HETEROCYCLES

■ Contents

■ Preface to Heterocycles Special Issue Honoring the 80th Birthday of Professor Dr. Somsak Ruchirawat: a Great Teacher and Compassionate Mentor

Minoru Isobe* and Poonsakdi Ploypradith*

*Nagoya University, Chikusa, Nagoya, Aichi 464-8601, Japan

■ Curriculum Vitae

Somsak Ruchirawat*

*

■ Publications List by Somsak Ruchirawat

Somsak Ruchirawat*

*Chulabhorn Research Institute, 54 Kamphaeng Phet 6 Rd.
Bangkok 10210, Thailand

■ The Utility of Oxoammonium Species in Organic Synthesis: Beyond Alcohol Oxidation

Shota Nagasawa, Yusuke Sasano, and Yoshiharu Iwabuchi*

*Graduate School of Pharmaceutical Sciences, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai, 980-8578, Japan

Abstract

Oxoammonium species are electrophilic chemical species generated via single electron oxidation of nitroxyl radicals. Although this species and its salts are known as useful oxidants and active species for (catalytic) oxidation of alcohols into carbonyl compounds in organic synthesis, the benefits of oxoammonium species for the oxidative transformations of numerous types of substrates apart from alcohols has been reported. This review summarizes the synthetic utility of oxoammonium species under both stoichiometric and catalytic conditions with the exception of alcohol oxidation.

■ Alkaloids and Alkaloid-Like Compounds are Potential Scaffolds of Antiviral Agents against SARS-CoV-2 (COVID-19) Virus

Prasat Kittakoop,* Dhanushka Darshana, Rapeepat Sangsuwan, and Chulabhorn Mahidol

*Chulabhorn Graduate Institute, Program in Chemical Sciences, Chulabhorn Royal Academy, Kamphaeng Phet 6 Road, Laksi, Bangkok 10210, Thailand

Abstract

COVID-19 pandemic has an enormous impact on humans, and it has disrupted daily life of people. Moreover, COVID-19 pandemic has significant negative effects on the world economics. To prevent the viral infection, vaccines are rapidly developed and available for certain strains of SARS-CoV-2 virus. However, the emerging of new variants has caused the problems for COVID-19 vaccines due to immune escape ability, challenging the vaccine development process which usually takes years. In this regard, there is a critical need of new antiviral compounds that can be used to combat SARS-CoV-2 virus safely and effectively. This review provides an overview on alkaloids and alkaloid-like compounds, which have antiviral activity against SARS-CoV-2 virus and related coronaviruses. Drug repurposing has played a crucial role for the drug discovery of COVID-19, and many effective antiviral agents against SARS-CoV-2 virus are from commonly used drugs or antiviral leads. Antiviral natural alkaloids and derivatives, which have the activity toward SARS-CoV-2 virus and related coronaviruses, are also discussed in this review.

■ 1,2,3-Triazole Scaffold in Recent Medicinal Applications: Synthesis and Anticancer Potentials

Vanida Choomuenwai,* Ronnakorn Leechaisit, Ratchanok Pingaew,* Veda Prachayasittikul, Supaluk Prachayasittikul, and Virapong Prachayasittikul

*Department of Chemistry, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand

Abstract

Cancer is one of commonly concerned health problems globally and its management is challenging. Besides an availability of diverse classes of anticancer agents, the existing drugs are noted for their limitations such as considerable toxicities, low potency and responsiveness, drug resistance, and others. 1,2,3-Triazole is an attractive heterocyclic scaffold possessing considerable characteristics and is presented in many pharmacologically active molecules. Accordingly, attention has been given to this scaffold in the recent years, especially, in an area of anticancer drug development. In this review, a collection of recently reported triazole based anticancer agents are discussed along with their synthetic methods, proposed molecular targets, and mechanisms of actions. A summary of other recently reported biological activities is also provided. In overview, recent studies suggested that the 1,2,3-triazole based compounds could elicit their anticancer effects against several cancer cell lines via an inhibition of cancer cell growth, an induction of apoptosis, an inhibition of involved enzymes such as aromatase, kinases, and others. Some interesting results from computational studies also discussed relating to the predictions of possible molecular targets. In summary, it is suggested that the 1,2,3-triazole serves as a potential scaffold with noteworthy opportunity for future development of novel anticancer agents to cope with current challenging issues in cancer management.

