Arens Product Research Articles

On measure algebras associated to locally compact groups

We shall consider measure algebras associated to locally compact groups, bounded operators between them and properties of the underlying measures. We take into account the second dual of measure algebras provided with the Arens products together with tools of Gélfand theory.

Precise Fabrication of Novel Multifunctional Poly(Ionic Liquid)s: Synergistic Catalysis of Dibasic Sites, Hydrophobic Microenvironment, and Mesoporous Confinement in Ultra-Efficient Production of Lignite-Based Monocyclic Arenes

Precise Fabrication of Novel Multifunctional Poly(Ionic Liquid)s: Synergistic Catalysis of Dibasic Sites, Hydrophobic Microenvironment, and Mesoporous Confinement in Ultra-Efficient Production of Lignite-Based Monocyclic Arenes

Copper-Catalyzed Oxidative Cross-Coupling of Electron-Deficient Polyfluorophenylboronate Esters with Terminal Alkynes.

We report herein a mild procedure for the copper‐catalyzed oxidative cross‐coupling of electron‐deficient polyfluorophenylboronate esters with terminal alkynes. This method displays good functional group tolerance and broad substrate scope, generating cross‐coupled alkynyl(fluoro)arene products in moderate to excellent yields. Thus, it represents a simple alternative to the conventional Sonogashira reaction.

Oxidative Alkenylation of Arenes Using Supported Rh Materials: Evidence that Active Catalysts are Formed by Rh Leaching

AbstractThis work focuses on the synthesis of supported Rh materials and study of their efficacy as pre‐catalysts for the oxidative alkenylation of arenes. Rhodium particles supported on silica (Rh/SiO2; ∼3.6 wt% Rh) and on nitrogen‐doped carbon (Rh/NC; ∼1.0 wt% Rh) are synthesized and tested. Heating mixtures of Rh/SiO2 or Rh/NC with benzene and ethylene or α‐olefins and CuX2 {X=OPiv (trimethylacetate) or OHex (2‐ethyl hexanoate)} to 150 °C results in the production of alkenyl arenes. When using Rh/SiO2 or Rh/NC as catalyst precursor, the conversion of benzene and propylene or toluene and 1‐pentene yields a ratio of anti‐Markovnikov to Markovnikov products that is nearly identical to the same ratios as the molecular catalyst precursor [Rh(μ‐OAc)(η2‐C2H4)2]2. These results and other observations are consistent with the formation of active catalysts by leaching of soluble Rh from the supported Rh materials.

Synthesis and Structure of Functionalized Zigzag Hydrocarbon Belts

AbstractDescribed in this paper are the synthesis and structure of novel and edge‐functionalized zigzag hydrocarbon belts. A stepwise “fjord‐stitching” strategy featuring repetitive intramolecular acylation reactions of a resorcin[4]arene derivative as the key steps afforded a biscarbonyl‐functionalized octahydrobelt[8]arene product. Facile ketone reduction with NaBH4 and nucleophilic addition with n‐butyllithium produced secondary and tertiary alcohol‐containing molecular belts, respectively. Selective oxidation reactions of biscarbonyl‐bearing octahydrobelt[8]arene with m‐CPBA and (PhSeO)2O furnished the corresponding lactone‐ and 1,4‐quinone‐embedded molecular belts. Depending on the functional groups on the edges, the acquired belt molecules adopt different shapes such as square prism, truncated cone, and elliptical cylinder.

Synthesis and Structure of Functionalized Zigzag Hydrocarbon Belts.

Described in this paper are the synthesis and structure of novel and edge-functionalized zigzag hydrocarbon belts. A stepwise "fjord-stitching" strategy featuring repetitive intramolecular acylation reactions of a resorcin[4]arene derivative as the key steps afforded a biscarbonyl-functionalized octahydrobelt[8]arene product. Facile ketone reduction with NaBH4 and nucleophilic addition with n-butyllithium produced secondary and tertiary alcohol-containing molecular belts, respectively. Selective oxidation reactions of biscarbonyl-bearing octahydrobelt[8]arene with m-CPBA and (PhSeO)2 O furnished the corresponding lactone- and 1,4-quinone-embedded molecular belts. Depending on the functional groups on the edges, the acquired belt molecules adopt different shapes such as square prism, truncated cone, and elliptical cylinder.

