Accepted Elasticity in Local Arithmetic Congruence Monoids

For certain \({a,b \in \mathbb{N}}\) , an Arithmetic Congruence Monoid M(a, b) is a multiplicatively closed subset of \({\mathbb{N}}\) given by \({\{x\in\mathbb{N}:x \equiv a \pmod{b}\} \cup\{1\}}\) . An irreducible in this monoid is any element that cannot be factored into two elements, each greater than 1. Each monoid element (apart from 1) may be factored into irreducibles in at least one way. The elasticity of a monoid element (apart from 1) is the longest length of a factorization into irreducibles, divided by the shortest length of a factorization into irreducibles. The elasticity of the monoid is the supremum of the elasticities of the monoid elements. A monoid has accepted elasticity if there is some monoid element that has the same elasticity as the monoid. An Arithmetic Congruence Monoid is local if gcd(a, b) is a prime power (apart from 1). It has already been determined whether Arithmetic Congruence Monoids have accepted elasticity in the non-local case; we make make significant progress in the local case, i.e. for many values of a, b.     

Terminology Related to the Phenomenon ‘Self‐Disproportionation of Enantiomers’ (SDE)

Terms related to the phenomenon self‐disproportion of enantiomers (SDE) are discussed, particularly with respect to recently suggested alternative terms. Of the numerous terms proffered to describe this phenomenon, it is recommended that the acronym SDE be retained based on its qualities and the fact that its perceived shortcomings are invalid. The term can be readily applied to any process that exhibits the phenomenon of transforming a scalemic sample into fractions containing different enantiomeric compositions in comparison to the enantiomeric composition of the starting sample, and is not restricted solely to chromatographic occurrences. Chromatographic observations, though, can be specifically described by the term enantiomer self‐disproportionation over achiral chromatography (ESDAC). Use of the term homochiral in concert with its intended original meaning is also advocated.     

Long‐Range Chemical Ligation from N→N Acyl Migrations in Tryptophan Peptides via Cyclic Transition States of 10‐ to 18‐Members

Chemical ligations to form native peptides from N→N acyl migrations in Trp‐containing peptides via 10‐ to 18‐membered cyclic transition states are described. In this study, a statistical, predictive model that uses an extensive synthetic and computational approach to rationalize the chemical ligation is reported. N→N acyl migrations that form longer native peptides without the use of Cys/Ser/Tyr residues or an auxiliary group at the ligation site were achieved. The feasibility of these traceless chemical ligations is supported by the N?C bond distance in N‐acyl isopeptides. The intramolecular nature of the chemical ligations is justified by using competitive experiments and theoretical calculations.     

Masked Rhodamine Dyes of Five Principal Colors Revealed by Photolysis of a 2‐Diazo‐1‐Indanone Caging Group: Synthesis,Photophysics, and Light Microscopy Applications

Caged rhodamine dyes (Rhodamines NN) of five basic colors were synthesized and used as “hidden” markers in subdiffractional and conventional light microscopy. These masked fluorophores with a 2‐diazo‐1‐indanone group can be irreversibly photoactivated, either by irradiation with UV‐ or violet light (one‐photon process), or by exposure to intense red light (λ～750 nm; two‐photon mode). All dyes possess a very small 2‐diazoketone caging group incorporated into the 2‐diazo‐1‐indanone residue with a quaternary carbon atom (C‐3) and a spiro‐9H‐xanthene fragment. Initially they are non‐colored (pale yellow), non‐fluorescent, and absorb at λ=330–350 nm (molar extinction coefficient (ε)≈10⁴ M^?1 cm^?1) with a band edge that extends to about λ=440 nm. The absorption and emission bands of the uncaged derivatives are tunable over a wide range (λ=511–633 and 525–653 nm, respectively). The unmasked dyes are highly colored and fluorescent (ε= 3–8×10⁴ M^?1 cm^?1 and fluorescence quantum yields (?)=40–85 % in the unbound state and in methanol). By stepwise and orthogonal protection of carboxylic and sulfonic acid groups a highly water‐soluble caged red‐emitting dye with two sulfonic acid residues was prepared. Rhodamines NN were decorated with amino‐reactive N‐hydroxysuccinimidyl ester groups, applied in aqueous buffers, easily conjugated with proteins, and readily photoactivated (uncaged) with λ=375–420 nm light or intense red light (λ=775 nm). Protein conjugates with optimal degrees of labeling (3–6) were prepared and uncaged with λ=405 nm light in aqueous buffer solutions (?=20–38 %). The photochemical cleavage of the masking group generates only molecular nitrogen. Some 10–40 % of the non‐fluorescent (dark) byproducts are also formed. However, they have low absorbance and do not quench the fluorescence of the uncaged dyes. Photoactivation of the individual molecules of Rhodamines NN (e.g., due to reversible or irreversible transition to a “dark” non‐emitting state or photobleaching) provides multicolor images with subdiffractional optical resolution. The applicability of these novel caged fluorophores in super‐resolution optical microscopy is exemplified.     

