Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

Synthesis of the common left-half part of pectenotoxins

The common left-half [C31-C33(OC1-C7)-C40] part of pectenotoxins has been synthesized convergently from the C31-C35, C36-C40, and C1-C7 parts. The C31-C35 part, prepared via a new route shorter than our previous route, was coupled with the C36-C40 part through reductive lithiation and addition reactions to give an adduct stereoselectively, which was converted to a cyclic acetal corresponding to the C31-C40 part. The left-half was synthesized by a three-step process including esterification of the C31-C40 part with the C1-C7 part.     

Sphericity governs both stereochemistry in a molecule and stereoisomerism among molecules

The concept of sphericity and relevant fundamental concepts that we have proposed have produced a systematized format for comprehending stereochemical phenomena. Permutability of ligands in conventional approaches is discussed from a stereochemical point of view. After the introduction of orbits governed by coset representations, the concepts of subduction and sphericity are proposed to characterize desymmetrization processes, with a tetrahedral skeleton as an example. The stereochemistry and stereoisomerism of the resulting promolecules (molecules formulated abstractly) are discussed in terms of the concept of sphericity as a common mathematical and logical framework. Thus, these promolecules are characterized by point group and permutation group symmetry. Prochirality, stereogenicity, prostereogenicity, and relevant topics are described in terms of the concept of sphericity.     

A New Synthesis of 3-Deoxy-D-Manno-Octulosonic Acid (KDO) From D-Mannose Via Condensation of Dioxene

Abstract

The title compound has long been known as an essential component of lipopolysaccharides (LPS) and capsular polysaccharides which exist in the outer membrane of Gram-negative bacteria. KDO has attracted additional attention as a consequence of some remarkable discoveries; i) mutants unable to produce KDO are non-viable.¹ ii) KDO is not present in mammalian cells,² iii) the 2-deoxy analog of β-KDO represents a new class of synthetic antimicrobial agent.^3,4 Although syntheses of KDO have been reported by many groups,^5–8 a more efficient synthetic method endowed with the potential for synthesis of not only complex glycoconjugates but also biologically significant analogs is required.     

Symmetry-itemized enumeration of RS-stereoisomers of allenes. I. The fixed-point matrix method of the USCI approach combined with the stereoisogram approach

After the RS-stereoisomeric group \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) of order 16 has been defined by starting point group \(\mathbf{D}_{2d}\) of order 8, the isomorphism between \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) and the point group \(\mathbf{D}_{4h}\) of order 16 is thoroughly discussed. The non-redundant set of subgroups (SSG) of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) is obtained by referring to the non-redundant set of subgroups of \(\mathbf{D}_{4h}\) . The coset representation for characterizing the orbit of the four positions of an allene skeleton is clarified to be \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) , which is closely related to the \(\mathbf{D}_{4h}(/\mathbf{C}_{2v}^{\prime \prime \prime })\) . According to the unit-subduced-cycle-index (USCI) approach (Fujita, Symmetry and combinatorial enumeration of chemistry. Springer, Berlin 1991), the subduction of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}(/\mathbf{C}_{s\widetilde{\sigma }\widehat{I}})\) is examined so as to generate unit subduced cycle indices with chirality fittingness (USCI-CFs). Then, the fixed-point matrix method of the USCI approach is applied to the USCI-CFs. Thereby, the numbers of quadruplets are calculated in an itemized fashion with respect to the subgroups of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) . After the subgroups of \(\mathbf{D}_{2d\widetilde{\sigma }\widehat{I}}\) are categorized into types I–V, type-itemized enumeration of quadruplets is conducted to illustrate the versatility of the stereoisogram approach.     

Multi-moment advection scheme for Vlasov simulations

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one-and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.     

New Identification of the Visible Bands of the C2 Swan System

The well known Swan system (d³Π_g-a³Π_u) of C₂ has been observed in absorption in a hollow cathode discharge in a mixture of C₂H₂ and helium. Three bands, (v′, v″)=(5, 7), (6, 8), and (7, 9), of the Swan system have been identified and rotationally analyzed. However, the transition wavenumbers are found not to be quite consistent with the literature values compiled by Phillips and Davis. The (7, 9) band has been observed and identified for the first time. New identifications of the (5, 7) and (6, 8) bands are presented. The observed wavenumbers are fit to the effective Hamiltonian derived by Brown and Merer for ³Π states. The molecular constants for both the upper and lower electronic states have been determined from the least squares fitting.