Enantioselective regiospecific addition of propargyltrichlorosilane to aldehydes catalyzed by biisoquinoline N,N’-dioxide

• Noble Brako,
• Sreerag Moorkkannur Narayanan,
• Amber Burns,
• Layla Auter,
• Valentino Cesiliano,
• Rajeev Prabhakar and
• Norito Takenaka

Beilstein J. Org. Chem. 2024, 20, 3069–3076, doi:10.3762/bjoc.20.255

• , University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146-0431, USA 10.3762/bjoc.20.255 Abstract Distilled propargyltrichlorosilane with >99% isomeric purity was prepared for the first time, and its asymmetric catalytic regiospecific addition reaction to aldehydes was developed through a

• . Accordingly, the development of efficient access to optically active chiral α-allenic alcohols continues to be of significant interest in organic chemistry [11][12][13]. The asymmetric catalytic addition of allenylation reagents to aldehydes provides direct access to chiral α-allenic alcohols in an

• enantioenriched form [11][12]. However, such metal/metalloid reagents and the corresponding metal catalyst-bound intermediates often equilibrate between possible regioisomeric forms and can undergo both, SE2 and SE2’ addition reactions, resulting in a mixture of homopropargylic alcohols and α-allenic alcohols [14

Extension of the π-system of monoaryl-substituted norbornadienes with acetylene bridges: influence on the photochemical conversion and storage of light energy

• Robin Schulte,
• Dustin Schade,
• Thomas Paululat,
• Till J. B. Zähringer,
• Christoph Kerzig and
• Heiko Ihmels

Beilstein J. Org. Chem. 2024, 20, 3061–3068, doi:10.3762/bjoc.20.254

• elemental analysis. All products showed the characteristic 1H NMR spectroscopic signals of norbornadienes, in particular two signals at ca. 2.10 ppm and 2.20 ppm (7-CH2) and two broad singlets between 3 and 4 ppm (bridgehead 1- and 4-CH). In addition, typical 13C NMR shifts of the aryl-substituted

• derivatives during the photoreaction, whereas the blue-shifted maximum of the photoproduct was formed. In addition, isosbestic points were observed for the derivatives 1h (A), 1i (B), 1k (D), and 1l (E). The irradiations of the derivatives 1h, 1i, 1k, and 1l were stopped once no more changes of the absorbance

• that the triplet energy of 1i is significantly lower than 2.4 eV and even triplet sensitizers with lower triplet energies than that of [Ru(phen)3](PF6)2 could be employed for this reaction, which might even allow red light-driven switching. In addition to these kinetic studies, the photoisomerization

Cyclodextrin-based rotaxanes for polymer materials: challenge on simultaneous realization of inexpensive production and defined structures

• Yosuke Akae

Beilstein J. Org. Chem. 2024, 20, 3026–3049, doi:10.3762/bjoc.20.252

• substitution/addition reactions became the standard for end-capping reactions, although a transition metal–catalyzed cross-coupling reaction has also been used to synthesize CD-based rotaxane. Typically, water-soluble components are prepared, after which the Suzuki coupling reaction in water is used to

• depended on the cavity size, the same as small-molecule inclusion. For example, PEG forms stable pseudopolyrotaxane structures with α, β, and γ-CDs, although polypropylene glycol (PPG) only forms a stable pseudopolyrotaxane structure with β-CD [41]. In addition to these linear polymer chains, various types

• synthesis, Harada and co-workers reported the end-capping reaction based on nucleophilic substitution by the amino groups on axle ends (Scheme 2) [43]. Similarly, other highly efficient reactions have been performed as end-capping reactions to produce polyrotaxane [13][14][15]. In addition to the simple

Tunable full-color dual-state (solution and solid) emission of push–pull molecules containing the 1-pyrindane moiety

• Anastasia I. Ershova,
• Sergey V. Fedoseev,
• Konstantin V. Lipin,
• Mikhail Yu. Ievlev,
• Oleg E. Nasakin and
• Oleg V. Ershov

Beilstein J. Org. Chem. 2024, 20, 3016–3025, doi:10.3762/bjoc.20.251

• caused a blue shift of the maximum at 511 nm, and a new maximum in the region of 380–400 nm appeared in the absorption spectra. The intensity of the short-wavelength band also increased upon addition of trifluoroacetic acid. At the same time, a second band centered at 440 nm also appeared in the emission

