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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Separating Xylene Isomers with a Calcium Metal–Organic Framework

Here, the purification of p-xylene (pX) from its xylene isomers represents a challenging but important industrial process. Herein, we report the efficient separation of pX from its ortho- and meta- isomers by a microporous calcium-based metal–organic framework material (HIAM-203) with a flexible skeleton. At 30 °C, all three isomers are accommodated but the adsorption kinetics of o-xylene (oX) and m-xylene (mX) are substantially slower than that of pX, and at an elevated temperature of 120 °C, oX and mX are fully excluded while pX can be adsorbed. Multicomponent column breakthrough measurements and vapor-phase/liquid-phase adsorption experiments have demonstrated the capability of HIAM-203 for efficient separation of xylene isomers. Ab initio calculations have provided useful information for understanding the adsorption mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Accessing Transient Isomers in the Photoreaction of Metastable‐State Photoacid

The photoreaction of a metastable‐state photoacid (mPAH) generally involves multiple isomers with various connected pathways of photoinduced structural changes during a single reaction cycle. However, only a limited number of isomers have been identified experimentally so far owing to the inherent complexity in combination with the presence of various competing electronic and vibrational processes, as well as the constantly varying interactions between mPAH isomers and solvent molecules. Here, in this work, an optical spectroscopic study on a benzimidazole‐based mPAH, a novel photoacid using benzimidazole as the structural moiety with the active proton, is reported. Through measurements of linear absorption and steady‐state fluorescence in neat solvents and binary mixtures, a pronounced effect of neat water and its binary mixture with glycerol is discovered on the photoreaction of this benzimidazole‐mPAH, manifested by the remarkably distinct spectral responses to irradiation from that observed for an organic solution under identical conditions. Measurements of time‐ and frequency‐resolved fluorescence emission further enable to access transient isomers and the associated spectral characteristics from other competing electronic excited‐state relaxation processes. Spectral deconvolution analysis and time‐dependent density functional theory calculations are applied to separate distinct spectral components and access their potential origin.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Discovery of nuclear isomers

Currently, 1917 nuclear isomers with half-lives longer than 100 ns have been discovered in 1310 different nuclides and 103 different elements. Here, while the physical properties of isomers have been compiled before, this is the first compilation of the isomer discoveries. For each isomer the reference, year, laboratory and country are documented.

Thoennessen, M. [Michigan State University, East L↗
DOE OSTI2023

The C 2 H 4 O isomers in the oxidation of ethylene

A combined rotational spectroscopy, thermochemistry, and kinetic modeling study explores the mechanism of acetaldehyde (ethanal), vinyl alcohol (ethenol), and ethylene oxide (oxirane) formation in the oxidation of ethylene (ethene). Multiplexed quantitative detection of oxidation intermediates and products exiting a SiO 2 / SiC microreactor at 1700 K is demonstrated with the BrightSpec W-band chirped-pulse Fourier transform millimeter-wave spectrometer. The broadband rotational spectrum contains transitions of formaldehyde (CH 2 O), methoxy (CH 3 O), methanol (CH 3 OH), ketene (CH 2 CO), acetaldehyde (CH 3 CHO), syn-vinyl alcohol (syn- CH 2 CHOH), anti-vinyl alcohol (anti-CH 2 CHOH), oxirane (c-CH 2 OCH 2 ), propyne (CH 3 CCH), and syn-propanal (syn-CH 3 CH 2 CHO). We focus on the three C 2 H 4 O species and deduce their concentration ratio [CH 3 CHO]:[CH 2 CHOH]:[c-CH 2 OCH 2 ] = 1:0.7(2):0.06(2) by comparing the observed line intensities to those simulated with the PGOPHER software. Detailed thermochemistry of the C 2 H 4 O isomers and conformers is provided by Active Thermochemical Tables. The observed excess concentrations of vinyl alcohol and oxirane relative to the more stable acetaldehyde compared to the equilibrium ratio at 1700 K (1:0.087:0.000024), point to direct chemical pathways to these higher energy isomers. The mechanism for the formation of the three C 2 H 4 O isomers is analyzed using a 0-D homogenous reactor kinetics simulation for ethylene oxidation. The ratios of the C 2 H 4 O isomers concentrations predicted by the kinetic model are compared to the experimental values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Control of Catalyst Isomers Using an N -Phenyl-Substituted RN(CH 2 CH 2 P i Pr 2 ) 2 Pincer Ligand in CO 2 Hydrogenation and Formic Acid Dehydrogenation