Kinetics of catalyst-free thermal and photo-oxidation of cumene

Kinetics of thermal and photo-oxidation of cumene in the absence of catalyst was studied using high-pressure differential scanning calorimetry and low-pressure photocalorimetry. Kinetics of oxidation was followed by cumene hydroperoxide (CHP), acetophenone, and phenol formation. The amount of CHP formed was deduced from the total heat of reaction of thermal degradation of CHP at 453 K and using a new gas chromatographic method. CHP solution in cumene oxidized at 453 K and 680 psi of oxygen reproducibly with the heat of reaction linearly dependent on peroxide concentration in cumene. It was confirmed that cumene thermal oxidation was slow at <453 K, but at ≥453 K could occur explosively. Autocatalysis by CHP during thermo-oxidation was confirmed. Apparent activation energy of the photo-oxidation of cumene was found to be E _a = 22.3 kJ mol^?1. The value corresponds to radical chain process of the cumene autoxidation. Under assumption of pseudo-first order reaction, the rate constant of CHP formation was found to change from k _CHP ≈ 0.76 s^?1 during the first 4 h of photo-oxidation to k _CHP ≈ 0.2 s^?1 at the later stages at 2.0 W cm^?2 of UV exposure dose. It was established that the initial presence of the CHP in cumene does not change the photo-oxidation kinetics, but shifts the kinetic curve to earlier time. Finite difference method was employed to numerically model kinetics of cumene oxidation. The result indicated higher than expected thermal and photo-stability of both, cumene and CHP.     

Photoinduced mechanism of formation and growth of polycyclic aromatic hydrocarbons in low-temperature environments via successive ethynyl radical additions

A novel ethynyl addition mechanism (EAM) has been established computationally as a practicable alternative to high-temperature hydrogen-abstraction-C2H2-addition (HACA) sequences to form polycyclic aromatic hydrocarbon (PAH) -like species under low-temperature conditions in the interstellar medium and in hydrocarbon-rich atmospheres of planets and their moons. Initiated by an addition of the ethynyl radical (C2H) to the ortho-carbon atom of the phenylacetylene (C6H5C2H) molecule, the reactive intermediate loses rapidly a hydrogen atom, forming 1,2-diethynylbenzene. The latter can react with a second ethynyl molecule via addition to a carbon atom of one of the ethynyl side chains. A consecutive ring closure of the intermediate leads to an ethynyl-substituted naphthalene core. Under single-collision conditions as present in the interstellar medium, this core loses a hydrogen atom to form ethynyl-substituted 1,2-didehydronaphthalene. However, under higher pressures as present, for example, in the atmosphere of Saturn's moon Titan, three-body reactions can lead to a stabilization of this naphthalene-core intermediate. We anticipate this mechanism to be of great importance to form PAH-like structures in the interstellar medium and also in hydrocarbon-rich, low-temperature atmospheres of planets and their moons such as Titan. If the final ethynyl addition to 1,2-diethynylbenzene is substituted by a barrierless addition of a cyano (CN) radical, this newly proposed mechanism can even lead to the formation of cyano-substituted naphthalene cores in the interstellar medium and in planetary atmospheres.     

Novel tailoring reaction for two adjacent coordinated nitriles giving platinum 1,3,5-triazapentadiene complexes