Tailored charge-neutral self-assembled L₂Zn₂ container for taming oxalate

• David Ocklenburg and
• David Van Craen

Beilstein J. Org. Chem. 2024, 20, 3007–3015, doi:10.3762/bjoc.20.250

• positively charged or charge-neutral, is their metal-driven self-assembly. Unfortunately, this can also be their Achilles' heel, as the underlying coordination bonds are fragile compared to covalent bonds. For example, metallocages can easily break apart by the addition of competitive anions which are highly

• determined by NMR (see Supporting Information File 1, Figures S7, S9, S11, S13, S15, and S17). 1H NMR dicarboxylate binding studies were carried out with oxalate (C22−) and longer variants C(2+n)2− up to adipate (with n = 4). Oxalate addition to [L2Zn2] results in an intermediate exchange with broadened NMR

• guests and competition experiments. 1H NMR titrations with malonate, succinate, glutarate, and adipate showed no clean binding (formation of mixtures) upon addition of these guests as TBA salt to [L2Zn2], with broad regions and multiple sets of signals persisting even after the addition of a large excess

Advances in radical peroxidation with hydroperoxides

• Oleg V. Bityukov,
• Pavel Yu. Serdyuchenko,
• Andrey S. Kirillov,
• Gennady I. Nikishin,
• Vera A. Vil’ and
• Alexander O. Terent’ev

Beilstein J. Org. Chem. 2024, 20, 2959–3006, doi:10.3762/bjoc.20.249

• range of polymers [1]. They are also applied as curing, hardening and crosslinking agents [2]. Global demand for organic peroxides is expected to increase as the use of engineered plastics increases and production capacity is expanded. In addition, the need for polymers is expected to increase due to

• mainly include: nucleophilic addition or nucleophilic substitution with H2O2 or ROOH [17][18], autoxidation with O2, pericyclic reactions of unsaturated bonds with O3 or O2, and metal-catalyzed peroxidation (Isayama–Mukaiyama hydrosilylperoxidation [19][20], for example) [21][22][23]. As the topic is

• and tert-butylperoxy moiety (Scheme 33) [89]. The mechanism of the process is probably based on the formation of radical species A and B, which disproportionate to form the intermediate C. Sequential addition of sulfonyl and tert-butylperoxy radicals to the double bond of intermediate C leads to

gem-Difluorovinyl and trifluorovinyl Michael acceptors in the synthesis of α,β-unsaturated fluorinated and nonfluorinated amides

• Monika Bilska-Markowska,
• Marcin Kaźmierczak,
• Wojciech Jankowski and
• Marcin Hoffmann

Beilstein J. Org. Chem. 2024, 20, 2946–2953, doi:10.3762/bjoc.20.247

• , we observed a striking illustration of this phenomenon. A Michael addition involving gem-difluorovinyl and trifluorovinyl acceptors was successfully achieved, demonstrating high stereoselectivity. This selectivity was further elucidated through theoretical calculations. Using this methodology, a

• series of new α,β-unsaturated amides, both fluorinated and nonfluorinated, were synthesized. Keywords: gem-difluorovinyl Michael acceptors; Michael addition; trifluorovinyl Michael acceptors; α,β-unsaturated amides; Introduction The Michael reaction, characterized by the addition of stable carbon

• advancements have broadened the scope of Michael donors and acceptors to encompass fluorine-containing compounds, enhancing the reaction's utility in synthesizing fluorinated derivatives [7][8]. Shibata and colleagues pioneered the use of fluorinated Michael donors, notably achieving enantioselective addition

4,6-Diaryl-5,5-difluoro-1,3-dioxanes as chiral dopants for liquid crystal compositions

• Maurice Médebielle,
• Peer Kirsch,
• Jérémy Merad,
• Carolina von Essen,
• Clemens Kühn and
• Andreas Ruhl

Beilstein J. Org. Chem. 2024, 20, 2940–2945, doi:10.3762/bjoc.20.246

• from neat chiral mesogens, or through the addition of a chiral dopant to an achiral nematic liquid crystal [5][6]. The ability of the dopant to induce chirality in the nematic phase is defined as the helical twisting power [HTP; β = (pc)−1; with p the helical pitch and c the molar concentration]. The

