TY - JOUR

T1 - Nuclear spin selective torsional states

T2 - Implications of molecular symmetry

AU - Belz, Steffen

AU - Deeb, Omar

AU - Gonźalez, Leticia

AU - Grohmann, Thomas

AU - Kinzel, Daniel

AU - Leibscher, Monika

AU - Manz, Jörn

AU - Obaid, Rana

AU - Oppel, Markus

AU - Xavier, George Densingh

AU - Zilberg, Shmuel

N1 - Funding Information:
We are grateful to Professors Yehuda Haas (The Hebrew University of Jerusalem) and Hans-Heinrich Limbach (Freie Universität Berlin) for stimulating discussions and continuous encouragement, and Mr. Florian Korinth for preparing Figs. 1 and 2. We thank Dr. Chris Eyles (Freie Universität Berlin) for careful reading the original version of the manuscript, and for valuable suggestions for the preparation of the final version. Financial support by the Deutsche Forschungsgemeinschaft via projects GO1059/7-3, LE 2138/2-1, and MA 515/25-3 is also gratefully acknowledged.

PY - 2013/6

Y1 - 2013/6

N2 - We consider a class of molecules with C2 symmetry axis and three segments A, B, C which can rotate independently about that axis, corresponding to two independent torsions (B vs. A and C vs. B). The torsions may be feasible either in the electronic ground or in the excited states. We determine the corresponding molecular symmetry group, i.e. the Abelian group G A16 representing 16 feasible permutations and permutation-inversions, and its permutation subgroup with eight permutations, together with their properties, e.g. their character tables and the corresponding 16 or 8 irreducible representations (IREPs), respectively. Accordingly, the molecules which belong to this class have at most eight different nuclear spin isomers (NSIs). A subset of them "survives" at low temperature, T → 0. The corresponding NSI selective wavefunctions contain products of torsional times nuclear wavefunctions with specific IREPs. The NSIs are characterized by these IREPs. As an example, we determine the molecular symmetry adapted torsional wavefunctions of the model 2-[4- (cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1,3-dioxole, abbreviated as CCD. In order to demonstrate the principles of the derivations, we employ a simple model, with the C2 symmetry axis oriented along the laboratory Z-axis, and with all degrees of freedom frozen in the equilibrium structure of CCD, except the two torsional degrees of freedom. The resulting torsional wavefunctions represent different NSIs of CCD, ready for subsequent applications, e.g. for demonstrations of NSI selective dynamics.

AB - We consider a class of molecules with C2 symmetry axis and three segments A, B, C which can rotate independently about that axis, corresponding to two independent torsions (B vs. A and C vs. B). The torsions may be feasible either in the electronic ground or in the excited states. We determine the corresponding molecular symmetry group, i.e. the Abelian group G A16 representing 16 feasible permutations and permutation-inversions, and its permutation subgroup with eight permutations, together with their properties, e.g. their character tables and the corresponding 16 or 8 irreducible representations (IREPs), respectively. Accordingly, the molecules which belong to this class have at most eight different nuclear spin isomers (NSIs). A subset of them "survives" at low temperature, T → 0. The corresponding NSI selective wavefunctions contain products of torsional times nuclear wavefunctions with specific IREPs. The NSIs are characterized by these IREPs. As an example, we determine the molecular symmetry adapted torsional wavefunctions of the model 2-[4- (cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1,3-dioxole, abbreviated as CCD. In order to demonstrate the principles of the derivations, we employ a simple model, with the C2 symmetry axis oriented along the laboratory Z-axis, and with all degrees of freedom frozen in the equilibrium structure of CCD, except the two torsional degrees of freedom. The resulting torsional wavefunctions represent different NSIs of CCD, ready for subsequent applications, e.g. for demonstrations of NSI selective dynamics.

KW - Group theory

KW - Molecular rotors

KW - Molecular symmetry

KW - Molecular torsion

KW - Nuclear spin isomers

KW - Quantum chemistry

KW - Symmetry-adapted quantum dynamics

UR - http://www.scopus.com/inward/record.url?scp=84880786820&partnerID=8YFLogxK

U2 - 10.1524/zpch.2013.0385

DO - 10.1524/zpch.2013.0385

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AN - SCOPUS:84880786820

SN - 0942-9352

VL - 227

SP - 1021

EP - 1048

JO - Zeitschrift fur Physikalische Chemie

JF - Zeitschrift fur Physikalische Chemie

IS - 6-7

ER -