C4060 Quantum Chemistry I

Faculty of Science
Spring 2005
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Pavel Janderka, CSc. (lecturer)
Mgr. Jaromír Toušek, Dr. (seminar tutor)
Guaranteed by
doc. RNDr. Pavel Janderka, CSc.
Chemistry Section – Faculty of Science
Contact Person: doc. RNDr. Pavel Janderka, CSc.
Timetable
Mon 7:00–8:50 03021
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 9 fields of study the course is directly associated with, display
Course objectives
This lecture is one of elementary lectures for students of chemistry and biochemistry. Lecture introduces some of the basic principles of quantum mechanics. First, it reviews a principal concepts and the formulations of quantum mechanics, concepts developed on a solutions of wave equation for simple models are extended to an atoms and these can be extended to a description of electronic structures of molecules. Some keywords of the lecture are following: structure of atom-relation between experiment and theory, principles of wave mechanics, simple models, theory of chemical bond (VB, MO), molecular orbital theory for polyatomic molecules.
Syllabus
  • 1. Experimental results - the origin of quantum mechanics, atomic spectra, Roentgen spectra, the particle character of electromagnetic radiation, wave-particle duality, de Broglie relation.

    2. Vocabulary, origin and principal conception of quantum theory, Bohr's model of atoms, Schroedinger equation. Wave function, properties, normalization of wave function, the Born interpretation of wave function. Energy levels, stationary state, degeneration.

    3. Presumption of quantum theory, operators, eigenvalues and eigenfunctions. Heisenberg's uncertainty principle.

    4. Simple model in quantum theory. Particle in one-dimensional potential well and in box,degeneracy and tunnelling, properties of solution, its using. Vibrational motion, harmonic oscillator, properties of solution. Rotational motion, rotation in two and three dimensions, angular momentum and quantization.

    5. Vector model. Spin, Pauli principle. Structure of atoms, atomic spectra. Grotrian diagramms.

    6. Hydrogen atom. Quantum mechanics model of hydrogen atom. Radial function, atomic orbitals, energies of AO, symmetry and space properties. Hybridization of AO. Quantum numbers of electron. Radial distibution functions. Hydrogenic atoms.

    7. Many-electron atoms. Helium, penetration and shielding. Building-up (Aufbau) principle, correlation of spin, spin - orbital interaction, the periodicity of ionization energies.

    8. Atomic orbitals and energy - the variation principle. Method of self-consistent field - SCF, Hartree-Fock method, Slater's determinant. Electron structure of many-electron atoms, singlet and triplet states term symbols, selection rules, multiplicity. Vector model of atom, Russell-Saunders coupling.

    9. Structure of molecules. Chemical bond, potential energy diagram of diatomic molecule. Adiabatic, Born-Oppenheimer approximation. The hydrogen molecule, the hydrogen molecule-ion - the variation method. The overlap integral.

    10. Valence bond theory - VB. Molecular orbital theory - MO, linear combination of atomic orbitals - MO LCAO. Coulombic and exchange integral. Linear coefficients, charge, density and bond order. Bonding and antibonding orbitals. Homo- and heteronuclear di-atomic molecules. Parity, termo symbols.

    11. Variation principle, secular equation, secular determinants, energetical levels, molecular orbitals of polyatomic systems. Band theory.

    12. pi - electron approximation, Hueckel approximation - HMO. Butadien, frontier orbitals. Heteroatoms. Molecular diagrams and application of quantum chemical calculations.

    13. Semi-empirical and ab initio metods, Density functional theory.

    14. Computer aided molecular modelling - tool of every chemists, molecular mechanics.

Literature
  • POLÁK, Rudolf and Rudolf ZAHRADNÍK. Kvantová chemie : základy teorie a aplikace. 1. vyd. Praha: Státní nakladatelství technické literatury, 1985, 466 s. URL info
  • ATKINS, P. W. Physical chemistry. 6th ed. Oxford: Oxford University Press, 1998, xvi, 1014. ISBN 0198501013. info
  • MOORE, Walter J. Fyzikální chemie. Translated by Čestmír Černý - Alexander Schütz. 2., nezměn. vyd. Praha: Státní nakladatelství technické literatury, 1981, 974 s. URL info
  • ATKINS, Peter William and R. S. FRIEDMAN. Molecular quantum mechanics [Atkins, 1997]. 3rd ed. Oxford: Oxford University Press, 1997, xvii, 545. ISBN 0-19-855947-X. info
  • BRDIČKA, Rudolf and Jiří DVOŘÁK. Základy fysikální chemie. 2., přeprac. vyd. Praha: Academia, 1977, 850 s. info
Assessment methods (in Czech)
Výuka je organizována ve čtrnácti dvouhodinových blocích. Jejich obsah odpovídá členění sylabu. Přednáška je doprovázena jednohodinovým seminářem, který má charakter výpočetního cvičení. V rámci semináře je prakticky procvičován aparát předkládaný v přednášce formou práce studentů u tabule, tj. praktickými výpočty a diskusí. V průběhu semestru je rozsah pochopení látky ověřován nejméně dvěma testy, při nichž se předpokládá individuální práce. Je povoleno použití vlastních poznámek, učebnic a dalších pomůcek. Zkouška je ústní, formou rozpravy postupně na dvě zadaná, témata, odpovídající obsahu sylabu přednášky. Rozsah rozpravy zpravidla nepřesahuje 30 minut.

Informace poskytované přednáškou, obsahově odpovídají příslušným okruhům Požadavků ke státní závěrečné zkoušce z Fyzikální chemie v magisterském studijním programu Chemie, magisterských studijních oborů Chemie kromě fyzikální chemie, u něhož se předpokládá další studium.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008.
  • Enrolment Statistics (Spring 2005, recent)
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