A novel pincer ligand, i Pr PN Ph P [PhN- (CH 2 CH 2 P i Pr 2 ) 2 ], which is an analogue of the versatile MACHO ligand, iPr PN H P [HN(CH 2 CH 2 P i Pr 2 ) 2 ], was synthesized and characterized. The ligand was coordinated to ruthenium, and a series of hydride-containing complexes were isolated and characterized by NMR and IR spectroscopies, as well as X-ray diffraction. Comparisons to previously published analogues ligated by iPr PN H P and iPr PN Me P [CH 3 N(CH 2 CH 2 P i Pr 2 ) 2 ] illustrate that there are large changes in the coordination chemistry that occur when the nitrogen substituent of the pincer ligand is altered. For example, ruthenium hydrides supported by the iPr PN Ph P ligand always form the syn isomer (where syn/anti refer to the relative orientation of the group on nitrogen and the hydride ligand on ruthenium), whereas complexes supported by iPr PN H P form the anti isomer and complexes supported by iPr PN Me P form a mixture of syn and anti isomers. We evaluated the impact of the nitrogen substituent of the pincer ligand in catalysis by comparing a series of iPr PN R P (R = H, Me, Ph)-ligated ruthenium hydride complexes as catalysts for formic acid dehydrogenation and carbon dioxide (CO 2 ) hydrogenation to formate. The iPr PN Ph P-ligated species is the most active for formic acid dehydrogenation, and mechanistic studies suggest that this is likely because there are kinetic advantages for catalysts that operate via the syn isomer. In CO 2 hydrogenation, the iPr PN Ph P-ligated species is again the most active under our optimal conditions, and we report some of the highest turnover frequencies for homogeneous catalysts. Experimental and theoretical insights into the turnover-limiting step of catalysis provide a basis for the observed trends in catalytic activity. Additionally, the stability of our complexes enabled us to detect a previously unobserved autocatalytic effect involving the base that is added to drive the reaction. Overall, by modifying the nitrogen substituent on the MACHO ligand, we have developed highly active catalysts for formic acid dehydrogenation and CO 2 hydrogenation and also provided a framework for future catalyst development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Isomer-specific, Cryogenic Ion Vibrational Spectroscopy Investigation of D2-and N2- Tagged, Protonated Formic Acid Complexes Using Two Color, IR-IR Photobleaching

Here we analyze cryogenic ion vibrational spectra of tagged protonated formic acid (PFA) with electronic structure and anharmonic vibrational calculations to establish the isomers generated by electrospray ionization (ESI) followed by buffer gas cooling to ~25 K. Two isomers are identified (the trans form (E,Z) and the cis form (E,E)) and generated in comparable abundance despite the fact that the calculated E,E structure lies 6.40 kJ mol-1 above the E,Z form. A large (~60 kJ mol-1) barrier separates them such that the E,E form can be kinetically trapped upon cooling in the ion trap. The anticooperativity between the H-bonds of the OH groups is explored by measuring the shift in the D2-bound OH fundamental when a second D2 is attached. Both isomers are observed in the N2-tagged counterparts, displaying the expected red-shifted OH bands. These results indicate that ESI generates both isomers and both must be considered when analyzing cluster spectra based on the PFA core ion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Full Exclusion of Branched Hexanes from Their Linear Isomer by a Robust Aluminum Metal–Organic Framework with Tailored Pore Structure

