Spec. Matrices 2019; 7:1–19 Research Article Open Access Kazumasa Nomura* and Paul Terwilliger Green Process Synth 2019; 8: 584–589 Self-dual Leonard pairs Fatemeh Gholipour1, Mohammad Rahmani2,* and Farhad Panahi1 https://doi.org/10.1515/spma-2019-0001 Efficient and selectiveReceived Maymicrowave-assisted 8, 2018; accepted September 22, 2018 O-methylation of phenolicAbstract: Let F denote compounds a eld and let V denote using 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 tetramethylammoniumirreducible hydroxide tridiagonal fashion. Such (TMAH) 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 ↔ https://doi.org/10.1515/gps-2019-0028 duality. In particular,There weare displayseveral reports an invertible in the literatureF-linear mapon theT synthesison V such that the map X TXT− is the duality Received October 12, 2018; accepted March 11, 2019. → A A∗. We expressof methylT as aaryl polynomial ethers using in A andmethylationA∗. We describeof phenolic how T acts on ags, decompositions, ↔ compounds (Figure 1). Abstract: In this study, an efficient method andfor O-methyla 24 bases- for V. In traditional methods toxic methylating agents tion of phenolic compound using tetramethylammonium Keywords: Leonardsuch pair, as methyl tridiagonal iodide matrix,[2,3] methyl self-dual bromide [3], dimethyl hydroxide (TMAOH) as a new alkylating agent under mic- sulfate1 [4-6] and diazomethane [7] have been used. rowave irradiation was developed. Ethanol was selected Classication: 17B37,15A21Methyl halides are toxic gaseous materials because they as a green reaction media to accomplish this protocol can methylate nucleic acids in living organisms [8]. To under environmentallybenign conditions. Less than half use dimethyl sulfate as alkylating agent stoichiometric hour time is needed to obtain good to excellent yields of amount of strong base for neutralization of acidic products at temperature of about 120°C. Using this pro- Introductionby-products is required [4,5]. Due to the growing awareness cedure, phenolic compounds could be converted to the of environmental issues, the commercial application of corresponding aryl methyl derivatives quickly. The results Let F denote a eldtheseand material let V aredenote restricted. a vector In order space to avoid over Fthewith use niteof positive dimension. We consider a indicated that different phenolic compounds bearing both pair A, A∗ of diagonalizablementioned methylatingF-linear maps agents on otherV, each methods of which have actsbeen on an eigenbasis for the other one in an electron-withdrawing and electron-donating groups are irreducible tridiagonaldeveloped. fashion. The O-methylation Such a pair is of called phenol a with Leonard methanol pair in (see [13, Denition 1.1]). The Leonard pair O-methylated effectively using TMAOH under microwave A, A∗ is said to bethe self-dual presence wheneverof a strong acid there has exists been an widely automorphism investigated of the endomorphism algebra of V that irradiation. This novel protocol has many improvements swaps A and A∗.[9-13]. In this This case method such anis an automorphism acid catalyzed is process unique, and and the called the duality A A∗. in view point of reaction yields, selectivity and conditions ↔ product selectivity depends on properties of the used acid compared to previous studies. Trimethylamine Theand literaturewater contains many examples of self-dual Leonard pairs. For instance (i) the Leonard pair associ- catalyst. In most cases, the conversions of phenols are were the side products of O-methylation reactionated with which an irreducible module for the Terwilliger algebra of the hypercube (see [4, Corollaries 6.8, 8.5]); (ii) a not satisfactory and the C-methylation is the competition can be recovered easily from the productLeonard mixture. pairThis of Krawtchouk type (see [10, Denition 6.1]); (iii) the Leonard pair associated with an irreducible reaction and a large amount of byproduct is produced methodology showed high selectivity for moduleO-methylation for the Terwilliger algebra of a distance-regular graph that has a spin model in the Bose-Mesner alge- which complicated the workup and purification process. A and no C-methylated products were observed.bra (see [1, Theorem], [3, Theorems 4.1, 5.5]); (iv) an appropriately normalized totally bipartite Leonard pair clean, and selective methylation protocols was developed (see [11, Lemmausing 14.8]); (v)dimethyl the Leonard carbonate pair consistingas a less-toxic of any tworeagent of a modular Leonard triple A, B, C (see [2, Keywords: microwave-assisted; O-methylation; phenolic Denition 1.4]);[14,15]. (vi) the The Leonard reaction pair of consistingphenol with of dimethyl a pair of carbonate opposite generators for the q-tetrahedron alge- compound; tetramethylammonium