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Attributed to helical spatial structures resembling orbital angular momentum (OAM) wavefronts, chiral fibers (CFs) manifest promising potential in manipulating OAM modes. However, conventional coupled-mode theory (CMT) constructed by the approximate circular-polarization basis, neglecting the effect of structure symmetry on the mode field, has reached its accuracy bottleneck in CF analysis. To solve this problem, a more insightful and experimentally-consistent high-order CMT (HOCMT) based on the angular symmetry chiral fiber (ASCF) model is first presented for analyzing the evolution of spin-entangled OAM modes in CFs with arbitrary core shapes. The theory is constructed by naturally extending the basis to OAM-constituted even and odd modes with structure-dependent high-order angular symmetry in the mode field. It is shown that the eigenmodes in ASCFs are elliptically polarized vector vortex states manipulated by structural parameters, with field distributions degenerating into boundary-related patterns. The connection between the photon OAM carried by the eigenmodes and the structural parameters is first established and visually represented by the high-order Poincaré sphere. Meanwhile, an experimentally modified coupled-mode equation is presented to address experimental deviations. Utilizing the HOCMT, we investigate the rules of ASCFs for manipulating arbitrary-order spin-entangled OAM modes. Finally, we experimentally demonstrate the accuracy and superiority of the HOCMT by analyzing and optimizing chiral long-period fiber gratings. Our work not only imparts intuitive insights into the effect of waveguide chirality on OAM modes but also provides a useful tool for analyzing and applying waveguides with chirality.

Owing to the C2 symmetry structure of 1,1‘-diphenyl-3,3‘,4,4‘-tetramethyl-2,2‘-biphosphole, 1 (BIPHOS), we investigated the coordination of this chiral bidentate ligand to transition metals in order to explore the potential of these complexes in asymmetric catalysis. Nickel, palladium, and platinum complexes [M(BIPHOS)X2] (2 (M = Ni, X = Br), 3 (M = Pd, X = Cl), 4 (M = Pt, X = Cl) were synthesized and fully characterized. Their structures were determined by X-ray crystallography. The cationic palladium complexes [Pd(BIPHOS)(CH3CN)2](BF4)2, 6, and [Pd(BIPHOS)(η3-C3H5)]Cl, 7, were also synthesized. The π-allyl−palladium complex 7 reveals a potential interest for catalytic allylic substitution. The reaction of 1 with [Pd(CH3CN)4](BF4)2 leads to the formation of the meso diastereoisomer [Pd(BIPHOS)2] (BF4)2, 5, which was fully characterized. Its structure was determined by X-ray crystallography. A bis(BIPHOS) complex of Rh(I), 8, was also obtained by reaction of 1 with [Rh(COD)Cl]2 or [Rh(COD)2]BF4.

The utility of high-symmetry, doubly substituted organosulfur compounds as chiral auxiliaries in asymmetric reactions is described.

The title organosulfur compounds 1 and 2 were prepared via Newman-Kwart rearrangment of the tetrathiocarbamate of 2,2',6,6'-tetrahydroxybiphenyl. The 2,2',6,6'-tetramercaptobiphenyl 3a, hitherto unknown, is not stable and it oxidizes easily to the bisdisulfide 1. An X-ray crystallographic analysis of 1 is reported.

The enantiomerically pure ethenoanthracenes (V) and (VII) are prepared via asym.

Here, we report a double-bent-ligand strategy which addresses a commonly encountered challenge in the construction of pillar-layered structures with corrugated layers which are common for nonlinearly coordinated ligands and low-symmetry chiral ligands. Specifically, we show here that out-of-alignment metal coordination sites between two adjacent and opposing layers caused by in-layer bent-type ligands could be joined by another ligand type with a matching bent angle. Two isoreticular metal–organic frameworks, CPM-63m and CPM-63a, are presented here to illustrate the implementation of this strategy. Specifically, [Zn2(RCOO)4] paddlewheel dimers are bridged by bent FDC2–(H2FDC = 2,5-furandicarboxylic acid) to form neutral kagome layers. The resulting corrugated layers are successfully pillared by bent MTZ–(HMTZ = 5-methyltetrazole) or ATZ–ligands (HATZ = 5-aminotetrazole). Furthermore, the MTZ–and ATZ–pillars offer open N-donor sites, and gas sorption studies of N2, CO2, CH4, C2H2, C2H4, and C2H6show that these materials are highly porous. In addition, they exhibit interesting inverse ethane/ethylene separation properties and good CO2/CH4separation.