Recent advances in transition-metal-free arylation reactions involving hypervalent iodine salts

• Ritu Mamgain,
• Kokila Sakthivel and
• Fateh V. Singh

Beilstein J. Org. Chem. 2024, 20, 2891–2920, doi:10.3762/bjoc.20.243

• formation of the Nu–Ar product and aryl iodide [21]. Second, the arylation can take place in the presence of a metal catalyst via oxidative addition, followed by reduction elimination [48][49]. Thirdly, it proceeds through a ligand-coupled arylation which involves a five-membered transition state to yield

• additives. An efficient conversion was detected when the substrate contains electron-rich functionalities. In contrast, the yield dropped notably when the amines were substituted with electron-deficient functionalities. In addition, asymmetric diaryliodonium salts were examined, and the transfer of the aryl

• compounds (Scheme 16) [68]. The novel iodine(III) intermediate was generated through nucleophilic substitution of a heteroatom nucleophile, which initiated the reaction. A subsequent aryl migration from the iodine to the heteroatom resulted in the formation of the arylated nucleophile. In addition to

C–H Trifluoromethylthiolation of aldehyde hydrazones

• Victor Levet,
• Balu Ramesh,
• Congyang Wang and
• Tatiana Besset

Beilstein J. Org. Chem. 2024, 20, 2883–2890, doi:10.3762/bjoc.20.242

• morpholine hydrazone derived from 4-nitrobenzaldehyde was selected as a model substrate (Table 1). The latter was engaged in a two-step process: 1) halogenation to provide the corresponding N,N-hydrazonoyl bromide, which will then undergo an anion metathesis upon the addition of AgSCF3 to the reaction

• mixture. When the reaction was conducted in the presence of NBS in acetonitrile for 10 min, followed by the addition of AgSCF3, the desired product was isolated in 91% yield. A total selectivity for the formation of the Z isomer was observed as ascertained by 2D NMR (for more details, see Supporting

Synthesis of pyrrole-fused dibenzoxazepine/dibenzothiazepine/triazolobenzodiazepine derivatives via isocyanide-based multicomponent reactions

• Marzieh Norouzi,
• Mohammad Taghi Nazeri,
• Ahmad Shaabani and
• Behrouz Notash

Beilstein J. Org. Chem. 2024, 20, 2870–2882, doi:10.3762/bjoc.20.241

• addition to the application of isocyanides in a variety of MCRs, one of the unique reactions involves the formation of zwitterions from isocyanides upon reaction with acetylene and active olefin compounds such as alkyl acetylenedicarboxylates and gem-diactivated olefins. Due to having nucleophilic and

• increase and the electron-donating substituents led to a decrease in the reaction efficiency (Scheme 3, 4a–k). In addition, benzothiazepine was used in this protocol and the corresponding pyrrole-fused benzothiazepine was obtained with a yield of 73% (Scheme 3, 4l). Also, various isocyanides were suitable

N-Glycosides of indigo, indirubin, and isoindigo: blue, red, and yellow sugars and their cancerostatic activity

• Peter Langer

Beilstein J. Org. Chem. 2024, 20, 2840–2869, doi:10.3762/bjoc.20.240

• [12][13]. In addition, there are more and more applications in the field of medicinal chemistry, especially for the treatment of cancer [14][15]. In the course of the renewed interest in the chemistry of indigo, indirubin, and isoindigo in the field of cancer research, N-glycosides of these compounds

• steps from indigo (1a). The reaction of 1a with potassium permanganate afforded product 12 which was transformed to dehydroindigo (13) by pyridine-mediated elimination of acetic acid. The reaction of 13 with tetra-O-trimethylsilyl-ʟ-rhamnopyranose (4b) in the presence of trimethylsilyl iodide, addition

• of n-propyl mercaptane with subsequent addition of acetic anhydride, pyridine and KHF2 afforded indigo-N-rhamnoside 5c as a 2:1 mixture of α/β-anomers. The relatively low yield is a result of side reactions and decomposition, due to the rather unstable nature of the product. The reaction of 5c with

Multicomponent synthesis of α-branched amines using organozinc reagents generated from alkyl bromides

• Baptiste Leroux,
• Alexis Beaufils,
• Federico Banchini,
• Olivier Jackowski,
• Alejandro Perez-Luna,
• Fabrice Chemla,
• Marc Presset and
• Erwan Le Gall

