Universität zu Köln

Schmiedt, Hanno (2016). Molecular symmetry, super-rotation, and semi-classical motion. New ideas for old problems. PhD thesis, Universität zu Köln.

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Abstract

Customary theoretical models for molecular dynamics are based on a few fundamental assumptions like the commonly known ball-and-stick picture of molecular structure. In this work two examples of the limits of conventional molecular theory are discussed: Extremely floppy molecules where no equilibrium geometric structure is definable and molecules exhibiting highly excited rotational states, where the large angular momentum poses considerable challenges to quantum chemical calculations. For the extremely floppy molecules a fundamentally new zero-order description is established. The ‘super-rotor model’ is based on a five-dimensional rigid rotor treatment depending only on a single adjustable parameter. The respective quantum numbers define a generalized angular momentum which collectively describe internal and overall rotational motion. It consistently predicts the symmetry and energies of (most of) the low-energy states of the prototype of floppy molecules, protonated methane, which were only recently found experimentally. For highly excited rotational states, a path-integral based semi-classical treatment is shown to be capable of predicting energies and symmetries of quantized states even without sophisticated matrix diagonalization tools. In a proof-of-princinple study of sulfur dioxide, this analysis is shown to agree with advanced quantum chemical calculations. In addition, a straightforward and mathematically consistent method is developed to determine the nuclear spin permutation and rotational symmetry of molecules consisting of an arbitrary number of identical nuclei with any nuclear spin quantum number. This method is applied to formulate tentative symmetry-based selection rules and statistical state-to-state reaction rates for particular reactive collisions. In summary, fundamental symmetry considerations and semi-classical models are shown to contribute considerably to the understanding and extension of traditional concepts of molecular theory.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Schmiedt, Hanno schmiedt@ph1.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-75275
Date:	14 November 2016
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute of Physics I
Subjects:	Physics Chemistry and allied sciences
Uncontrolled Keywords:	Keywords Language Molecules, molecular symmetry, super-rotation, nuclear spin, angular momentum, protonated methane, semi-classical rotation, reactive collisions English
Date of oral exam:	24 January 2017
Referee:	Name Academic Title Schlemmer, Stephan Prof. Dr. Jensen, Per Prof. PhD
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/7527