Driven by the demand for heterogeneous asymmetry catalysis, studies of chiral surfaces have become important aspects of modern surface science. With the maturity of surface science techniques, this has enriched the success in the study of low-symmetry chiral surfaces at the molecular level. In this review we summarise the methods to create chiral surfaces and the symmetry properties of chiral surfaces. Physical methods that have been used to recognise and understand the structure and properties of chiral surfaces are discussed in detail.

Driven by the demand for heterogeneous asymmetry catalysis, studies of chiral surfaces have become important aspects of modern surface science. With the maturity of surface science techniques, this has enriched the success in the study of low-symmetry chiral surfaces at the molecular level. In this review we summarise the methods to create chiral surfaces and the symmetry properties of chiral surfaces. Physical methods that have been used to recognise and understand the structure and properties of chiral surfaces are discussed in detail.

This paper unifies the following ideas for the study of chirality polynomials in transitive skeletons: (1) Generalization of chirality to permutation groups not corresponding to three-dimensional symmetry point groups leading to the concepts of signed permutation groups and their signed subgroups; (2) Determination of the total dimension of the chiral ligand partitions through the Frobenius reciprocity theorem; (3) Determination of signed permutation groups, not necessarily corresponding to three-dimensional point groups, of which a given ligand partition is a maximum symmetry chiral ligand partition by the Ruch-Schönhofer partial ordering, thereby allowing the determination of corresponding chirality polynomials depending only upon differences between ligand parameters; such permutation groups having the point group as a signed subgroup relate to qualitative completeness. In the case of transitive permutation groups on four sites, the tetrahedron and polarized square each have only one chiral ligand partition, but the allene and polarized rectangle skeletons each have two chiral ligand partitions related to their being signed subgroups of the tetrahedron and polarized square, respectively. The single transitive permutation group on five sites, the polarized pentagon, has a degenerate chiral ligand partition related to its being a signed subgroup of a metacyclic group with 20 elements. The octahedron has two chiral ligand partitions, both of degree six; a qualitatively complete chirality polynomial is therefore homogeneous of degree six. The cyclopropane (or trigonal prism or trigonal antiprism) skeleton is a signed subgroup of both the octahedron and a twist group of order 36; two of its six chiral ligand partitions come from the octahedron and two more from the twist group. The polarized hexagon is a signed subgroup of the same twist group but not of the octahedron and thus has a different set of six chiral ligand partitions than the cyclopropane skeleton. Two of its six chiral ligand partitions come from the above twist group of order 36 and two more from a signed permutation group of order 48 derived from the P3[P2] wreath product group with a different assignment of positive and negative operations than the octahedron.

The high-symmetry chiral macrocyclic polyamides and polyamines were synthesized by using (+)-tartaric acid as a chiral source. The title compound, one of the amines, is the first D6-symmetry organic molecule with known absolute configuration.

The concepts of compositeness and symmetry on the microstructure of matter have had a significant influence on the quest for the origin of particles and the universe. The studies on the property and phenomenology of hadrons as composite particles have led many insights and discoveries in particle physics, such as flavor symmetry, chiral symmetry, PCAC, strong interaction, dynamical symmetry breaking, indirect and direct CP violations, quark model from three flavors to three families, chiral dynamical model, quantum chromodynamics, quark confinement. I briefly present some interesting progresses and insights made in our group based on compositeness and symmetry. It can be seen that both the indirect and direct CP symmetry violation in kaon decays as well as the isospin ΔI = 1/2 selection rule can simultaneously be explained in the standard model with the Kobayashi-Maskawa CP-violating phase and the chiral dynamic loop effect. We present a brief description on the symmetry-preserving loop regularization (LORE) method which is realized in four dimensional space-time. The LORE method introduces two energy scales and maintains the initial divergence behavior, which overcomes some shortages in other regularization schemes. A chiral dynamical model of QCD can be derived by using the LORE method to understand the spontaneous chiral symmetry breaking via the dynamically generated composite Higgs potential, which can provide a consistent prediction for the mass spectra of both the nonet scalar and pseudoscalar ground state mesons. By extending such a model to a chiral thermodynamic model with the closed-time-path Green function approach, it enables us to characterize the critical behavior of QCD and the restoration of chiral symmetry breaking.