Beilstein J. Org. Chem. 2024, 20, 2834–2839, doi:10.3762/bjoc.20.239

• alkyl iodides [24]. It was indeed noticed that the reactivity of primary iodides in the multicomponent carbonyl alkylative amination (CAA) reaction was quite sluggish compared to the secondary counterparts. In addition, primary alkyl bromides were found to be almost inactive in the process. Therefore

• . In addition, whereas tert-butylzinc iodide was efficient in the multicomponent coupling (99% yield), tert-butylzinc bromide led to a very low yield (16% 5kaa). The coupling presented some other limitations. It was not possible to carry out the reaction when a primary amine was employed. In addition

• significant assets associated to the use of alkyl bromides, which are more easily prepared (or commercially available), less costly, and more stable than the corresponding alkyl iodides. In addition, the reaction can be conducted in commercial THF or 2-MeTHF and without special precautions. We also found a

Synthesis of tricarbonylated propargylamine and conversion to 2,5-disubstituted oxazole-4-carboxylates

• Kento Iwai,
• Akari Hikasa,
• Kotaro Yoshioka,
• Shinki Tani,
• Kazuto Umezu and
• Nagatoshi Nishiwaki

Beilstein J. Org. Chem. 2024, 20, 2827–2833, doi:10.3762/bjoc.20.238

• ] because of their easily modifiable dipeptide frameworks. Several methods exist for accessing PCPAs, such as the amination of 1-halo-1-alkynes [16][17], tandem reactions of α-imino esters with nucleophiles and electrophiles [18], and the nucleophilic addition of an acetylide to α-carbonylated N-acylimines

• derivative has been employed (Scheme 1) [13][14]. Recently, we have demonstrated that the central carbonyl group of DEMO is highly electrophilic, facilitating the nucleophilic addition of less reactive reagents such as acid amides [23][24][25][26]. When the reaction was conducted in the presence of acetic

• anhydride, the intermediately formed hemiacetal underwent acetylation, leading to N,O-acetals 1. In this method, an acid amide can be used as an amine masked with an acyl group. Subsequent elimination of acetic acid occurred to afford 2 in situ upon treatment with a base, enabling nucleophilic addition with

Investigation of a bimetallic terbium(III)/copper(II) chemosensor for the detection of aqueous hydrogen sulfide

• Parvathy Mini,
• Michael R. Grace,
• Genevieve H. Dennison and
• Kellie L. Tuck

Beilstein J. Org. Chem. 2024, 20, 2818–2826, doi:10.3762/bjoc.20.237

• an antenna chromophore and a receptor for Cu2+ ions; the Cu2+ complex was shown to be a chemosensor for the detection of aqueous hydrogen sulfide. The chemosensor exhibited significant reversibility over multiple cycles, observed with the sequential addition of Na2S followed by Cu2+ ions. The limit

• for the detection of both gaseous and/or aqueous H2S are shown in Figure 1 [12][16][17]. These sensors all function via the copper sequestration mechanism, where upon addition of hydrogen sulfide to the quenched bimetallic species, luminescence modulation occurs. In our quest for highly selective

• ). Response of Tb.1 with Cu2+ ions The addition of excess Cu2+ ions to Tb.1 was expected to result in complete saturation of emission signals. However, upon the titration of Cu2+ ions to 5 μM Tb.1 (10 mM Tris-HCl buffer containing 5% DMSO, pH 7.4), emission signal saturation was not observed until 5

Synthesis and antimycotic activity of new derivatives of imidazo[1,2-a]pyrimidines

• Dmitriy Yu. Vandyshev,
• Daria A. Mangusheva,
• Khidmet S. Shikhaliev,
• Kirill A. Scherbakov,
• Oleg N. Burov,
• Alexander D. Zagrebaev,
• Tatiana N. Khmelevskaya,
• Alexey S. Trenin and
• Fedor I. Zubkov

Beilstein J. Org. Chem. 2024, 20, 2806–2817, doi:10.3762/bjoc.20.236

• polyfunctional precursors 1, 2, and 3, two pathways are theoretically possible (Scheme 2 and Scheme 3). The first one involves the N-nucleophilic Michael addition to the activated multiple bond of the imide, leading to the formation of linear intermediates 6 or 8 (pathways A1 and B1) at the expense of the endo

