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Two Different Facile and Efficient Approaches Spec. Matrices 2019; 7:1–19 Research Article Open Access Kazumasa Nomura* and Paul Terwilliger Green Process Synth 2019; 8: 742–755 Self-dual Leonard pairs Behzad Zeynizadeh, Farkhondeh Mohammad Aminzadeh and Hossein Mousavi* https://doi.org/10.1515/spma-2019-0001 Two different facileReceived and May efficient 8, 2018; accepted September approaches 22, 2018 for the synthesis ofAbstract: variousLet F denote N-arylacetamides a eld and let V denote a vector space over F with nite positive dimension. Consider a pair A, A∗ of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an via N-acetylation ofirreducible arylamines tridiagonal fashion. and Such a pair is called a Leonard pair. We consider the self-dual case in which there exists an automorphism of the endomorphism algebra of V that swaps A and A∗. Such an automorphism is unique, and called the duality A A∗. In the present paper we give a comprehensive description of this straightforward one-pot reductive acetylation↔ duality. In particular, we display an invertible F-linear map T on V such that the map X TXT− is the duality → A A∗. We express T as a polynomial in A and A∗. We describe how T acts on ags, decompositions, of nitroarenes promoted↔ by recyclable CuFe2O4 nanoparticles in waterand 24 bases for V. Keywords: Leonard pair, tridiagonal matrix, self-dual https://doi.org/10.1515/gps-2019-0044 Classication: 17B37,15A21their extensive applications in various area such as peptide Received December 17, 2018; accepted May 28, 2019. synthesis, agrochemicals, polymers, functional materials, dyes, fragrances and also existence in pharmaceuticals Abstract: Two simple, efficient, and environmentally (Figure 1) and natural products (Figure 2) [11-25]. Due to benign protocols for the synthesis of various N-arylacet- the importance of amide compounds, developing simple, amides via N-acetylation of arylamines and straightforIntroduction- practical, environmentally benign, cost- and time-effective ward one-pot reductive acetylation of aromatic nitro com- manners for their synthesis is very valuable and necessary. pounds promoted by CuFe O nanoparticlesLet inF waterdenote at a eld and let V denote a vector space over F with nite positive dimension. We consider a 2 4 Undoubtedly, acetylation of arylamines is a very simple reflux have been developed. The prepared CuFepair OA, MNPsA∗ of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an 2 4 approach for the preparation of amides which is widely are well known and fully characterized by irreduciblevarious tech tridiagonal- fashion. Such a pair is called a Leonard pair (see [13, Denition 1.1]). The Leonard pair used in chemistry labs and chemical industry [26]. There- niques. Furthermore, the CuFe O NPs easilyA, Aseparated∗ is said to be self-dual whenever there exists an automorphism of the endomorphism algebra of V that 2 4 fore, the development of this mentioned method is justifia- from the reaction environment using an externalswaps magneticA and A∗. In this case such an automorphism is unique, and called the duality A A∗. ble. It is worthwhile to note that aromatic nitro compounds ↔ field and can be reused for several times without signifi- The literatureare containsmuch cheaper many than examples arylamines of self-dual in terms Leonard of price pairs.and For instance (i) the Leonard pair associ- cant loss of its activity for both mentioned reactions. ated with an irreducibleone of the modulemost important for the substrates Terwilliger for algebra the preparation of the hypercube of (see [4, Corollaries 6.8, 8.5]); (ii) a Leonard pair ofarylamines Krawtchouk via typereduction (see [10,process. Denition So, designing 6.1]); (iii)new the proto Leonard- pair associated with an irreducible Keywords: N-arylacetamide; N-acetylation of arylamine; module for thecols Terwilliger for the synthesis algebra of of amides a distance-regular via straightforward graph one-pot that has a spin model in the Bose-Mesner alge- reductive acetylation of nitroarene; CuFe O ; green chemistry 2 4 bra (see [1, Theorem],reductive [3, acetylation Theorems of 4.1,aromatic 5.5]); nitro (iv) ancompounds appropriately without normalized totally bipartite Leonard pair (see [11, Lemmaisolation 14.8]); (v)of the the arylamine Leonard intermediates pair consisting is very of anyinteresting. two of a modular Leonard triple A, B, C (see [2, 1 Introduction Denition 1.4]);In (vi) this the regard, Leonard it should pair be consisting noted that one-pot of a pair multicompo of opposite- generators for the q-tetrahedron alge- bra, acting on annent evaluation reactions (MCRs) module are (see remarkable [5, Proposition instruments 9.2]). for The ver example- (i) is a special case of (ii), and the satile preparation of a wide diversity of organic compounds Performing organic reactions into the green solventsexamples espe (iii),- (iv) are special cases of (v). especially biologic active molecules which have advanta- cially water is very favorable for academic researchersLet A and, A∗ denote a Leonard