The main goal of this course is the understanding of basic concepts of quantum mechanics.
Learning outcomes
At the end of the course students will possess the following skills: understanding the basic quantum mechanics concepts on simple yet real chemical systems; grasp the principles of computational quantum chemistry; the creation of orbital-interaction diagrams for simple real molecules.
Syllabus
  • 1. Basic notions of quantum mechanics. The notion of the wavefunction, the wavefunction postulate. Stationary Schrodinger equation. The notion of an operator, an eigenfunction of an operator, an eigenvalue corresponding to an operator and an eigenfunction. Hermitian operator: definition and properties. The coordinate operator, momentum operator, operator of the square of angular momentum, operator of the projection of the angular momentum in the z axis, energy operator - Hamiltonian. Commuting operators and common set of eigenfunctions. 2. Hydrogen atom. Hamiltonian for the fixed H atom and with the introduction of the reduced mass. Coordinate set for a spherically symmetrical system. Eigenstates for negative and positive eigenvalues. The notion of degeneracy, eigenfunctions. Radial factors, radial distribution function. Angular factors as eigenfunctions of momentum operators. Complex and real angular functions. Means of plotting atomic orbitals, the notion of orthogonality. 3. Many-electron atoms. Atomic units. Hamiltonian for the He atom. The meaning of the "orbital" notion. Total wavefunction in relation to one-electron wavefunctions. Total energy in relation to one-electron energies. Exchange symmetry of the wavefunction, electron spin, antisymmetry. Electron configuration of Li, Pauli principle. Slater determinant. Slater orbital. Aufbau principle, Klechowsky and Hund's rules. The evolution of atomic properties in the periodical system. 4. H2+ molecule. Three-particle Hamiltonian. Born-Oppenheimer approximation of the wavefunction. The method of molecular orbitals (MO) as linear combination of atomic orbitals (LCAO). Solution (a) employing symmetry and (b) using the variational method. Overlap integral, interaction integral as functions of internuclear distance. Secular equation, resulting energies and wavefunctions. MO graphical representations, symmetry properties, bonding and antibonding MO. Interaction diagram. 5. Simple Hückel method. Approximation of independent pi-electrons. Hückel determinant, values alpha and beta. Eigenfunctions and eigenvalues. Diagrams for energy levels. Charge densities, pi electron densities, HMO energies: the relation to experimental observables. The principle of extended Hückel method, bases, overlap and interaction integrals, parameter K, eigenfunctions and eigenvalues. Electronic structure of planar hydrocarbons. 6. Molecular symmetry. Symmetry groups. Matrices and their multiplication. Matrix representation of symmetry group. Reducible and irreducible representations. Symbols used for irreducible representations. Symmetry-adapted linear combinations. The use of character tables: zero and non-zero overlap integrals. Symmetry driven orbital interaction. 7. Two-orbital interaction: Molecules A2 and AB. The interaction of two identical and two different AOs. Level occupation, total energy. Overlap and symmetry. Four-AO interaction. Diatomic molecules A2 and AB: basis functions, pi and sigma MOs, s-p interaction, interaction diagrams, electron configurations, bond lengths and energies. 8. Interaction between two fragment orbitals. Linear and bent molecules AH2: The notion of a fragment orbital, symmetry elements, MOs, correlation diagram for linear and bent geometry, geometries of AH2 molecules. Application to BeH2. 9. AH3 and AH4 molecules. MOs of trigonal planar AH3. Orbital correlation diagram for trigonal planar and pyramidal AH3. Planar of pyramidal geometries? Tetrahedral molecules AH4. Shapes of AH4 systems.
Literature
    recommended literature
  • LOWE, John P. Quantum chemistry. 2nd ed. San Diego: Academic Press, 1993, xx, 711. ISBN 0124575552. info
  • JEAN, Yves and François VOLATRON. An introduction to molecular orbitals. Edited by Jeremy K. Burdett. New York: Oxford University Press, 1993, xiv, 337. ISBN 0195069188. info
Teaching methods
Lectures, exercises, consultations.
Assessment methods
Written exam based 75% on practical skills practiced in the seminar, 25% on lectured theory. The theoretical questions will be motivated by the "Multiple-choice questions" tasks at the end of the Lowe textbook chapters from the areas we will cover. Students have the option of voluntarily taking an oral retest, during which the grade from the written part can be improved or unchanged, it cannot be worsened.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/C9920