Improvement of Weyl’s Inequality

Consider the construction of an operator from the sum of two component operators. Weyl’s inequality gives a lower bound to an eigenvalue of the constructed operator using a single eigenvalue from each of the component operators. Using such minimal information gives a poor bound, however, and when the eigenvectors that correspond to the said eigenvalues of the component operators are known, Weyl’s inequality can be significantly improved by considering the overlap of the two eigenvectors. This improvement can sometimes be further improved when several eigenvectors of each component operator are known so that the overlap of sub-eigenspaces are considered instead. The improvement is best when there is minimal overlap and Weyl’s inequality returns when the overlap is complete. An example with the hydrogen molecular ion is presented which illustrates the superiority over Weyl’s inequality when eigenvector or sub-eigenspace information is utilized.     

Paneth’s epistemology of chemical elements in light of Kant’s Opus postumum

Friedrich Paneth’s conception of “chemical element” has functioned as the official definition adopted by the International Union of Pure and Applied Chemistry since 1923. Paneth maintains a distinction between empirical and “transcendental” concepts of element; furthermore, chemical science requires fluctuation between the two. The origin of the empirical-transcendental split is found in Immanuel Kant’s classic Critique of Pure Reason (1781/1787). The present paper examines Paneth’s foundational concept of element in light of Kant’s attempt, late in life, to revoke key distinctions made in his Critique, including that of regulative and constitutive functions of reason. In a section of his Opus postumum devoted to the “Transition from the Metaphysical Foundations of Natural Science to Physics,” Kant bends his philosophical system to address the newly emerging sciences of matter of his time. Specifically, he tried, without success, to develop the transcendental ground for microscale motions of bodies encountered in physical, electrical and chemical processes. Paneth’s discussion of chemical element does not take the Opus postumum into account, which is why it begins with a rejection of Kant’s rejection (in his earlier writings) of chemistry’s status as science. I make the case that Paneth’s definition of element effectively maintains something very like Kant’s critical separation of regulative and constitutive principles, while a advancing the concept of chemical science.     

The Biochemistry of Life’s Energy

On December 10, 1997, the 101st anniversary of Alfred Nobels death, in Stockholms Concert Hall Swedish King Carl XVI Gustav awarded one half of the 1997 Nobel Prize in Chemistry (3.75 million kronor, about $500,000) to Professor Emeritus Paul Delos Boyer, age 79, of the University of California, Los Angeles and Dr. John Ernest Walker, age 56, of the Medical Research Council Laboratory of Molecular Biology, Cambridge, England for their elucidation of the enzymatic mechanism underlying the synthesis of adenosine triphosphate (ATP) and one half (3.75 million kronor, about $500,000) to Professor Emeritus Jens Christian Skou, age 79, of Århus University, Århus, Denmark for the first discovery of an ion-transporting enzyme, Na⁺, K⁺-ATPase.     

The estimation of ether’s enthalpies of formation

Taking hydrocarbon as gerneratrix, the differences of enthalpies of formation of ether and their corresponding generatrixes were compared and concluded and the equation to estimate ether’s enthalpy of formation, which was Δ_f H _e^°/(kJ/mol) = K(Δ_f H _m^ℴ − 90 + A) was obtained. The results can be elucidated with bond dissociation energies data, bond-enthalpy of formation method, induction effect and conjugative effect. The more essential account to explain the results can be got by using quantum chemistry theories, etc. Using replacement and comparison method, the way of estimation of organic compounds’ thermodynamic properties including enthalpy of formation can be obtained either. The article is published in the original.     

Theoretical Studies of Water’s and Methanol’s Effects on Alcoholysis of N-Benzyl-3-oxo-β-sultam

The mechanisms about the water’s and methanol’s effects on the alcoholysis of N-benzyl-3-oxo-β-sultam together with their differences have been studied by using density func- tional theory at the B3LYP/6-31G* level. The results, in comparison with a previous study on the relative reaction without the assistance of water and methanol, show that the added water or methanol can remarkably reduce the energy barrier of alcoholysis reaction of N-benzyl-3-oxo- β-sultam and the most favorite pathway is the breaking of C–N bond instead of S–N. It is also found that the reaction energy barrier of methanol-assisted alcoholysis is a little higher than that of the water-assisted one.     

Reaction of levoglucosenone with Dane’s diene

Cycloaddition of levoglucosenone to 7-methoxy-4-vinyl-1,2-dihydronaphthalene has been studied under different conditions, including heating under atmospheric pressure, in a sealed ampule, and under high pressure, as well as under microwave irradiation and in the presence of various catalysts. The chiral Diels–Alder adduct thus obtained can be used in the synthesis of estrone and its analogs.     