• in Scheme 3). In addition, clearly distinguishable cross-peaks between the protons of the CH2-5 group and both endo and exo-carbonyl groups are observed. This allowed us to explicitly exclude from the analysis structures 13 and 15, which contain both endo-methylene groups, as part of a

• 6a, which undergoes subsequent cyclization steps more favorably, leading to the formation of the target product 4a (∆G = −3.02 kcal/mol). This suggests that the first step of intermediate formation is the critical one. It is also noteworthy that the Michael addition via intermediate 6a is an

C–C Coupling in sterically demanding porphyrin environments

• Liam Cribbin,
• Brendan Twamley,
• Nicolae Buga,
• John E. O’ Brien,
• Raphael Bühler,
• Roland A. Fischer and
• Mathias O. Senge

Beilstein J. Org. Chem. 2024, 20, 2784–2798, doi:10.3762/bjoc.20.234

• examples are azide-porphyrin derivatives reported by Flanagan et al. [43]. Here, five crystal structures were obtained of meso-para-phenyl arm-extended porphyrins (26, 27, 28, 29, 33) and two crystal structures for meso-meta-phenyl derivatives 36 and 37. In addition, single crystal structures of 11 and 46

Access to optically active tetrafluoroethylenated amines based on [1,3]-proton shift reaction

• Yuta Kabumoto,
• Eiichiro Yoshimoto,
• Bing Xiaohuan,
• Masato Morita,
• Motohiro Yasui,
• Shigeyuki Yamada and
• Tsutomu Konno

Beilstein J. Org. Chem. 2024, 20, 2776–2783, doi:10.3762/bjoc.20.233

• published that the asymmetric conjugate addition of 4-methylphenylboronic acid towards (E)-5-bromo-4,4,5,5-tetrafluoro-1-phenyl-2-penten-1-one (8) in the presence of a rhodium catalyst coordinated with (S)-BINAP gave the corresponding Michael adduct 9 in 94% enantiomeric excess (reaction 2, Scheme 1) [22

Copper-catalyzed yne-allylic substitutions: concept and recent developments

• Shuang Yang and
• Xinqiang Fang

Beilstein J. Org. Chem. 2024, 20, 2739–2775, doi:10.3762/bjoc.20.232

• -enynes with dimethylamine moiety (Scheme 11, 6x and 6y). In addition to tetramethylenediaminomethane, other tetraalkyldiaminomethanes can also be used as supplants of dialkylamines, leading to products with dialkylamine units with high yields and enantioselectivities (Scheme 11, 6a, 6g, 6i and 6z

• ester was also a suitable substrate for the reaction (Scheme 20, 20p). In addition, the presence of substituents such as hydroxy or chlorine groups on the anthrones had no impact on the reaction (Scheme 20, 20q–t). Chiral coumarins, renowned for their bioactive properties, form the cornerstone of

• radical-involved mechanism. In addition, a positive nonlinear relationship between the product and ligand indicated that the dinuclear copper is the active catalyst, which was also proved by single crystal X-ray analysis. However, kinetic experiments showed the reaction is first-order on copper, implying

Interaction of a pyrene derivative with cationic [60]fullerene in phospholipid membranes and its effects on photodynamic actions

• Hayato Takagi,
• Çetin Çelik,
• Ryosuke Fukuda,
• Qi Guo,
• Tomohiro Higashino,
• Hiroshi Imahori,
• Yoko Yamakoshi and
• Tatsuya Murakami

Beilstein J. Org. Chem. 2024, 20, 2732–2738, doi:10.3762/bjoc.20.231

• , respectively. In this study, by mimicking our previous system of triad molecules and living cells, we report a simplified model system with a cationic C60 derivative (catC60) and a liposome with embedded 1-pyrenebutyric acid (PyBA) to demonstrate that the addition of PyBA was important to achieve fast and

• experiments of differential scanning calorimetry analyses with varied amount of catC60 or C60 (Figure 2a), the addition of catC60 caused the disappearance of phase transition of DMPC liposomes in a dose-dependent manner and more efficiently than the case with C60. These results suggested that catC60 was more

• Figure 4a, the intensity decreased upon increasing the concentration of the catC60 in the liposomes, showing the quench of PyBA fluorescence by catC60, presumably by interacting in the liposome membrane. The incomplete quenching after the addition of PyBA at a concentration comparable to that of catC60