■ Heterocyclic Stilbene and Bibenzyl Derivatives in Liverworts: Distribution, Structures, Total Synthesis and Biological Activity

Yoshinori Asakawa* and Fumihiro Nagashima

*Institute of Pharmacognosy, Tokushima Bunri University, Tokushima 770-8514, Japan

Abstract

Liverworts are a rich source of lipophilic terpenoids, and aromatic compounds especially bibenzyl and bis-bibenzyl derivatives. This review is concerned with the distribution of heterocyclic stilbenes and bibenzyls in liverworts, belonging to the Acrobolbaceae, Aytoniaceae, Frullaniaceae, Lejeuneaceae, Plagiochilaceae, and Radulaceae families. Some Radula species elaborate bibenzyl cannabinoids, which possess remarkably similar biological activity to that of the Δ9-tetrahydrocannabinoids, the psycho- and anti-inflammatory active metabolites found in Cannabis sativa.

■ 8-Hydroxyquinolines: A Promising Pharmacophore Potentially Developed as Disease-Modifying Agents for Neurodegenerative Diseases: A Review

Veda Prachayasittikul,* Ratchanok Pingaew, Supaluk Prachayasittikul, and Virapong Prachayasittikul

*Center of Data Mining and Biomedical Informatics, Faculty of Medical Technology, Mahidol University, Bangkok 10700, Thailand

Abstract

8-Hydroxyquinoline (8HQ) is an attractive heterocyclic scaffold with well-known metal chelating property, broad-ranging pharmacological activities, and preferrable drug-likeness, thus, it had gained a continual attention in areas of drug development, especially, drug repurposing. Alzheimer’s disease (AD) is one of globally health concern in an era of aging society and its management is considered challenging as effective disease-modifying drugs are still clinically unavailable. Loss of metal ion homeostasis is one of key factors contributing to pathogenesis and progression of AD in which its imbalance could trigger many related key factors and harmful events, especially, oxidative neuronal damages. Hence, restoration of homeostasis and distribution of brain’s metal ions served to be a promising strategy for development of disease-modifying agents. In this review, essential key points relating to AD pathogenesis, roles of metal ions in AD, and pioneer 8HQ-based compounds are introduced. A series of recently reported 8HQ-based neuroprotective compounds (i.e., derivatives, hybrids, conjugates, and metal complexes) focusing on compounds acting as metal chelators are reviewed. Related 8HQ-based neuroprotective compounds with other mechanisms of actions are also discussed. Additionally, summary of key contents is included to provide an overview of current development situations. Taken together, this article would be beneficial and inspiring for the related future drug design and development to tackling an increasing prevalence of neurodegenerations in the global aging society.

■ Five-Membered Nitrogen Heterocycles as New Lead Compounds in Drug Discovery

Agustono Wibowo, Mohd Fazli Mohammat, Zurina Shaameri, Fatin Nur Ain Abdul Rashid, Noor Hidayah Pungot, and Ahmad Sazali Hamzah*

*Organic Synthesis Laboratory, Institute of Science, Universiti Teknologi MARA (UiTM), 42300 Bandar Puncak Alam, Selangor Darul Ehsan, Malaysia

Abstract

Five-membered nitrogen heterocyclic compounds are a very important group with various pharmaceutical properties. The different substitutions and functionalization of these compounds contributed to various biological activities. Five-membered nitrogen heterocyclic scaffolds are used for synthesizing numerous natural and synthetic compounds with a significant biological application. They include antidiabetic, anticancer, antimalarial, antiviral, antimicrobial, anti-inflammatory, antibacterial, and anti-neurodegenerative agents. This mini-review provides an overview of the biological activities and the synthetic methods for preparing the five-membered nitrogen heterocyclic scaffolds and their functionalization. In the final part, this mini-review also listed some commercial drugs containing five-membered nitrogen heterocyclic motifs, highlighting the versatility of the five-membered nitrogen heterocyclic core in drug discovery.

■ Sparsomycin – a Review and Re-assessment

Geoffrey A. Cordell* and Sharna-kay Daley

*Natural Products Inc., Evanston, IL, 60202, U.S.A.

