Universität zu Köln

Schmiedt, Hanno ORCID: 0000-0001-6450-3713, Jensen, Per ORCID: 0000-0001-5133-7621 and Schlemmer, Stephan ORCID: 0000-0002-1421-7281 (2016). Unifying the rotational and permutation symmetry of nuclear spin states: Schur-Weyl duality in molecular physics. J. Chem. Phys., 145 (7). MELVILLE: AMER INST PHYSICS. ISSN 1089-7690

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Abstract

In modern physics and chemistry concerned with many-body systems, one of the mainstays is identical-particle-permutation symmetry. In particular, both the intra-molecular dynamics of a single molecule and the inter-molecular dynamics associated, for example, with reactive molecular collisions are strongly affected by selection rules originating in nuclear-permutation symmetry operations being applied to the total internal wavefunctions, including nuclear spin, of the molecules involved. We propose here a general tool to determine coherently the permutation symmetry and the rotational symmetry (associated with the group of arbitrary rotations of the entire molecule in space) of molecular wavefunctions, in particular the nuclear-spin functions. Thus far, these two symmetries were believed to be mutually independent and it has even been argued that under certain circumstances, it is impossible to establish a one-to-one correspondence between them. However, using the Schur-Weyl duality theorem we show that the two types of symmetry are inherently coupled. In addition, we use the ingenious representation-theory technique of Young tableaus to represent the molecular nuclear-spin degrees of freedom in terms of well-defined mathematical objects. This simplifies the symmetry classification of the nuclear wavefunction even for large molecules. Also, the application to reactive collisions is very straightforward and provides a much simplified approach to obtaining selection rules. Published by AIP Publishing.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schmiedt, Hanno UNSPECIFIED orcid.org/0000-0001-6450-3713 UNSPECIFIED Jensen, Per UNSPECIFIED orcid.org/0000-0001-5133-7621 UNSPECIFIED Schlemmer, Stephan UNSPECIFIED orcid.org/0000-0002-1421-7281 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-266404
DOI:	10.1063/1.4960956
Journal or Publication Title:	J. Chem. Phys.
Volume:	145
Number:	7
Date:	2016
Publisher:	AMER INST PHYSICS
Place of Publication:	MELVILLE
ISSN:	1089-7690
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language REACTIVE COLLISIONS; SELECTION-RULES Multiple languages Chemistry, Physical; Physics, Atomic, Molecular & Chemical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26640