On some algebraic difference equations in , related to families of conics or cubics: generalization of the Lyness' sequences

In this paper and in a forthcoming one, we study difference equations in of the types (2)(4)(6) which are linked to families of conics, cubics and quartics, respectively. These equations generalize Lyness' one u_n+2u_n=a+u_n+1 studied in several papers, whose behavior was completely elucidated in [G. Bastien, M. Rogalski, in press] through methods which are transposed in the present paper for the study of (1) and (2), and in the forthcoming one for (3). In particular we prove in the present paper a form of chaotic behavior for solutions of difference equations (1) and (2), and find all the possible periods for these solutions.     

Synthetic studies on the cornexistins: synthesis of (+/-)-5-epi-hydroxycornexistin

The synthesis of 5-epi-hydroxycornexistin (44), a diastereoisomer of the herbicidal natural product hydroxycornexistin (2) has been completed. Palladium mediated sp(2)-sp(3) coupling of the stannane 25 and the chloride 31 and ring-closing metathesis of the resulting diene 32 has been used to construct the tricyclic lactone 34a, which possesses the nine-membered carbocyclic core found in the natural product, in good yield. The synthesis of 5-epi-hydroxycornexistin (44) has established the feasibility of using a furan as precursor for the cyclic anhydride unit present in the natural product and has demonstrated the viability of other late-stage transformations that will be used to prepare hydroxycornexistin (2).     

Synthesis of a sialic acid alpha(2-3) galactose building block and its use in a linear synthesis of sialyl Lewis X

[reaction: see text] The ubiquity of the sialic acid alpha(2-3) galactose linkage in oligosaccharides of biological relevance necessitates a building block for the incorporation of this motif into oligosaccharides prepared by modular synthesis. The linear synthesis of the sialyl Lewis X tumor-associated antigen (1) has been accomplished in good yield using a sialic acid alpha(2-3) galactose disaccharide building block. The disaccharide building block was synthesized efficiently from readily available galactal by a high-yielding and selective sialylation reaction.     

Fractional-charge and fractional-spin errors in range-separated density-functional theory

ABSTRACT

We investigate fractional-charge and fractional-spin errors in range-separated density-functional theory (DFT). Specifically, we consider the range-separated hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation density functional, and the RSH+MP2 method which adds long-range, second-order Møller-Plesset (MP2) correlation. Results on atoms and molecules show that the fractional-charge errors obtained in RSH are much smaller than in the standard Kohn-Sham (KS) scheme applied with semilocal or hybrid approximations, and also generally smaller than in the standard HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than standard MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation density-functional approximations are smaller than the corresponding contributions for the full-range exchange and correlation density-functional approximations, RSH gives fractional-spin errors that are larger than in the standard KS scheme and only slightly smaller than in standard HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-separated DFT approaches for eliminating self-interaction and static-correlation errors.     

Interaction of Metamitron and Fenhexamid with Ca2+-Montmorillonite Clay Surfaces: A Density Functional Theory Molecular Dynamics Study

Metamitron (Meta), an herbicide, and fenhexamid (Fen), a fungicide, are authorized by the European Union to be used in agriculture. This article reports theoretical calculations about Meta and Fen in interaction with a clay surface: a Ca-montmorillonite (Mont). Conformational searches have been performed thanks to Car–Parrinello molecular dynamics simulations from which geometries have been extracted. Interaction and adsorption energies have been calculated for isomers of Meta or Fen in interaction with Mont to understand the relative stability of various kinds of complexation. Substantial adsorption energies are comparable for Meta and Fen: around −40 kcal/mol. For Fen-Mont, the CO monodentate family is surprisingly the lowest in energy. Moreover, the 10 lowest-energy isomers involve complexation on Fen carbonyl oxygens. The Meta-Mont lowest-energy family, N-N, does not involve π delocalization breaking within Meta. At the same time, the stronger the interaction energy is, the larger the structural modifications within Mont are, particularly concerning the interacting cation distance to the surface. The non-negligible charge transfer and the magnitude of the adsorption energy speak in favor of the chemisorption of the pesticide on the surface. © 2019 Wiley Periodicals, Inc.     

Qualitative counting closed geodesics

Geometriae Dedicata - We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We...     

Artificial Light‐Harvesting Complexes Enable Rieske Oxygenase Catalyzed Hydroxylations in Non‐Photosynthetic cells

In this study, we coupled a well‐established whole‐cell system based on E. coli via light‐harvesting complexes to Rieske oxygenase (RO)‐catalyzed hydroxylations in vivo. Although these enzymes represent very promising biocatalysts, their practical applicability is hampered by their dependency on NAD(P)H as well as their multicomponent nature and intrinsic instability in cell‐free systems. In order to explore the boundaries of E. coli as chassis for artificial photosynthesis, and due to the reported instability of ROs, we used these challenging enzymes as a model system. The light‐driven approach relies on light‐harvesting complexes such as eosin Y, 5(6)‐carboxyeosin, and rose bengal and sacrificial electron donors (EDTA, MOPS, and MES) that were easily taken up by the cells. The obtained product formations of up to 1.3 g L^?1 and rates of up to 1.6 mm h^?1 demonstrate that this is a comparable approach to typical whole‐cell transformations in E. coli. The applicability of this photocatalytic synthesis has been demonstrated and represents the first example of a photoinduced RO system.     

Sequential Formation of Heteroternary Cucurbit[10]uril (CB[10]) Complexes

The globular and monocationic guest molecule trimethyl-azaphosphatrane ( AZAP , a protonated Verkade superbase) was shown to form a host:guest 1 : 1 complex with the cucurbit[10]uril (CB[10]) macrocycle in water. Molecular dynamics calculations showed that CB[10] adopts an 8-shape with AZAP occupying the majority of the internal space, CB[10] contracting around AZAP and leaving a significant part of the cavity unoccupied. This residual space was used to co-include planar and monocationic co-guest ( CG ) molecules, affording heteroternary CB[10]⋅ AZAP ⋅ CG complexes potentially opening new perspectives in supramolecular chemistry.