# PřF:C9920 Introduction to QC - Course Information

## C9920 Introduction to Quantum Chemistry

**Faculty of Science**

Autumn 2022

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Taught in person. **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**- Tue 15:00–16:50 B11/305
- Timetable of Seminar Groups:

*H. Semrád*

C9920/02: Tue 17:00–17:50 C12/311,*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**- there are 7 fields of study the course is directly associated with, display
**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**- 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

*recommended literature*- LOWE, John P.
**Teaching methods**- Lectures, exercises, consultations.
**Assessment methods**- Written exam (requiring in a major part the formulation of answers, in a minor part a choice from several possibilities) and oral exam (2 items from the syllabus by the teacher's choice, 20 minute time for preparation). Examples of examination tests can be found in the information system.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course is taught annually.
**Listed among pre-requisites of other courses**

- Enrolment Statistics (recent)

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