Synthesis of spiroindolenines through a one-pot multistep process mediated by visible light

• Francesco Gambuti,
• Jacopo Pizzorno,
• Chiara Lambruschini,
• Renata Riva and
• Lisa Moni

Beilstein J. Org. Chem. 2024, 20, 2722–2731, doi:10.3762/bjoc.20.230

• two anilines are incorporated in the final product, we speculated that the diversification of them could lead to different products. Anyway, first attempts to use two different anilines in the reaction failed, giving complex mixtures of α-aminoamidines even using sequential or slow addition of

Synthesis of benzo[f]quinazoline-1,3(2H,4H)-diones

• Ruben Manuel Figueira de Abreu,
• Peter Ehlers and
• Peter Langer

Beilstein J. Org. Chem. 2024, 20, 2708–2719, doi:10.3762/bjoc.20.228

• with a certain fine-structure for compounds 5a, 5g, and 5i and structure-less absorption features for compounds 5d, 5f, and 5h containing electron-donating functional groups are observed. In addition, the presence of strongly electron-donating N,N-dimethylamino groups leads to increased extinction

5th International Symposium on Synthesis and Catalysis (ISySyCat2023)

• Anthony J. Burke and
• Elisabete P. Carreiro

Beilstein J. Org. Chem. 2024, 20, 2704–2707, doi:10.3762/bjoc.20.227

• novel lipophilic cinchona squaramide organocatalyst. This organocatalyst was evaluated in a benchmark Michael addition of acetylacetone to trans-β-nitrostyrene, yielding the Michael adduct with high yield and enantioselectivity. The hydrophobic chain of the catalyst allowed the organocatalyst to be

Synthesis of fluoroalkenes and fluoroenynes via cross-coupling reactions using novel multihalogenated vinyl ethers

• Yukiko Karuo,
• Keita Hirata,
• Atsushi Tarui,
• Kazuyuki Sato,
• Kentaro Kawai and
• Masaaki Omote

Beilstein J. Org. Chem. 2024, 20, 2691–2703, doi:10.3762/bjoc.20.226

• 2a in good yields (Table 1, entries 9–11). Cross-coupling with palladium bis(trifluoroacetate), which is more reactive than palladium diacetate, gave the corresponding product in high yield of 96% (Table 1, entry 12). Without the addition of triphenylphosphine, the reaction proceeded in only 12

• to 4 mol % led to the conversion of 1a into 3a in 77% yield (Table 2, entry 13). In addition, using 2.0 equiv of 5a gave 3a in high 80% yield (Table 2, entry 14). Based on these results, we determined entry 13 in Table 1 and entry 14 in Table 2 as the optimum reaction conditions. We used 1 as a

• cyclopropylboronic acid (4n) achieved to give 2n in a 71% yield (Table 3, entry 13). When thiopheneboronic acid 4o was used as a coupling partner, the thiophene ring could be installed on 1a in a comparatively low yield of 31% (Table 3, entry 14). In addition, we investigated the substrate scope of 1 in the Suzuki

Photoluminescence color-tuning with polymer-dispersed fluorescent films containing two fluorinated diphenylacetylene-type fluorophores

• Kazuki Kobayashi,
• Shigeyuki Yamada,
• Motohiro Yasui and
• Tsutomu Konno

Beilstein J. Org. Chem. 2024, 20, 2682–2690, doi:10.3762/bjoc.20.225

• as electron-donating groups was shown to promote intramolecular charge transfer (ICT) and shifted the PL wavelength to longer wavelengths, resulting in yellow or orange fluorescence in the solid state [21][22]. In addition, cross-linking between the amino group and attached benzene ring effectively

• %, indicating that the PL band of 1c was very small because of non-radiative deactivation, in addition to the low PL component of 1c. The PL color of the PMMA film blended in a 95:5 ratio was dark blue, with color coordinates of (0.17, 0.14). Based on these results, various mixing ratios of 1a and 1c ranging

• component 1a or 1c. In other words, tuning the PL color was possible by controlling the mixing ratio. In addition, when the mixing ratio of 1a to 1c was 70:30, the chromaticity coordinates were (0.20, 0.32), which are relatively close to the ideal color coordinates of (0.33, 0.33) for white. The results for