High-efficiency separation of hexane isomers through selective molecular exclusion represents an important yet challenging task in the petrochemical industry. It has stringent requirements on the adsorbents' pore shape and dimensions. Here we report the complete exclusion of branched hexanes from their linear isomer by an aluminum metal-organic framework, CAU-21-ODB (ODB = 4,4'-oxydibenzoate) with high stability. The unique gourd-shaped channels with suitable pore aperture lead to substantial uptake of nHEX (141 mg/g at 30 °C) but negligible adsorption of its branched isomers under identical conditions. Furthermore, the capability of CAU-21-ODB for the separation of hexane isomers has been verified by multicomponent breakthrough experiments. DFT calculations further confirm the size-exclusion based separation mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An Experimental and Theoretical Study of the High Temperature Reactions of the Four Butyl Radical Isomers

The high temperature gas phase chemistry of the four butyl radical isomers (n-butyl,sec-butyl, iso-butyl, andtert-butyl) was investigated in a combined experimental and theoretical study. Organic nitrites were used as convenient and clean sources of each of the butyl radical isomers. Rate coefficients for dissociation of each nitrite were obtained experimentally and are at, or close to, the high pressure limit. Low pressure experiments were performed in a diaphragmless shock tube with laser schlieren densitometry at post-shock pressures of 65, 130, and 260 Torr and post-shock temperatures of 700-1000 K. Additional experiments were conducted with iso-butyl radicals at 805 K and 8.7 bar to elucidate changes in mechanism at higher pressures. These experiments were performed in a miniature shock tube with synchrotron-based photoionization mass spectrometry. The mass spectra confirmed that scission of the O-NO bond is the primary channel by which the precursors dissociate, but they also provided evidence of a minor channel (<7.7%) through HNO loss and formation of an aldehyde. These high pressure experiments were also used to determine the disproportionation/recombination ratio for iso-butyl radicals as 0.3. Reanalysis of the lower-temperature literature and the present data yielded rate constants for the disproportionation reaction, iso-butyl + iso-butyl = iso-butene + iso-butane. A chemical kinetics model was developed for the reactions of the butyl isomers that included new paths for highly energized adducts. These adducts are formed by the addition of H, CH 3 or C 2 H 5 to the butyl radicals. Accompanying theoretical investigations show that chemically activated pathways are competitive with stabilization of the adduct by collision under the conditions of the laser schlieren experiments. These calculations also show that at 10 bar and T< 1000 K stabilization is the only important reaction, but at higher temperatures, even at 10 bar, chemically activated product channels should also be considered. Branching fractions and rate coefficients are presented for these reactions. Furthermore, this study also highlights the importance of the radical structure for determining branching ratios for disproportionation and recombination of alkyl radicals, and these were facilitated by theoretical calculations of recombination rate coefficients for the four butyl radical isomers. Overall, the results reveal previously unknown features of butyl radical chemistry under conditions that are relevant to a wide range of applications and reaction mechanisms are presented that incorporate pressure dependent rate coefficients for the key steps.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Influence of substitution pattern on the dynamics of internal conversion and intersystem crossing in thiopyridone isomers

We report a combined experimental and theoretical investigation of the ultrafast internal conversion (IC) and intersystem crossing (ISC) dynamics of two thiopyridone (TP) isomers in solution. Our study used ultrafast transient X-ray absorption spectroscopy (XAS) at the sulfur K-edge, in conjunction with electronic excited state surface hopping molecular dynamics and simulations of the excited state XAS, to investigate the impact of the functional group substitution pattern and solvent on the dynamics of IC and ISC. The combination of the localized X-ray probe and the simulation results enables, in part, the differentiation between ππ* and nπ* character excited states, as well as singlet and triplet states. Access to nπ* character excitations has particular value since they often prove challenging to assess with optical spectroscopy. For 2-TP, the photoexcited S 2 (ππ*) state rapidly undergoes IC to the S 1 (nπ*) state below the instrument response time, followed by ISC to the T 1 (ππ*) state on a timescale of 600 fs in acetonitrile. For 4-TP, the timescale of S 2 to S 1 IC increases to 330 fs and the timescale of ISC increases to more than 10 ps. The differences between isomers are rationalized by considering the key role of the, nπ* intermediates in mediating the intersystem crossing of these systems. Varying the substitution pattern of the molecule can stabilize or destabilize these intermediates leading to the increase in ISC rate in the ortho isomer as compared to the para isomer, while changing the solvent from acetonitrile to water had minimal effect on the electronic excited state relaxation mechanism.

