Mirror Symmetry Breaking in Liquids and Their Impact on the Development of Homochirality in Abiogenesis: Emerging Proto-RNA as Source of Biochirality?

Recent progress in mirror symmetry breaking and chirality amplification in isotropic liquids and liquid crystalline cubic phases of achiral molecule is reviewed and discussed with respect to its implications for the hypothesis of emergence of biological chirality. It is shown that mirror symmetry breaking takes place in fluid systems where homochiral interactions are preferred over heterochiral and a dynamic network structure leads to chirality synchronization if the enantiomerization barrier is sufficiently low, i.e., that racemization drives the development of uniform chirality. Local mirror symmetry breaking leads to conglomerate formation. Total mirror symmetry breaking requires either a proper phase transitions kinetics or minor chiral fields, leading to stochastic and deterministic homochirality, respectively, associated with an extreme chirality amplification power close to the bifurcation point. These mirror symmetry broken liquids are thermodynamically stable states and considered as possible systems in which uniform biochirality could have emerged. A model is hypothesized, which assumes the emergence of uniform chirality by chirality synchronization in dynamic “helical network fluids” followed by polymerization, fixing the chirality and leading to proto-RNA formation in a single process.

Enhanced thermoelectric performance in topological crystalline insulator n-type Pb0.6Sn0.4Te by simultaneous tuning of the band gap and chemical potential

Iodine doping perturbs the local mirror symmetry and widens the band gap in TCI, Pb0.60Sn0.40Te, making it a promising n-type thermoelectric material.

[N′-(4-Decyloxy-2-oxidobenzylidene)-3-hydroxy-2-naphthohydrazidato-κ3N,O,O′]dimethyltin(IV): crystal structure and Hirshfeld surface analysis

The title diorganotin compound, [Sn(CH3)2(C28H32N2O4)], features a distorted SnC2NO2coordination geometry almost intermediate between ideal trigonal–bipyramidal and square-pyramidal. The dianionic Schiff base ligand coordinates in a tridentate fashionviatwo alkoxide O and hydrazinyl N atoms; an intramolecular hydroxy-O—H...N(hydrazinyl) hydrogen bond is noted. The alkoxy chain has an all-transconformation, and to the first approximation, the molecule has local mirror symmetry relating the two Sn-bound methyl groups. Supramolecular layers sustained by imine-C—H...O(hydroxy), π–π [between decyloxy-substituted benzene rings with an inter-centroid separation of 3.7724 (13) Å], C—H...π(arene) and C—H...π(chelate ring) interactions are formed in the crystal; layers stack along thecaxis with no directional interactions between them. The presence of C—H...π(chelate ring) interactions in the crystal is clearly evident from an analysis of the calculated Hirshfeld surface.

Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.

J FUNCTIONS, NON-NEF TORIC VARIETIES AND EQUIVARIANT LOCAL MIRROR SYMMETRY OF CURVES

We provide a straightforward computational scheme for the equivariant local mirror symmetry of curves, i.e. mirror symmetry for [Formula: see text] for k ≥ 1, and detail related methods for dealing with mirror symmetry of non-nef toric varieties, based on the theorems of Refs. 2 and 13. The basic tools are equivariant I functions and their Birkhoff factorization.