Abstract

The chemistry, biology, and biosynthesis of the microbial alkaloid sparsomycin (1) are summarized and re-assessed to identify future research initiatives for this biologically significant metabolite.

■ The Xanthate Route to Benzazepinones and Their Aza Congeners

Béatrice Quiclet-Sire and Samir Z. Zard*

*Department of Chemistry, Ecole Polytechnique, CNRS UMR 7652, 91128 Palaiseau, France

Abstract

The present brief overview highlights and discusses the synthetic potential of the degenerative radical addition of xanthates for the synthesis of benzazepinones and their aza congeners. Various routes are presented, including direct cyclisations onto the aromatic or heteroaromatic ring, intermolecular radical additions followed by ring closure, and Beckmann ring expansion of tetralones produced by radical addition-cyclisation. Many of the compounds described are medicinally relevant and not readily available by more conventional methods.

■ Synthesis and Optical Properties of Azuleno[1,2-b]benzothiophene and Selenophene

Mio Matsumura,* Taiki Kamiya, Masato Kawakubo, Yukako Hayashi, Tadashi Hyodo, Yuki Murata, Kentaro Yamaguchi, and Shuji Yasuike*

*School of Pharmaceutical Sciences, Aichi Gakuin University, 1-100 Kusumoto-cho, Chikusa-ku, Nagoya 464-8650, Japan

Abstract

Benzothiophene- and benzoselenophene-fused azulene derivatives were synthesized by Cu-catalyzed tandem cyclization via the Ullmann-type S/Se– arylation and Csp2–H chalcogenation of 2-(2′-bromophenyl)azulene. The maximum absorption of tetracyclic products was red-shifted from that of 2-phenylazulene, which does not contain a bridged chalcogen atom. Single-crystal X-ray analysis of azuleno[1,2-b]benzoselenophene revealed that the benzo[b]selenophene and azulene rings are almost coplanar.

■ The Synthesis of Simplified Analogues of Crambescin B Carboxylic Acid and Their Inhibitory Activity of Voltage-Gated Sodium Channels: New Aspects of Structure–Activity Relationships

Atsuo Nakazaki,* Shunsuke Mouri, Yoshiki Nakane, Yuki Ishikawa, Mari Yotsu-Yamashita, and Toshio Nishikawa

*Faculty of Science and Engineering, Iwate University, Ueda, Morioka 020-8551 (Japan)

Abstract

We describe the synthesis of six new analogues of crambescin B carboxylic acid from L-aspartic acid and the elucidation of their structure-activity relationships by a cell-based colorimetric assay. All the synthesized analogues except for the C4-analogue were found to have inhibitory activities against voltage-gated sodium channels (VGSCs) in nM order in a cell-based colorimetric assay.

■ Synthesis and Stereochemical Analysis of Planar Chiral Nine-Membered Aza-Orthocyclophyne

Yuuya Kawasaki, Sumire Tanaka, Kazunobu Igawa, and Katsuhiko Tomooka*

*Institute for Materials Chemistry and Engineering, Department of Molecular and Material Sciences, and IRCCS Kyushu University, Kasuga, Fukuoka 816-8580, Japan

Abstract

Aza-orthocyclophyne 3b with an oxy-substituent on the 16 position of the benzene ring was synthesized, and it was revealed that the stereochemical stability of 3b is consistent with the order of 1,3-steric repulsion between the C2 methylene protons and the oxy-substituent.

■ Synthesis of Benzo[d]pyrrolo[1,2-a]imidazoles by Iminocyclopropane Rearrangement of C-Cyclopropylbenzimidazoles

Adam P. Montoya, Matthew G. LaPorte, and Peter Wipf*

*Department of Chemistry, University of Pittsburgh, Pittsburgh PA 15260, USA

Abstract

The MgI2 or NH4I mediated iminocyclopropane rearrangement of trisubstituted acrylonitrile benzimidazoles provides an attractive access to novel pyrrolo[1,2-a]imidazoles. The rearrangement precursors, C-cyclopropylbenzimidazoles, are obtained by a Corey-Chaykovsky cyclopropanation of the acrylonitrile. We determine the scope of the iminocyclopropane rearrangement to 2,3-dihydro-1H-benzo[d]pyrrolo[1,2-a]imidazole-3-carbonitrile and 2,4-dihydro-2,4-disubstituted as well as 1,2,4-trisubstituted 1H-benzo[d]pyrrolo[1,2-a]imidazole-3-carbonitriles, and describe some of the limitations and side reactions, including the formation of aromatized 4H-benzo[d]pyrrolo[1,2-a]imidazole-3-carbonitriles.