Garratt, Douglas [SLAC National Accelerator Labora↗
DOE OSTI2026

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. II. Isomer-resolved unimolecular dynamics

Transient carbon-centered hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation are characterized by their time- and energy-resolved unimolecular dissociation dynamics to hydroxyl (OH) and cyclic ether products. Two distinct •QOOH isomers are examined with radical sites at a primary carbon of one of the methyl groups (β-Me) or a secondary carbon (β-Et) of the ethyl group. Energy-dependent unimolecular rates are obtained from the time-dependent appearance of OH products for the two isomers and compared with statistical microcanonical rates computed using RRKM theory, including heavy-atom tunneling, based on high-level theoretical calculations. A benchmark-corrected approach is utilized to compute high-accuracy stationary-point energies, most importantly, transition-state barriers, for the •QOOH_Me and •QOOH_Et isomers in isopentane oxidation, building on higher-level reference calculations for the oxidation of ethane (C 2 H 5 O 2 ) and propane (C 3 H 7 O 2 ), respectively. Here, the measured rates are compared with RRKM calculations incorporating the benchmark-corrected transition-state parameters, a vibrationally adiabatic multidimensional hindered-rotor treatment of key torsions, and quantum tunneling. Agreement between experiment and theory validates the statistical description and shows faster decay for •QOOH_Et due to its lower barrier. Both β-QOOH isomers decay almost exclusively to OH + cyclic ether products under the conditions studied.

Oxidation processes↗
DOE OSTI2020

Metastable nuclear isomers as dark matter accelerators

Inelastic dark matter and strongly interacting dark matter are poorly constrained by direct detection experiments since they both require the scattering event to deliver energy from the nucleus into the dark matter in order to have observable effects. We propose to test these scenarios by searching for the collisional deexcitation of metastable nuclear isomers by the dark matter particles. The longevity of these isomers is related to a strong suppression of γ- and β-transitions, typically inhibited by a large difference in the angular momentum for the nuclear transition. The collisional deexcitation by dark matter is possible since heavy dark matter particles can have a momentum exchange with the nucleus comparable to the inverse nuclear size, hence lifting tremendous angular momentum suppression of the nuclear transition. This deexcitation can be observed either by searching for the direct effects of the decaying isomer, or through the rescattering or decay of excited dark matter states in a nearby conventional dark matter detector setup. Existing nuclear isomer sources such as naturally occurring 180m Ta, 137m Ba produced in decaying Cesium in nuclear waste, 177m Lu from medical waste, and 178m Hf from the Department of Energy storage can be combined with current dark matter detector technology to search for this class of dark matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Selective isomer emission via funneling of exciton polaritons

Polaritons in organic systems has shown the potential to modify chemical properties and to mediate long-range energy transfer between individual chromophores, among other capabilities. Here, we demonstrate that strong coupling and formation of organic exciton-polaritons can be used to selectively tune the isomer emission of organic molecules. By taking advantage of their delocalized and hybrid character, polaritons emerging in the strong coupling regime open a new relaxation pathway that allows for an efficient funneling of the excitation between the molecular isomers. We implement this by strong coupling to trans-DCS (E-4-dimethylamino-4'cyanostilbene)molecules, which present two isomers in different amounts when immersed in a polymer matrix. Thanks to this new relaxation pathway, the photoexcitation that is first shared by the common polaritonic mode is then selectively funneled to the excited states of one of the isomers, recognizing pure emission from the isomeric states that do not contribute to emission under normal conditions.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1986

