Nuclear spin selective torsional states: Implications of molecular symmetry

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.