pair on V. We can determine whether A, A∗ is self-dual in the following way. ges such as high atom economy, escape of time-consuming d industrial chemical companies due to its manyBy [13, desirable Lemma 1.3] each eigenspace of A, A∗ has dimension one. Let θ denote an ordering of the eigen- protection-deprotection steps, and environmentally friend- { i}i= features such as low-cost, non-toxicity, safety, abundantly d values of A. Forliness, ≤ makingi ≤ d let themvi denoteabsolutely a θbetteri-eigenvector than classical for A multi-. The ordering θi i= is said to be standard and also environmentally friendless compared with d { } d whenever A∗ actsstep on synthetic the basis pathwaysvi i= [27-37].in an irreducible tridiagonal fashion. If the ordering θi i= is standard organic solvents [1-10]. d { } { } then the ordering Notably,θd−i i= inis alsorecent standard, years, spinel and ferrite no further nanoparticles ordering is standard. Similar comments apply to In recent years, construction of amide linkages is oned { } d A∗. Let θ denotewith the a general standard formula ordering MFe ofO the, where eigenvalues M(II) is a ofd-blockA. Then A, A∗ is self-dual if and only if θ of the valuable reactions in organic synthesis because{ i }ofi= 2 4 { i}i= is a standard orderingtransition of metal the eigenvalues (such as Mn, of Co,A∗ (seeNi, Cu, [7, Zn) Proposition have been 8.7]). in the vanguard of nanoscience and nanotechnology due to their unique specifications like nanometer size, * Corresponding author: Hossein Mousavi, Department of Organic high saturation magnetization, large surface area to Chemistry, Faculty of Chemistry, Urmia University, Urmia, Iran volume ratio, high electric resistivity, low eddy current e-mail: [email protected] *Corresponding Author: Kazumasa Nomura: Tokyo Medical and Dental University, Ichikawa, 272-0827,Japan, Behzad Zeynizadeh and Farkhondeh Mohammad Aminzadeh,E-mail: [email protected] loss, very good optical properties in the visible region Department of Organic Chemistry, Faculty of Chemistry,Paul Urmia Terwilliger: andDepartment also their of Mathematics,extensive applications University ofin Wisconsin,sensors, memory Madison, WI53706, USA, E-mail: University, Urmia, Iran. [email protected] devices, magnetically controlled drug delivery, Open Access. © 2019 Zeynizadeh et al., published byOpen De Gruyter. Access. ©This2019 work Kazumasa is licensed Nomura under and the Paul Creative Terwilliger, Commons published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License. Attribution alone 4.0 License. B. Zeynizadeh et al.: al.: Synthesis of various N-arylacetamides 743 Figure 1: Representative examples of amide-containing drugs. Figure 2: Examples of amide-containing natural products. 744 B. Zeynizadeh et al.: Synthesis of various N-arylacetamides hyperthermia in the treatment of cancer diseases, medical diagnostics, magnetic resonance image (MRI) enhance- ment, telecommunication, pigments, and catalysis [38- 45]. Furthermore, compared with iron oxides, spinel fer- rites provide flexibility to control both crystal structures and magnetic properties by choosing different non-iron metals in spinel ferrite backbone and controlling their molar concentrations. Among various type of spinel ferrite magnetic nanoparticles (MNPs), CuFe2O4 nanocomposite, in addition to numerous applications, has shown satis- factory performance as the recyclable catalyst in various Scheme 1: Two different facile and efficient approaches for the organic transformations such as synthesis of heterocyclic synthesis of various N-arylacetamides promoted by CuFe O MNPs. compounds [46-52], Ullmann C-O coupling reaction [53], 2 4 direct synthesis of chemical structures containing both phenol ester and benzothiazole moieties via dehydroge- energy-dispersive X-ray (EDX) spectroscopy, inductively native coupling reactions [54], reduction of p-nitrophe- coupled plasma-optical emission spectrometry (ICP-OES), nol [55], one-pot odorless carbon-sulfur bond formation vibrating sample magnetometer (VSM) and also BET-BJH reactions [56], directed phenol/formamide coupling [57], analyses. synthesis of diaryl/aryl alkyl sulfides via cross-coupling In the FT-IR spectrum of the prepared CuFe2O4 process [58], S-arylation of thioureas by aryl halides [59], (Figure 3), the absorption band at 586.8 cm-1 is ascribed to one-pot four-component Dakin-West reaction (synthesis the stretching vibration frequency of octahedral site, and of β-acetamido ketones) [60], Friedel-Crafts acylation [61], the absorption band at 405.8 cm-1 is related to the tetrahe- N-arylation of heterocycles [62], direct C-H amination of dral site. benzothiazoles [63], oxidative hydroxylation of arylbo- As can be seen from Figure 4, the XRD pattern of the ronic acids [64], palm oil methanolysis [65], oxidation of mentioned CuFe2O4 nanocomposite reveals that all the benzyl alcohol [66], synthesis of unnatural arundines[67], peaks matched with the standard XRD pattern of CuFe2O4 N-arylation of indole and imidazole with aryl halide [68], (JCPDS card no.
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