Palladium-mediated Suzuki-Miyaura Cross-Coupling Reaction of Potassium Boc-protected aminomethyltrifluoroborate with DNA-Conjugated aryl bromides for DNA-Encoded chemical library synthesis

A mild reaction for DNA-compatible, palladium promoted Suzuki-Miyaura cross-coupling reaction of potassium Boc-protected aminomethyltrifluoroborate with DNA-conjugated aryl bromides has been developed efficiently. This novel DNA encoded chemistry reaction proceeded well with a wide range of functional group tolerance, including aryl bromides and heteroaryl bromides. Further, the utility our DNA conjugated aminomethylated arene products is demonstrated by reaction with various types of reagents (including amide formation with carboxylic acids, alkylation with aldehydes, and carbamoylation with amines) as would be desired for the production of a DNA encoded library.

Advances in Rhodium-Catalyzed Oxidative Arene Alkenylation.

ConspectusAlkyl and alkenyl arenes are of substantial value in both large-scale and fine chemical processes. Billions of pounds of alkyl and alkenyl arenes are produced annually. Historically, the dominant method for synthesis of alkyl arenes is acid-catalyzed arene alkylation, and alkenyl arenes are often synthesized in a subsequent dehydrogenation step. But these methods have limitations that result from the catalytic mechanism including (1) common polyalkylation, which requires an energy intensive transalkylation process, (2) quantitative selectivity for Markovnikov products for arene alkylation using α-olefins, (3) for substituted arenes, regioselectivity that is dictated by the electronic character of the arene substituents, (4) inability to form alkenyl arenes in a single process, and (5) commonly observed slow reactivity with electron-deficient arenes. Transition-metal-catalyzed aryl-carbon coupling reactions can produce alkyl or alkenyl arenes from aryl halides. However, these reactions often generate halogenated waste and typically require a stoichiometric amount of metal-containing transmetalation reagent. Transition-metal-catalyzed arene alkylation or alkenylation that involves arene C-H activation and olefin insertion into metal-aryl bonds provides a potential alternative method to prepare alkyl or alkenylation arenes. Such reactions can circumvent carbocationic intermediates and, as a result, can overcome some of the limitations mentioned above. In particular, controlling the regioselectivity of the insertion of α-olefins into metal-aryl bonds provides a strategy to selectively synthesize anti-Markovnikov products. But, previously reported catalysts often show limited longevity and low selectivity for anti-Markovnikov products.In this Account, we present recent developments in single-step arene alkenylation using Rh catalyst precursors. The reactions are successful for unactivated hydrocarbons and exhibit unique selectivity. The catalytic production of alkenyl arenes operates via Rh-mediated aromatic C-H activation, which likely occurs by a concerted metalation-deprotonation mechanism, olefin insertion into a Rh-aryl bond, β-hydride elimination from the resulting Rh-hydrocarbon product, and net dissociation of alkenyl arene with formation of a Rh hydride. Reaction of the Rh hydride with Cu(II) oxidant completes the catalytic cycle. Although Rh nanoparticles can be formed under some conditions, mechanistic studies have revealed that soluble Rh species are likely responsible for the catalysis. These Rh catalyst precursors achieve high turnovers with >10,000 catalytic turnovers observed in some cases. Under anaerobic conditions, Cu(II) carboxylates are used as the oxidant. In some cases, aerobic recycling of Cu(II) oxidant has been demonstrated. Hence, the Rh arene alkenylation catalysis bears some similarities to Pd-catalyzed olefin oxidation (i.e., the Wacker-Hoechst process). The Rh-catalyzed arene alkenylation is compatible with some electron-deficient arenes, and they are selective for anti-Markovnikov products when using substituted olefins. Finally, when using monosubstituted arenes, consistent with a metal-mediated C-H activation process, Rh-catalyzed alkenylation of substituted arenes shows selectivity for meta- and para-alkenylation products.

Carbene‐Catalyzed Formal [3+3] Cycloaddition Reaction for Access to Substituted 2‐Phenylbenzothiazoles

A carbene‐catalyzed oxidative cycloaddition reaction is developed for efficient access to multi‐functionalized 2‐phenylbenzothiazoles. A broad scope of heavily substituted arenes bearing 2‐benzothiazole groups have been prepared in good to excellent yields. The remote C(sp2)–H bond in the substituted arene products can be activated by Pd catalysts in regio‐selective fashion with the direction of the 2‐benzothiazole groups.