■ New Sugar Based γ-Amino Silyl Ether Organocatalysts for Asymmetric Michael Addition of β-Keto Esters with Nitroolefins

Divakar Ganesan, Perumalsamy Parasuraman, Zubeda Begum, Rajkumar Thiyagarajan, Chigusa Seki, Yuko Okuyama, Eunsang Kwon, Koji Uwai, Michio Tokiwa, Suguru Tokiwa, Mitsuhiro Takeshita, and Hiroto Nakano*

*Graduate School of Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran 050-8585

Abstract

New sugar based γ-amino silyl ether organocatalysts were synthesized and their catalytic ability was examined in asymmetric Michael addition of β-keto esters with nitroolefins affording chiral Michael adducts with quaternary carbon stereocenter in good to excellent chemical yields, diastereoselectivities and moderate enantioselectivities (up to 97%, up to dr. 85:15, up to 56% ee).

■ Azuleno[6,5-b]indoles: Palladium-Catalyzed Oxidative Ring-Closing Reaction of 6-(Arylamino)azulenes

Taku Shoji,* Yukino Ariga, Shunji Ito, and Masafumi Yasunami

*Department of Science, Graduate School of Science and Technology, Shinshu University, Matsumoto 390-8621, Nagano, Japan

Abstract

6-Bromoazulene derivative with two n-butoxycarbonyl groups was prepared by the modification procedure of Nozoe’s azulene synthesis. The aromatic nucleophilic substitution reaction of the 6-bromoazulene derivatives having two-ester functions with aniline derivatives proceeded to give the corresponding 6-(arylamino)azulene derivatives. Palladium-catalyzed oxidative ring-closing reaction of the 6-(arylamino)azulene derivatives provided the azuleno[6,5-b]indoles in moderate to good yields.

■ Application of Reversible Detection Method for N-Terminus Amino Groups: Solid Phase Synthesis of Stylissatin B

Ao Tan, Keigo Takamatsu, Fusheng Xu, Seren Osanai, and Hiroyuki Konno*

*Department of Biological Engineering, Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510, Japan.

Abstract

The first synthesis of the proline-rich cyclic heptapeptide stylissatin B is described. Reversible detection method of N-terminus amino groups using tetrachloro-N-hydroxyphthalimide was applied as the Fmoc-solid phase peptide synthesis. The end points of all reactions of solid support could be pursued by the detection methods.

■ Novel Synthesis and Properties of Optically Pure N-Trifluoroacetylphenylglycine Hydroxysuccinimide Ester

Zeping Wang, Shoko Ishikawa, Fumina Ohashi, Reo Sagisaka, Yuta Murai, Zetryana Puteri Tachrim, Takeyuki Suzuki, and Makoto Hashimoto*

*Division of Applied Bioscience, Graduate School of Agriculture, Hokkaido University, Kita 9, Nishi 9, Kita-ku, Sapporo, Hokkaido, Japan

Abstract

Phenylglycine is non-proteinogenic α-amino acid, and its partial structure is found in some biologically active compounds. C-Terminal modification of N-acyl-protected phenylglycine sometimes causes racemization due to the fact that the phenyl ring is directly connected to the α-position of the α-amino acid skeleton. In this report, synthesis and the property of N-trifluoroacetylphenylglycine hydroxysuccinimide ester was archived.

■ Synthesis of Novel Fluorescent Bicyclic Amidines and Evaluation of Their Photophysical Properties

Wannaporn Disadee,* Kittiporn Trisupphakant, and Somsak Ruchirawat

*Laboratory of Medicinal Chemistry, Chulabhorn Research Institute, Lak Si, Bangkok 10210, Thailand

Abstract

A metal-free process for the synthesis of novel bicyclic amidines was developed. The key conversions involved a cascade of double intramolecular cyclization of Michael adducts under a mild condition to provide 39 analogs in up to 93% yield. Photophysical properties of the representatives, a parent molecule and its free base form were studied on different solvents. From the results, a free base form exhibited strong fluorescent emission wavelength in up to 491 nm and large Stoke shift in up to 140 nm, offering positive information for their future development.