Interstellar isomers

Both observational and theoretical studies of molecular clouds are hindered by many difficulties. One way to partially circumvent the difficulties of characterizing the chemistry within these objects is to study the relative abundances of isomers which are synthesized from a common set of precursors. Unfortunately, only one such system has been confirmed, the HCN/HNC pair of isomers. While the basic outlines of its chemistry have been known for some years, there are still many aspects of the chemistry which are unclear. Another potential pair of isomers is HCO+/HOC+; HCO+ is an abundant instellar molecule and a tentative identification of HOC+ has been made in Sgr B2. This identification is being challenged, however, based on theoretical and laboratory evidence that HOC+ reacts with H2. Another potential pair of interstellar isomers is methyl cyanide (CH3CN, acetonitrile) and methyl isocyanide (CH3NC). The cyanide is well known, however the isocyanide has yet to be observed despite theoretical predictions that appreciable quantities should be present.

Defrees, D.↗
NASA NTRS1986

Enhanced Raman spectroscopic study of rotational isomers on metal surfaces

Surfaced-enhanced Raman spectroscopy has been used to study rotational isomers of succinonitrile and N-methyl-thioacetamide on Cu and Ag surfaces. Both the gauche and trans conformers of succinonitrile are found to chemisorb on the metal surface. The doubly degenerate nu(C-triple bond-N) in the free molecules is removed when succinonitrile adsorbs on copper, which indicates that the two (C-triple bond-N) groups are no longer chemically equivalent. Both conformers are found to coordinate to the copper surface through the pi system of one of the two (C-triple bond-N) groups. In the case of N-methyl-thioacetamide, the population of the cis isomer is greatly increased on Cu and Ag surfaces. This is probably due to surface-induced cis-trans isomerization, in which the predominant trans isomer is converted to the cis isomer.

Loo, B. H.↗
NASA NTRS1988

Structural isomers of C2N(+) - A selected-ion flow tube study

Reactivities of the structural isomers CCN(+) and CNC(+) were examined in a selected-ion flow tube at 300 + or - 5 K. The less reactive CNC(+) isomer was identified as the product of the reactions of C(+) + HCN and C(+) + C2N2; in these reactions only CNC(+) can be produced because of energy constraints. Rate coefficients and branching ratios are reported for the reactions of each isomer with H2, CH4, NH3, H2O, C2H2, HCN, N2, O2, N2O, and CO2. Ab initio calculations are presented for CCN(+) and CNC(+); a saddle point for the reaction CCN(+) yielding CNC(+) is calculated to be 195 kJ/mol above CNC(+). The results provide evidence that the more reactive CCN(+) isomer is unlikely to be present in measurable densities in interstellar clouds.

Knight, J. S.↗
NASA NTRS2005

Interstellar Isomers: The Importance of Bonding Energy Differences

We present strong detections of methyl cyanide (CH3CN), vinyl cyanide (CH2CHCN), ethyl cyanide (CH3CH2CN) and cyanodiacetylene (HC4CN) molecules with the Green Bank Telescope (GBT) toward the Sgr B2(N) molecular cloud. Attempts to detect the corresponding isocyanide isomers were only successful in the case of methyl isocyanide (CH3NC) for its J(sub K) = 1(sub 0) - 0(sub 0) transition, which is the first interstellar report of this line. To determine the spatial distribution of CH3NC, we used archival Berkeley-Illinois-Maryland Association (BIMA) array data for the J(sub K) = 1(sub 0) - 0(sub 0) transitions but no emission was detected. From ab initio calculations, the bonding energy difference between the cyanide and isocyanide molecules is greater than 8500 per centimeter (greater than 12,000 K). Thus, cyanides are the more stable isomers and would likely be formed more preferentially over their isocyanide counterparts. That we detect CH3NC emission with a single antenna (Gaussian beamsize(omega(sub B))=1723 arcsec(sup 2)) but not with an interferometer (omega(sub b)=192 arcsec(sup 2)), strongly suggests that CH3NC has a widespread spatial distribution toward the Sgr B2(N) region. Other investigators have shown that CH3CN is present both in the LMH hot core of Sgr B2(N) and in the surrounding medium, while we have shown that CH3NC appears to be deficient in the LMH hot core. Thus, largescale, non-thermal processes in the surrounding medium may account for the conversion of CH3CN to CH3NC while the LMH hot core, which is dominated by thermal processes, does not produce a significant amount of CH3NC. Ice analog experiments by other investigators have shown that radiation bombardment of CH3CN can produce CH3NC, thus supporting our observations. We conclude that isomers separated by such large bonding energy differences are distributed in different interstellar environments, making the evaluation of column density ratios between such isomers irrelevant unless it can be independently shown that these species are co-spatial.