Molecular Nitrogen as an Extraordinary Accelerator for Hydrodeoxygenation

Molecular nitrogen (N2) has been long believed to be an inert gas. Recently in Nature Catalysis, Duan et al. reported that N2 could dramatically promote the catalytic performance of hydrodeoxygenation over ruthenium-based catalysts and that as-formed hydrogenated nitrogen species contributed to the reduction of the activation energy required for carbon-oxygen bond cleavage inside p-cresol.

ARENS PRODUCTS, ARENS REGULARITY AND RELATED PROBLEMS

We study the second dual algebra of a Banach algebra and related problems. We resolve some questions raised by Ülger, which are related to Arens products. We then discuss a question of Gulick on the radical of the second dual algebra of the group algebra of a discrete abelian group and give an application of Arens regularity to Fourier and Fourier–Stieltjes transforms.

Ortho/Ipso Alkylborylation of Aryl Iodides.

This work describes a method for the difunctionalization of aryl iodides to generate polysubstituted arenes via Pd catalysis. The reaction hinges on the unique interplay between norbornene and the metal catalyst to impart a guided ortho C-H alkylation event followed by a programmatic ipso borylation to provide a diverse array of substituted arene products. The utility of this transformation is demonstrated through the functionalization of the boronic ester to a variety of valuable functionalities.

Enhanced Selective Production of Arenes and Regenerating Rate in Aryl Ether Hydrogenolysis over Mesoporous Nickel in Plug-Flow Reactors

Ordered mesoporous nickel (mesoNi) was successfully synthesized with a hard templating method by using KIT-6 ordered mesoporous silica as a template. With small-angle X-ray diffraction (SAXRD), transmission electron microscopy (TEM) and N2 sorption technique, the mesoporous structures of synthesized catalysts were characterized with desired high surface area (84.2 m2·g−1) and narrow pore size distribution. MesoNi exhibited outstanding catalytic cleavage activity for lignin model compounds (benzyl phenyl ether, BPE) with high selectivity of arenes in the flow reactor system. MesoNi also showed higher regeneration rates than non-porous ones, which were confirmed from deactivation and regeneration mechanism studies in the flow reaction system with varied high temperature and pressure. The adsorbed poisoning species on the mesoporous Ni surface were analyzed and phenol could be the main poisoning species. The excellent catalytic cleavage performance of mesoNi originates from their unique mesoporous structure, which offers high surface area and Ni active sites. The outstanding catalytic performance shows that this process provides a promising candidate for improved lignin valorization with general applicability.

Analysis on semihypergroups: function spaces, homomorphisms and ideals

The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by Dunkl (Am Math Soc 179:331–348, 1973), Jewett (Adv Math 18(1):1–101, 1975) and Spector (Apercu de la theorie des hypergroups, (French) Analyse harmonique sur les groupes de Lie (Sem. Nancy–Strasbourg, 1973–75), Springer, New York, 1975) independently around 1972. We introduce and study several natural algebraic and analytic structures on semihypergroups, which are well-known in the case of topological groups and semigroups. In particular, we first study almost periodic and weakly almost periodic function spaces (basic properties, their relation to the compactness of the underlying space, introversion and Arens product on their duals among others). We then introduce homomorphisms and ideals, and thereby examine their behaviour (basic properties, structure of the kernel and relation of amenability to minimal ideals) in order to gain insight into the structure of a Semihypergroup itself. In the process, we further investigate where and why this theory deviates from the classical theory of semigroups.