■ Construction of Tetrahydroquinolines with Spirocyclic Structures at the 4-Position

Yuko Wakahara, Takahiro Noro, Juri Sakata, Hirofumi Ueda, and Hidetoshi Tokuyama*

*Graduate School of Pharmaceutical Sciences, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan

Abstract

The construction of tetrahydroquinolines with a spirocyclic structure at the 4-position was studied. The five-step sequence includes construction of benzocyclopentanone oxime by Knoevenagel condensation of cyclic ketones with Meldrum’s acid followed by Michael addition of aryl Grignard Reagent, intramolecular Friedel–Crafts acylation, condensation with hydroxylamine, and reductive ring expansion reaction using diisobutylaluminium hydride. The utility of this method was demonstrated by construction of a variety of tetrahydroquinolines possessing a four to eight-membered spirocyclic ring as well as adamantane and indane structures at the 4-position.

■ 2-Arylazoimidazoles Revamped by Quarternization or Dimerization; Another Gain in Functionality of an Industrial Dyestuff Family by Task-Specific Side-Chain Substituents

Sandro Neuner, Heidi A. Schwartz, Christoph Kreutz, Thomas Müller, Paul Mayer, Günther Bonn, Thomas Gelbrich, Ulrich J. Griesser, Klaus Wurst, Volker Kahlenberg, Sven Nerdinger,* and Herwig Schottenberger*

*Sandoz GmbH, Biochemiestr. 10, 6250 Kundl, Austria

Abstract

Based on [(E)-2-(4-fluorophenyl)diazenyl]-1H-Imidazole,[210180-24-0], a versatile late stage intermediate for the divergent synthesis of direct dyes, a novel series of N,N`-disubstituted azoimidazolium salts was prepared. In particular, benzylation, 4-vinylbenzylation, phenacylation, sulfopropylation, ethylation, as well as propargylation allowed for the access of derivatives (1-6), which are useful for follow-up conversions, e.g. click reactions, or free radical polymerization. The compounds were routinely characterized spectroscopically. The diethylated tetrafluoroborate salt 5 was additionally analyzed by 19F-NMR. Hot stage microscopy of contact melts of 5 with the less commonly used anionic nucleophiles azide and rhodanide illustrate the rapid formation of deeply colored products confirming the nucleophilic aromatic replacement of fluoride in the 4-fluorophenyl substituent. Remarkably, in addition to the conceived functional quarternizations, a neutral dimer chromophore (7) resulted from using epichlorohydrin as a linking agent. Single crystal X-ray structure determinations are reported for all newly described compounds.

■ N-Heterocyclic Analogs of Indenocorannulene

Ansu Li, Jun Xu, Kim K. Baldridge, and Jay S. Siegel*

*School of Pharmaceutical Science and Technology, Tianjin University, 92 Weijin Road, Nankai District, Tianjin, 300072, China

Abstract

Four chiral N-heterocyclic monoindenocorannulenes were prepared by fusing pyridine, quinoline, and indole across the peri-positions of corannulene via tandem Suzuki-aryl-aryl coupling and C-Cl activated ring closure reactions. The UV-Vis, fluorescence, and CV properties of these N-doped polynuclear aromatics are discussed. Resolution of enantiomers is performed on chiral stationary phase HPLC and the absolute configurations are assigned by comparison of experimental and quantum mechanically predicted ECD spectra.

■ Synthesis of 1-Azaspiro[4,5]-7-decen-2-one from L-Asparagine and L-Aspartic Acid

Punlop Kuntiyong,* Sunisa Moongmai, Natida Thongluar, and Ittiphat Klayparn

*Department of Chemistry, Faculty of Science, Silpakorn University, Sanamchandra Palace, Muang Nakhon Pathom 73000, Thailand

Abstract

A synthetic strategy for 1-azaspiro[4.5]-7-decen-2-one based on N-acyliminium spirocyclization is reported. The common core structure found in biologically active alkaloids such as FR901483, TAN1251 and lepadiformine was synthesized via chiral N-alkyl-3-dibenzylaminosuccinimide intermediates. The chiral succinimides were synthesized in 2 steps from L-aspartic acid or 3 steps from L-asparagine.

