529-0003-00L Advanced Quantum Chemistry
| Semester | Autumn Semester 2016 |
| Lecturers | M. Reiher, S. Knecht |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 529-0003-00 G | Advanced Quantum Chemistry Lecture Tue 12:00-14:00, Exercise Classes Thursday 10:00-11:00 Vorlesung Di 12-14 Uhr, Uebung Donnerstag 10-11 Uhr | 3 hrs |
| M. Reiher, S. Knecht |
Catalogue data
| Abstract | Advanced, but fundamental topics central to the understanding of theory in chemistry and for solving actual chemical problems with a computer. Examples are: * Operators derived from principles of relativistic quantum mechanics * Relativistic effects + methods of relativistic quantum chemistry * Open-shell molecules + spin-density functional theory * New electron-correlation theories |
| Learning objective | The aim of the course is to provide an in-depth knowledge of theory and method development in theoretical chemistry. It will be shown that this is necessary in order to be able to solve actual chemical problems on a computer with quantum chemical methods. The relativistic re-derivation of all concepts known from (nonrelativistic) quantum mechanics and quantum-chemistry lectures will finally explain the form of all operators in the molecular Hamiltonian - usually postulated rather than deduced. From this, we derive operators needed for molecular spectroscopy (like those required by magnetic resonance spectroscopy). Implications of other assumptions in standard non-relativistic quantum chemistry shall be analyzed and understood, too. Examples are the Born-Oppenheimer approximation and the expansion of the electronic wave function in a set of pre-defined many-electron basis functions (Slater determinants). Overcoming these concepts, which are so natural to the theory of chemistry, will provide deeper insights into many-particle quantum mechanics. Also revisiting the workhorse of quantum chemistry, namely density functional theory, with an emphasis on open-shell electronic structures (radicals, transition-metal complexes) will contribute to this endeavor. It will be shown how these insights allow us to make more accurate predictions in chemistry in practice - at the frontier of research in theoretical chemistry. |
| Content | 1) Introductory lecture: basics of quantum mechanics and quantum chemistry 2) Einstein's special theory of relativity and the (classical) electromagnetic interaction of two charged particles 3) Klein-Gordon and Dirac equation; the Dirac hydrogen atom 4) Numerical methods based on the Dirac-Fock-Coulomb Hamiltonian, two-component and scalar relativistic Hamiltonians 5) Response theory and molecular properties, derivation of property operators, Breit-Pauli-Hamiltonian 6) Relativistic effects in chemistry and the emergence of spin 7) Spin in density functional theory 8) New electron-correlation theories: Tensor network and matrix product states, the density matrix renormalization group 9) Quantum chemistry without the Born-Oppenheimer approximation |
| Lecture notes | A set of detailed lecture notes will be provided, which will cover the whole course. |
| Literature | 1) M. Reiher, A. Wolf, Relativistic Quantum Chemistry, Wiley-VCH, 2014, 2nd edition 2) F. Schwabl: Quantenmechanik für Fortgeschrittene (QM II), Springer-Verlag, 1997 [english version available: F. Schwabl, Advanced Quantum Mechanics] 3) R. McWeeny: Methods of Molecular Quantum Mechanics, Academic Press, 1992 4) C. R. Jacob, M. Reiher, Spin in Density-Functional Theory, Int. J. Quantum Chem. 112 (2012) 3661 http://onlinelibrary.wiley.com/doi/10.1002/qua.24309/abstract 5) K. H. Marti, M. Reiher, New Electron Correlation Theories for Transition Metal Chemistry, Phys. Chem. Chem. Phys. 13 (2011) 6750 http://pubs.rsc.org/en/Content/ArticleLanding/2011/CP/c0cp01883j 6) K.H. Marti, M. Reiher, The Density Matrix Renormalization Group Algorithm in Quantum Chemistry, Z. Phys. Chem. 224 (2010) 583 http://www.oldenbourg-link.com/doi/abs/10.1524/zpch.2010.6125 7) E. Mátyus, J. Hutter, U. Müller-Herold, M. Reiher, On the emergence of molecular structure, Phys. Rev. A 83 2011, 052512 http://pra.aps.org/abstract/PRA/v83/i5/e052512 Note also the standard textbooks: A) A. Szabo, N.S. Ostlund. Verlag, Dover Publications B) I. N. Levine, Quantum Chemistry, Pearson C) T. Helgaker, P. Jorgensen, J. Olsen: Molecular Electronic-Structure Theory, Wiley, 2000 D) R.G. Parr, W. Yang: Density-Functional Theory of Atoms and Molecules, Oxford University Press, 1994 E) R.M. Dreizler, E.K.U. Gross: Density Functional Theory, Springer-Verlag, 1990 |
| Prerequisites / Notice | Strongly recommended (preparatory) courses are: quantum mechanics and quantum chemistry |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| ECTS credits | 7 credits |
| Examiners | M. Reiher, S. Knecht |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | oral 30 minutes |
| This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| No public learning materials available. | |
| Only public learning materials are listed. |
Groups
| No information on groups available. |
Restrictions
| There are no additional restrictions for the registration. |
