On the impossibility of localised states for molecular rotors with cyclic potentials

Abstract

We discover a surprising property of an important class of molecular rotors. These rotors have one (e.g. a methyl group) or two (e.g. the planar boron rotor ) moieties that consist of identical nuclei rotating in cyclic model potential energy surfaces with equivalent potential wells (e.g. for CH, for ). The familiar semiclassical picture of this contorsion assumes that the potential wells support equivalent global minimum structures with corresponding localised wave functions being embedded in the individual potential wells. In contrast, we show that the wave functions of these rotors can never be squeezed into a single potential well, and hence, global minimum structures do not exist. Our quantum mechanical derivation describes the rotors in the frame of the proper cyclic molecular symmetry group and makes use of the spin-statistics theorem and the hypothesis of nuclear spin isomers. We show that if the identical nuclei have zero spins, then a hypothetical localised state would violate the spin-statistic theorem. Otherwise, the hypothetical localised state is ruled out as unphysical superposition of different nuclear spin isomers of the molecular rotors.