Emergence of Anyons on the Two-Sphere in Molecular Impurities

Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle.

Electron and Positron Scattering by Non-Central Potentials: Matrix Elements and Symmetry Properties in the First Born Approximation

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the D∞h point group optimizing the computational effort. Keywords — Positron and electron scattering, Fourier transform of the Gaussian product theorem, McMurchie-Davidson procedure, Obara-Saika procedure, linear molecules .

Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣ν1,ν2,ν3ℓ3;J,k,m⟩, tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3, which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v(M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h(AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h(AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications.

Characterization and Comparative Analyses of Mitochondrial Genomes in Single-Celled Eukaryotes to Shed Light on the Diversity and Evolution of Linear Molecular Architecture

Determination and comparisons of complete mitochondrial genomes (mitogenomes) are important to understand the origin and evolution of mitochondria. Mitogenomes of unicellular protists are particularly informative in this regard because they are gene-rich and display high structural diversity. Ciliates are a highly diverse assemblage of protists and their mitogenomes (linear structure with high A+T content in general) were amongst the first from protists to be characterized and have provided important insights into mitogenome evolution. Here, we report novel mitogenome sequences from three representatives (Strombidium sp., Strombidium cf. sulcatum, and Halteria grandinella) in two dominant ciliate lineages. Comparative and phylogenetic analyses of newly sequenced and previously published ciliate mitogenomes were performed and revealed a number of important insights. We found that the mitogenomes of these three species are linear molecules capped with telomeric repeats that differ greatly among known species. The genomes studied here are highly syntenic, but larger in size and more gene-rich than those of other groups. They also all share an AT-rich tandem repeat region which may serve as the replication origin and modulate initiation of bidirectional transcription. More generally we identified a split version of ccmf, a cytochrome c maturation-related gene that might be a derived character uniting taxa in the subclasses Hypotrichia and Euplotia. Finally, our mitogenome comparisons and phylogenetic analyses support to reclassify Halteria grandinella from the subclass Oligotrichia to the subclass Hypotrichia. These results add to the growing literature on the unique features of ciliate mitogenomes, shedding light on the diversity and evolution of their linear molecular architecture.

Спектральные моменты характеристик бинарных взаимодействий между линейными молекулами

A new approach to derive symmetrized expressions of leading classical moments of spectral distributions characterizing different anisotropic terms of the interaction potential for the case of two liear molecules is presented. The results allow to calculate diffuse shapes formed by transitions between continuous eigenstates of a molecular pair and open the way to account for the nonMarkov effects (due to finite collision durations) in the rotatonal relaxation matrix of an arbitrary rank. The approach is also applied to the spectral moments of vector and tensor characteristics determining the band intensities in the collision-induced spectra of linear molecules. Generally, the use of symmetrized expressions lead to considerably faster computer codes.