The tailoring reaction of the two adjacent nitrile ligands in cis-[PtCl(2)(RCN)(2)] (R = Me, Et, CH(2)Ph, Ph) and [Pt(tmeda)(EtCN)(2)][SO(3)CF(3)](2) (8.(OTf)(2); tmeda = N,N,N',N'-tetramethylethylenediamine) upon their interplay with N,N'-diphenylguanidine (DPG; NH=C(NHPh)(2)), in a 1:2 molar ratio gives the 1,3,5-triazapentadiene complexes [PtCl(2){NHC(R)NHC(R)=NH}] (1-4) and [Pt(tmeda){NHC(Et)NHC(Et)NH}][SO(3)CF(3)](2) (10.(OTf)(2)), respectively. In contrast to the reaction of 8.(OTf)(2) with NH=C(NHPh)(2), interaction of 8.(OTf)(2) with excess gaseous NH(3) leads to formation of the platinum(II) bis(amidine) complex cis-[Pt(tmeda){NH=C(NH(2))Et}(2)][SO(3)CF(3)](2) (9.(OTf)(2)). Treatment of trans-[PtCl(2)(RCN)(2)] (R = Et, CH(2)Ph, Ph) with 2 equiv of NH=C(NHPh)(2) in EtCN (R = Et) and CH(2)Cl(2) (R = CH(2)Ph, Ph) solutions at 20-25 degrees C leads to [PtCl{NH=C(R)NC(NHPh)=NPh}(RCN)] (11-13). When any of the trans-[PtCl(2)(RCN)(2)] (R = Et, CH(2)Ph, Ph) complexes reacts in the corresponding nitrile RCN with 4 equiv of DPG at prolonged reaction time (75 degrees C, 1-2 days), complexes containing two bidentate 1,3,5-triazapentadiene ligands, i.e. [Pt{NH=C(R)NC(NHPh)=NPh}(2)] (14-16), are formed. Complexes 14-16 exhibit strong phosphorescence in the solid state, with quantum yields (peak wavelengths) of 0.39 (530 nm), 0.61 (460 nm), and 0.74 (530 nm), respectively. The formulation of the obtained complexes was supported by satisfactory C, H, and N elemental analyses, in agreement with FAB-MS, ESI-MS, IR, and (1)H and (13)C{(1)H} NMR spectra. The structures of 1, 2, 4, 11, 13, 14, 9.(picrate)(2), and 10.(picrate)(2) were determined by single-crystal X-ray diffraction.     

Computational investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part I. Theoretical calculation of spectroscopically observable parameters

Theoretical calculations are performed for the X2E"2 and A 2E"3 states of the cycloheptatrienyl (tropyl) radical C7H7. An important goal of these calculations is to predict and to guide the analysis of the experimentally observed A 2E"3-X 2E"2 electronic spectrum. Vibrational frequencies of the tropyl radical at the conical intersection and stationary points of its X and A state Jahn-Teller distorted potential energy surfaces are given. Spectroscopically obtainable parameters describing the Jahn-Teller effect are calculated for the X and A electronic states. Additionally, the stabilization energies for the X and A states are computed at the CASSCF(7,7) and EOMEA-CCSD levels of theory using various basis sets.     

Kinetics and mechanism of triethylamine-catalyzed 1,3-proton shift: Optimized and substantially improved reaction conditions for biomimetic reductive amination of fluorine-containing carbonyl compounds

Kinetic study of the triethylamine (TEA)-catalyzed isomerization of imine, derived from benzylamine and trifluoroacetophenone to the corresponding N-benzylidene-2,2,2-trifluoro-1-(phenyl)ethylamine has revealed concerted nature of the mechanism of this reaction via a virtually unionized transition state. As a synthetic bonus of this kinetic study, we found that application of a polar solvent (acetonitrile) and four equivalents of TEA provide for optimal reaction conditions at high concentrations. We demonstrate that application of these reaction conditions allows to substantially increase the reaction rates, chemical yields and results in cleaner formation of the target products.     

The influence of the loop between residues 223-235 in beetle luciferase bioluminescence spectra: a solvent gate for the active site of pH-sensitive luciferases

Beetle luciferases emit a wide range of bioluminescence colors, ranging from green to red. Firefly luciferases can shift the spectrum to red in response to pH and temperature changes, whereas click beetle and railroadworm luciferases do not. Despite many studies on firefly luciferases, the origin of pH-sensitivity is far from being understood. Through comparative site-directed mutagenesis and modeling studies, using the pH-sensitive luciferases (Macrolampis and Cratomorphus distinctus fireflies) and the pH-insensitive luciferases (Pyrearinus termitilluminans, Phrixotrix viviani and Phrixotrix hirtus) cloned by our group, here we show that substitutions dramatically affecting bioluminescence colors in both groups of luciferases are clustered in the loop between residues 223-235 (Photinus pyralis sequence). The substitutions at positions 227, 228 and 229 (P. pyralis sequence) cause dramatic redshift and temporal shift in both groups of luciferases, indicating their involvement in labile interactions. Modeling studies showed that the residues Y227 and N229 are buried in the protein core, fixing the loop to other structural elements participating at the bottom of the luciferin binding site. Changes in pH and temperature (in firefly luciferases), as well as point mutations in this loop, may disrupt the interactions of these structural elements exposing the active site and modulating bioluminescence colors.