hydroxide bra, acting on anwas evaluation also carried module out (seeunder [5, Propositiongas/liquid phase 9.2]). transfer The example (i) is a special case of (ii), and the examples (iii), (iv)catalysis are special conditions cases in of the (v). presence of K2CO3 coated with Let A, A∗ denotepolyethylene a Leonard glycol pair [16,17]. on V. WeUsing can this determine reagent, whether anisole A, A∗ is self-dual in the following way. d 1 Introduction By [13, Lemma 1.3]was each obtained eigenspace in high ofyieldsA, A along∗ has with dimension a high selectivity. one. Let θ denote an ordering of the eigen- { i}i= However this reagent has serious limitations to be used d values of A. For ≤ i ≤ d let vi denote a θi-eigenvector for A. The ordering θi i= is said to be standard O-Methylation of phenolic compounds is an important for high boiling pointd phenols [18]. The vapor phase { } d whenever A∗ acts on the basis vi i= in an irreducible tridiagonal fashion. If the ordering θi i= is standard strategy in organic chemistry due to its high applicability methylationd of phenol{ } with dimethyl carbonate was also { } then the ordering θd−i i= is also standard, and no further ordering is standard. Similar comments apply to in synthesis of many petrochemicals, fine chemicals,d performed{ } over ion-exchanged zeolites in the continuous- d A∗. Let θ denote a standard ordering of the eigenvalues of A. Then A, A∗ is self-dual if and only if θ pharmaceuticals, fragrances, dyes and agrochemicals{ i }[1].i= flow conditions [19-22]. However, this reaction is carried { i}i= is a standard orderingout at ofhigh the temperature eigenvalues and of Atwo∗ (see byproducts [7, Proposition including 8.7]). o-cresol and 2,6-xylenol are produced beside to anisole. * Corresponding author: Mohammad Rahmani, Department of In this situation, methylation of both phenol and Chemical Engineering, Amirkabir University of Technology (Tehran p-cresol using dimethyl carbonate were performed Polytechnic), Tehran, 15875-4413, Iran, Tel.: +9821-64543198, *Corresponding Author:in a continuously Kazumasa Nomura: fed stirredTokyo Medicaltank reactor and Dental [18]. University, The Ichikawa, 272-0827,Japan, e-mail: [email protected] E-mail: [email protected] Fatemeh Gholipour and Farhad Panahi, Department of Chemical O-methylation of phenol with dimethyl carbonate has Paul Terwilliger: Department of Mathematics, University of Wisconsin, Madison, WI53706, USA, E-mail: Engineering, Amirkabir University of Technology, Mahshahr, Iran also been reported over 1-butyl-3-methylimidazolium [email protected] Open Access. © 2019 Gholipour 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. F. Gholipour et al.: Efficient and selective microwave-assisted O-methylation of phenolic compounds 585 chloride [23,24], potassium carbonate [25], magnesium O-methylation of phenolic compounds was achieved oxide [26], Mg-Al mixed oxides [27]. Unfortunately, in all under more environmental conditions without using of the mentioned methods for methylation using dimethyl stoichiometric amount of base and using TMAOH as an carbonate, C-alkylation by-products are always detected. abundant available and cheap methylating agent. Trimethylsulfonium salts was also used for methylation of phenols [28]. This reaction is carried out in the presence of methanol and potassium carbonate while the conversion was not satisfactory. In this situation, quaternary amines 2 Experimental such as phenyltrimethylammonium salts was employed for O-methylation of phenolic compounds in alkaloids 2.1 General chemistry [29]. For example, phenyltrimethylammonium chloride, in the presence of potassium carbonate in dry All phenols and naphthols and tetramethylammonium dimethylformamide (DMF) afforded glaucine from its hydroxide were commercially available and purchased starting material in good yield [30]. The O-methylation of from Merck and Aldrich chemical companies. phenols with trimethylammonium acetate was occurred Tetramethylammonium hydroxide is 25% solution in at temperature of 200-230°C and use of CaO as a base water. All products were known and their spectroscopic [31]. Tetramethylammonium chloride is also reported data were compared with those of authentic compounds. to be used as a methylating agent for the methylation Analyses of the products were done on a GC-MS (Agilent of phenols in the presence of K2CO3 or Cs2CO3 as base 6890 N-GC-5973 N-MSD chromatograph, using a and dimethoxymethane as a solvent at 145°C under 30 m × 0.25 mm Restek, Rtx-5SILMS column with a film microwave conditions [29]. Other reagents used for layer of 0.25 μm. The initial temperature of column was O-methylation of phenols under microwave conditions are 50°C for 1 min, followed by programming at 10°C/min trimethylphosphit and trimethyl phosphate [32].