Modular Synthesis of Bicyclic and Tricyclic (Aza‐) Arenes from Nucleophilic (Aza‐)Arenes with Electrophilic Side Arms via [4+2] Annulation Reactions

AbstractAn efficient strategy for the synthesis of bicyclic and tricyclic (aza‐)arenes from a nucleophilic (aza‐)arene with an electrophilic side arm was developed. The (aza‐)arene precursor has both nucleophilic and electrophilic sites, which were fixed at a 1,4‐distance. The bicyclic and tricyclic (aza‐)arene products were constructed via [4+2] annulation by using scandium(III) triflate as a catalyst and enolizable ketones or aldehydes as the counterpart reagents. A variety of six‐membered carbocycles and heterocycles, such as indolizines, indoles, naphthalenes, carbazoles, and pyrido[1,2‐α]indoles, were successfully synthesized. Some one‐pot sequential reactions were also developed, in which the 1,4‐donor‐acceptor precursors can be synthesized via oxidation of alcohols or a proper condensation reaction.magnified image

M−WEAK AMENABILITY OF (2n)−TH DUALS OF BANACH ALGEBRAS

Let A be a Banach algebra such that its (2n)−th dual for some(n ≥ 1) with first Arens product is m−weakly amenable for some (m > 2n).We introduce some conditions by which if m is odd [even], then A is weakly [2-weakly] amenable.

Multiple Aromatic C-H Bond Activations by an Unsaturated Dirhenium Carbonyl Complex.

Reactions of Re2(CO)8(μ-C6H5)(μ-H), 1, with naphthalene and anthracene have yielded the first multiply-CH activated arene products through the reductive elimination of benzene from 1 and multiple oxidative-additions of the dirhenium octacarbonyl grouping to these polycyclic aromatic compounds under very mild conditions. In addition, compound 1 was found to react with itself to yield the bis-Re2-metalated C6H4 bridged compound Re2(CO)8(μ-H)(μ-1,μ-3-C6H4)Re2(CO)8(μ-H), 3. Reaction of 1 with naphthalene yielded two doubly CH activated isomers, Re2(CO)8(μ-H)(μ-η2-1,2-μ-η2-3,4-C10H6)Re2(CO)8(μ-H), 4, 41% yield, and Re2(CO)8(μ-H)(μ-η2-1,2-μ-η2-5,6-C10H6)Re2(CO)8(μ-H), 5, via the mono CH activated intermediate Re2(CO)8(μ-η2-C10H7)(μ-H), 2. Compound 4 contains two Re2(CO)8(μ-H) groups on one C6 ring formed by CH activations at the 2- and 4-positions. Compound 5 contains two Re2(CO)8(μ-H) groups; one formed by CH activation at the 2-position on one C6 ring and the other formed by CH activation at the 6-position (or centrosymmetrically related 2'-position) on the second C6 ring. The Re2(CO)8(μ-H) groups are coordinated to the C6 rings by binuclear σ + π coordination to two adjacent carbon atoms in the rings. Compound 1 reacts with anthracene to yield the mono-CH activated compound Re2(CO)8(μ-η2-1,2-C14H9)(μ-H), 6, and two doubly CH activated compounds, Re2(CO)8(μ-H)(μ-η2-1,2-μ-η2-3,4-C14H8)Re2(CO)8(μ-H), 7, and Re2(CO)8(μ-H)(μ-η2-1,2-μ-η2-5,6-C14H8)Re2(CO)8(μ-H), 8. Compounds 7 and 8 are isomers that are structurally similar to 4 and 5. Compounds 7 and 8 can also be obtained in good yields from the reaction of 6 with 1. In the presence of a 5/1 ratio of 1/anthracene, a small amount (5% yield) of the tetra-substituted anthracene product [Re2(CO)8(μ-H)]4(μ-η2-1,2-μ-η2-3,4-μ-η2-5,6-μ-η2-7,8-C14H6), 9, was formed. Compound 9 contains four σ + π coordinated Re2(CO)8(μ-H) groups formed by oxidative additions of the CH bonds of anthracene to the Re2(CO)8 groups at the 2, 4, 6, and 8 positions of the three ring system. Molecular orbital calculations have been performed for all new compounds in order to develop an understanding of the bonding of the ring systems to the Re2(CO)8(μ-H) groups. All new compounds were characterized by single-crystal X-ray diffraction analyses.

