On the role of rotating tetrahedra for generating auxetic behavior in NAT and related systems

Systems with negative Poisson’s ratios (auxetic) exhibit the unexpected feature of expanding laterally when uniaxially stretched and becoming narrower when compressed. Here, we examine the role of the tetrahedra found in the frameworks of the predicted auxetic zeolites natrolite (NAT), thomsonite (THO) and edingtonite (EDI) for generating negative Poisson’s ratios in an attempt to relate the auxeticity in the (0 0 1) plane to rotations of the tetrahedra in the zeolite framework. The behavior of the tetrahedra is then examined in terms of their 2D projections in the (0 0 1) plane and we show that in the extreme scenario, where the three-dimensional tetrahedra in the zeolite framework are perfectly rigid and simply rotate relative to each other, then their 2D projected behavior in the (0 0 1) plane becomes equivalent to the idealized two-dimensional ‘rotating squares model’ with a Poisson’s ratio of ?1.     

Reduction of quantum systems and the local Gauss law

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796–1808, 2002; J Math Phys 46:032303, 2004).     

Trifluoromethylation of Carbonyl and Unactivated Olefin Derivatives by C(sp3)−C Bond Cleavage

Herein, we report a Cu-mediated trifluoromethylation of carbonyl-type compounds and unactivated olefins enabled by visible-light irradiation via σ C(sp³)−C bond-functionalization. The reaction is distinguished by its modularity, mild conditions and wide scope—even in the context of late-stage functionalization—thus offering a complementary approach en route to valuable C(sp³)−CF₃ architectures from easily accessible precursors.     

On the density of foliations without algebraic solutions on weighted projective planes

We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces.     

Origins of the Reactivity in 1,3-Dipolar Cycloadditions of Acyl Isocyanide Ylides

1,3-Dipolar cycloadditions are the preferred method to generate five-membered heterocyclic rings. Surprisingly, cycloadditions based on acyl-isocyanide ylides have remained underexplored by the chemical community. Acyl-isocyanide ylides readily react with dipolarophiles, such as substituted alkenes, to yield Δ¹-pyrroline derivatives. As an explanation for the observed reactivity of this reaction is lacking, extensive density functional theory calculations were performed to scrutinize the mechanistic features of the transformation. Herein we explain the experimental outcome of the reaction using a variety of reactivity theories and predict opposed regioselectivity for electron-poor and electron-rich dipolarophiles. With the insights obtained, we hope to incentivize the design of new cycloaddition reactions based on the acyl-isocyanide ylides motif.     

α-Difluoroalkylation of Benzyl Amines with Trifluoromethylarenes

An α-difluoroalkylation of benzyl amines with trifluoromethylarenes is disclosed herein. This protocol is characterized by its operational simplicity, excellent chemoselectivity and broad scope—even with advanced synthetic intermediates—, thus offering a new entry point to medicinally-relevant α-difluoroalkylated amines from simple, yet readily accessible, precursors.     

Copper-Catalyzed C(sp3)-Amination of Ketone-Derived Dihydroquinazolinones by Aromatization-Driven C−C Bond Scission

Herein, we describe the development of a copper-catalyzed C(sp³)-amination of proaromatic dihydroquinazolinones derived from ketones. The reaction is enabled by the intermediacy of open-shell species arising from homolytic C−C bond-cleavage driven by aromatization. The protocol is characterized by its operational simplicity and generality, including chemical diversification of advanced intermediates.