Remijan, Anthony J.↗
DOE OSTI2023

Sequential Separation of Linear, Mono–, and Di–Branched Hexane Isomers on a Robust Coordination Polymer with Nonbonding Flexibility

Efficient separation of hexane isomers is a crucial process for upgrading gasoline. Herein, the sequential separation of linear, mono-, and di-branched hexane isomers by a robust stacked 1D coordination polymer termed as Mn-dhbq ([Mn(dhbq)(H 2 O) 2 ], H 2 dhbq = 2,5-dihydroxy-1,4-benzoquinone) is reported. The interchain space of the activated polymer is of optimal aperture size (5.58 Å) that could exclude 2,3-dimethylbutane, while the chain structure can discriminate n-hexane with high capacity (1.53 mmol g –1 at 393 K, 6.67 kPa) by high-density open metal sites (5.18 mmol g –1 ). With the temperature- and adsorbate-dependent swelling of interchain spaces, the affinity between 3-methylpentane and Mn-dhbq can be deliberately controlled from sorption to exclusion, and thus a complete separation of ternary mixture can be achieved. Column breakthrough experiments confirm the excellent separation performance of Mn-dhbq. Furthermore, the ultrahigh stability and easy scalability further highlight the application prospect of Mn-dhbq for separation of hexane isomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Physical structure of constitutional isomers influences antiproliferation activity of thiosemicarbazone-alkylthiocarbamate copper complexes

A series of hybrid thiosemicarbazone-alkylthiocarbamate copper complexes with similar electronic environments but distinct physical structures have been prepared, characterized, and evaluated for antiproliferation activity. The complexes include the constitutional isomers (1-phenylpropane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 1 ) and (1-phenylpropane-1-one-(N-methylthiosemicarbazonato)-2-imine-(O-ethylthiocarbamato))copper(II) (CuL 2 ) along with (1-propane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 3 ). Complexes CuL 1 and CuL 2 differ in the positions of the pendent thiosemicarbazone (TSC) and alkylthiocarbamate (ATC) moieties on the 1-phenylpropane backbone. Complex CuL 3 employs a propane backbone with the TSC in the 2-position as in CuL 1 . The isomer pair CuL 1 and CuL 2 have equivalent electronic environments with indistinguishable Cu II/I potentials (E 1/2 = -0.86 V vs. ferrocenium/ferrocene) and electron paramagnetic resonance (EPR) spectra (g ∥ = 2.26, g ⊥ = 2.08). The electronic structure of CuL 3 has a similar E 1/2 of -0.84 V and identical EPR parameters to CuL 1, 2 . Single crystal X-ray diffraction studies confirm a consistent donor environment with no substantial variation in the Cusingle bondN or Cusingle bondS bond distances and angles between the complexes. The antiproliferation activities of the CuL 1–3 were evaluated against the lung adenocarcinoma cell line (A549) and nonmalignant lung fibroblast cell line (IMR-90) using the MTT assay. CuL 1 had the highest A549 activity ( A549 EC 50 = 0.065 μM) and selectivity ( IMR-90 EC 50 / A549 EC 50 = 20). The constitutional isomer CuL 2 displayed decreased A549 activity (0.18 μM) and selectivity (10.6). The complex CuL 3 displayed activity (0.009 μM) similar to CuL 1 but with a lack of selectivity (1.0). Cellular copper loading determined by ICP-MS was consistent with the activity and selectivity trends. The complexes CuL 1–3 did not induce reactive oxygen species (ROS) generation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