Fourier Spaces and Completely Isometric Representations of Arens Product Algebras

AbstractMotivated by the definition of a semigroup compactication of a locally compact group and a large collection of examples, we introduce the notion of an (operator) homogeneous left dual Banach algebra (HLDBA) over a (completely contractive) Banach algebra $A$ . We prove a Gelfand-type representation theorem showing that every HLDBA over A has a concrete realization as an (operator) homogeneous left Arens product algebra: the dual of a subspace of $A^{\ast }$ with a compatible (matrix) norm and a type of left Arens product $\Box$ . Examples include all left Arens product algebras over $A$ , but also, when $A$ is the group algebra of a locally compact group, the dual of its Fourier algebra. Beginning with any (completely) contractive (operator) $A$ -module action $Q$ on a space $X$ , we introduce the (operator) Fourier space $({\mathcal{F}}_{Q}(A^{\ast }),\Vert \cdot \Vert _{Q})$ and prove that $({\mathcal{F}}_{Q}(A^{\ast })^{\ast },\Box )$ is the unique (operator) HLDBA over $A$ for which there is a weak $^{\ast }$ -continuous completely isometric representation as completely bounded operators on $X^{\ast }$ extending the dual module representation. Applying our theory to several examples of (completely contractive) Banach algebras $A$ and module operations, we provide new characterizations of familiar HLDBAs over A and we recover, and often extend, some (completely) isometric representation theorems concerning these HLDBAs.

Catalytic Synthesis of Superlinear Alkenyl Arenes Using a Rh(I) Catalyst Supported by a "Capping Arene" Ligand: Access to Aerobic Catalysis.

Alkyl and alkenyl arenes are used in a wide range of products. However, the synthesis of 1-phenylalkanes or their alkenyl variants from arenes and alkenes is not accessible with current commercial acid-based catalytic processes. Here, it is reported that an air-stable Rh(I) complex, (5-FP)Rh(TFA)(η2-C2H4) (5-FP = 1,2-bis( N-7-azaindolyl)benzene; TFA = trifluoroacetate), serves as a catalyst precursor for the oxidative conversion of arenes and alkenes to alkenyl arenes that are precursors to 1-phenylalkanes upon hydrogenation. It has been demonstrated that coordination of the 5-FP ligand enhances catalyst longevity compared to unligated Rh(I) catalyst precursors, and the 5-FP-ligated catalyst permits in situ recycling of the Cu(II) oxidant using air. The 5-FP ligand provides a Rh catalyst that can maintain activity for arene alkenylation over at least 2 weeks in reactions at 150 °C that involve multiple Cu(II) regeneration steps using air. Conditions to achieve >13 000 catalytic turnovers with an 8:1 linear:branched (L:B) ratio have been demonstrated. In addition, the catalyst is active under aerobic conditions using air as the sole oxidant. At 80 °C, an 18:1 L:B ratio of alkenyl arenes has been observed, but the reaction rate is substantially reduced compared to 150 °C. Quantum mechanics (QM) calculations compare two predicted reaction pathways with the experimental data, showing that an oxidative addition/reductive elimination pathway is energetically favored over a pathway that involves C-H activation by concerted metalation-deprotonation. In addition, our QM computations are consistent with the observed selectivity (11:1) for linear alkenyl arene products.

Maximizing the production of aromatic hydrocarbons from lignin conversion by coupling methane activation

Maximizing the production of aromatic hydrocarbons from lignin conversion by coupling methane activation without solvent was investigated over Zn-Ga modified zeolite catalyst. The co-loading of Zn and Ga greatly improves lignin conversion, arene yield along with BTEX (i.e., benzene, toluene, ethylbenzene, and xylene) selectivity, which gives 37.4 wt% yield of aromatic hydrocarbons with 62.2 wt% selectivity towards BTEX at 400 °C and 3.0 MPa. Methane presence has a negligible impact on lignin conversion, but improves arene yield and BTEX selectivity. Liquid 13C, 1H and 2H NMR investigations confirm the incorporation of methane into the final arene products. The NMR results reveal that methane might be incorporated into both the methyl group and aromatic ring, possibly via methylation of aryl moieties and co-aromatization of alkyl moieties. Pyridine and ammonia as probes for surface acidity analysis of the developed catalysts demonstrate that HZSM5 modification with Zn and Ga species could redistribute BAS (Brønsted acid sites) and LAS (Lewis acid sites) and significantly increase the fraction of weak acidic sites on the catalyst, rendering better catalytic performance on the depolymerization of lignin to arene products with higher BTEX selectivity. The results reported in this work may open a novel route to a promising technique for lignin valorization into aromatics and cost-efficient utilizations of biomass and natural gas resources.