PřF:C9920 Quantum Chemistry Introduction - Course Information

C9920 Introduction to Quantum Chemistry and Electronic Structure of Molecules

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
Contact Person: doc. Mgr. Markéta Munzarová, Dr. rer. nat.
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science

Timetable

Wed 12:00–14:50 C12/311

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

Characterization of the course: It is a one-semestral introduction to the foundations of quantum chemistry and its applications to the reproduction, the interpretation, and the 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. At the end of the course students should be able to understand of basic quantum mechanics concepts on simple yet real chemical systems; grasping of principles of computational quantum chemistry; learning of basic rules of the qualitative MO theory that (1)enable an orientation in computed data and (2) make a link towards concepts used by experimentalists.

Syllabus

• 1. Basic notions of quantum mechanics. The notion of the wavefunction, the wavefunction postulate. Stationary Schroedinger 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 introduciton 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 inetrnuclear 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 trigonaly planar AH3. Orbital correlation diagram for trigonaly planar and pyramidal AH3. Planar of pyramidal geometries? Tetrahedral molecules AH4. Shapes of AH4 systems. 10. Solids. Orbitals and bands in one dimension. Bloch functions, k, band structures. How does the band run? Density of states. Distorsion of simple systems. Two and three dimensional systems. High-spin and low-spin considerations.

Literature

recommended literature
• LOWE, John P. Quantum chemistry. 2nd ed. San Diego: Academic Press. xx, 711. ISBN 0124575552. 1993. info
• LEVINE, Ira N. Quantum chemistry. 5th ed. Upper Saddle River: Prentice Hall. x, 739. ISBN 0136855121. 1999. info
• JEAN, Yves and François VOLATRON. An introduction to molecular orbitals. Edited by Jeremy K. Burdett. New York: Oxford University Press. xiv, 337. ISBN 0195069188. 1993. info
• ALBRIGHT, Thomas A., Jeremy K. BURDETT and Myung-Hwan WHANGBO. Orbital interactions in chemistry. New York: Wiley. xv, 447. ISBN 0471873934. 1985. URL info

Teaching methods

Lectures, exercises, consultations.

Assessment methods

Written test.

Language of instruction

Czech

Further Comments

Study Materials
The course is taught annually.

Listed among pre-requisites of other courses

• C9930 Methods of Quantum Chemistry
  C9920  

• Enrolment Statistics (Autumn 2012, recent)
  
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