■ Oxidative Fragmentation of Cytisine as an Entry to the Bis(piperidine) Scaffold of Virgidivarine

Worawat Niwetmarin* and Timothy Gallagher*

*School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

Abstract

Using virgidivarine as a focus, we have extended the oxidative fragmentation of (-)-cytisine as a source of functionalized heterocyclic fragments to provide a novel bis(piperidine) 2′-epivirgidivarine. This stereochemically-defined scaffold offers synthetic versatility within an “sp3-rich” environment that makes it amenable to further manipulation and development within the context of de novo drug design.

■ Lipase-Catalyzed Site-Selective Deacetylation of 2-Methoxy-3-methylnaphthalene-1,4-diol Diacetate for Construction of Characteristic Substituted 1,2,3,4-Tetrahydroisoquinoline Derivative of Novel Ecteinascidin Marine Natural Product

Masashi Yokoya,* Ryo Sato, and Naoki Saito

*Graduate School of Pharmaceutical Sciences, Meiji Pharmaceutical University, 2-522-1 Noshio, Kiyose, Tokyo 204-8588, Japan

Abstract

We developed a site-selective deacetylation of 2-methoxy-3-methylnaphthalene-1,4-diol diacetate catalyzed by Candida antarctica lipase B, which furnished 1-hydroxy-2-methoxy-3-methylnaphthalen-4-yl acetate in 88% yield. This product was transformed into 2-methoxy-3-methylnaphthalen-1-ol in a five-step sequence (30.5% overall yield from 7a). It is a novel procedure for preparing a characteristic A ring substituted system for both safracin antibiotics (2) and ecteinascidin marine natural products (1).

■ Isolation of Ikahonone, 4-Methyl-2,4-dihydroxy-3-pentanone from Bacillus cereus IFM12235

Yasumasa Hara,* Mareno Chiba, Keiichiro Watanabe, and Masami Ishibashi*

*Graduate School of Pharmaceutical Sciences, Chiba University, 1-8-1 Inohana, Chuo-ku, Chiba 260-8675, Japan

Abstract

A new ketone, ikahonone (1), and five known compounds (2-6) were isolated from Bacillus cereus IFM12235 collected in Japan. The structure of compound 1 was elucidated using spectral studies, including NMR. The absolute configurations of 1 and 2 were determined by comparing electronic circular dichroism (ECD) spectra with known compounds and calculating the ECD spectra of 1 and 2. Three compounds (2-4) were previously prepared by synthesis, and first isolated as natural products in the present study.

■ Abnormal Strecker Reaction of 3-Formylindole and Aniline

Tomohiro Yazawa, Masaya Nakajima,* and Tetsuhiro Nemoto*

*Graduate School of Pharmaceutical Sciences, Chiba University, 1-8-1 Inohana, Chuo-ku, Chiba 260-8675, Japan

Abstract

Reaction of 3-formylindole, aniline, and TMSCN under conditions of the Strecker reaction yielded a Friedel-Crafts reaction product rather than the usual aminonitrile. This abnormal Strecker reaction can be applied to various aniline and 3-formylindole derivatives. DFT calculations revealed that the most thermodynamically stable product is generated in the reaction.

■ Improved Synthesis of Naldemedine Tosylate and Crystal Structures of Four Related Solid Forms

Josef Spreitz, Thomas Gelbrich, Sven Nerdinger,* Marijan Stefinovic, and Ulrich J. Griesser

*Sandoz GmbH, Biochemiestrasse 10, 6250 Kundl, Austria

Abstract

The production of drug substances requires a robust and scalable process capable of delivering the active pharmaceutical ingredient (API) in excellent chemical and polymorphic purity. With this goal in mind we have developed an improved procedure for the preparation of naldemedine tosylate, which crystallizes directly from the reaction mixture as pure polymorph form II. Solid state studies revealed a series of additional new physical forms whose crystal structure have been determined by single-crystal X-ray diffraction.