The chemist’s concept of molecular structure

The concept of molecular structure is fundamental to the practice and understanding of chemistry, but the meaning of this term has evolved and is still evolving. The Born–Oppenheimer separation of electronic and nuclear motions lies at the heart of most modern quantum chemical models of molecular structure. While this separation introduces a great computational and practical simplification, it is neither essential to the conceptual formulation of molecular structure nor universally valid. Going beyond the Born–Oppenheimer approximation introduces new paradigms, bringing fresh insight into the chemistry of fluxional molecules, proteins, superconductors and macroscopic dielectrics, thus opening up new avenues for exploration. But it requires that our ideas of molecular structure need to evolve beyond simple ball-and-stick-type models.

Celebrating Michael Faraday’s Discovery of Benzene

Abstract

In 1825, Michael Faraday, working in his workshop at the Royal Institution, discovered what he called bicarburet of hydrogen, now known as benzene. One hundred years later, his discovery was celebrated at the Royal Institution by a host of national and international delegates. Just over thirty years after Faraday’s discovery, the industrial importance of benzene was realised with the establishment of the synthetic dyestuffs industry. In this paper, the Faraday Benzene Centenary Celebration is discussed in detail and compared with other celebrations that have linked benzene with colour, in particular the 1890 celebration in Germany of the benzene ring formula and the 1906 celebration of the foundation of the coal-tar dye industry. It is instructive to review the different economic and political agendas underlying these events, each within the context of a particular time and place.     

Viscosity of liquid alloys: generalization of Andrade’s equation

Abstract  

The Andrade relation for the viscosity of liquid metals has been reformulated in terms of the Debye temperature for liquid metals. This semi-empirical relation has been extended to obtain a relation to calculate the composition and temperature dependence of the viscosity of liquid alloys using parameters which can be determined experimentally. The important inputs are the enthalpy of formation, ΔH, and the excess volume of mixing, ΔΩ. The composition dependence of the viscosity and its deviation from linear behavior could be positive or negative depending on the sign and magnitude of ΔH and ΔΩ. Several limiting cases of the semi-empirical relation for the viscosity of liquid alloys are compared and discussed. The results of the semi-empirical relation for viscosity isotherms for binary and ternary liquid alloys are mostly in reasonable agreement with available experimental results.     

A skeptic’s review of the New SI

Proposals in draft form have been circulated for new Système International (SI) measurement units that are expected to be official instruments of the Treaty of the Metre by 2015. This review outlines the substance of the proposals and examines some of the consequences of the continuing evolution of the SI toward inter-dependence of base units and quantities since its introduction in 1960. The proposals in question fix at an exact value a number of inter-related fundamental natural constants such as the speed of light, the Planck constant, the elementary charge and Boltzmann’s constant. All SI units are then so defined that their magnitude is set by those fixed values. Notably, the ongoing confusions about chemical measurements and the thermodynamic ‘mole’ are exacerbated. On the big principles of the basic purpose of the SI to facilitate communication and the fixing of fundamental physical constants of nature, there are significant problems and unanswered questions. They risk: damage to the enterprise of science; wide economic loss including increased transaction costs and barriers to global trade; barriers to new technologies and to improvements in measurement accuracy; loss of measurement compatibility or consistency; and a circular global measurement system vulnerable to undetectable systematic errors with serious adverse consequences for environmental decision making among many other vital human activities. The New SI requires frank and open discussion throughout science, technology, industry, trade, and global policy well before irreversible decisions are made.     

Synthesis of aromatic polyamidines in Eaton’s reagent

Aromatic polyamidines are prepared via the polycondensation of dicarboxamides and diamines in Eaton’s reagent. The polymers are investigated by elemental analysis and IR and NMR spectroscopy. Polyamidines are well soluble in concentrated sulfuric acid and concentrated formic acid and in polar organic solvents, and temperatures corresponding to their 10% weight losses are in the range 245–280°C.     

Acylation of Fischer’s Base with Methyl Aroylpyruvates

Methyl (Z)-4-aryl-2-hydroxy-4-oxobut-2-enoates (methyl aroylpyruvates) reacted with 1,3,3-trimethyl- 2-methylidene-2,3-dihydro-1H-indole (Fischer’s base) to give (2Z,5E)-1-aryl-3-hydroxy-5-(1,3,3-trimethyl-2,3-dihydro-1H-indol-2-ylidene)pent-2-ene-1,4-diones.     

Hierarchical enumeration of Kekulé’s benzenes,Ladenburg’s benzenes,Dewar’s benzenes,and benzvalenes by using combined-permutation representations

The group hierarchy for each skeleton of ligancy 6 is formulated to be: point group (PG \({\varvec{G}}_{\sigma }\)) \(\subseteq \) RS-stereoisomeric group (RS-SIG \({\varvec{G}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) stereoisomeric group (SIG \(\widetilde{{\varvec{G}}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) isoskeletomeric group (ISG \(\widetilde{\widetilde{{\varvec{G}}}}_{\sigma \widetilde{\sigma }\widehat{I}}\) = \({\varvec{S}}^{[6]}_{\sigma \widehat{I}}\)), where we start from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{6h}\) for the Kekulé benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{3h}\) for the Ladenburg benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the Dewar benzene skeleton, or from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the benzvalene skeleton. After these groups are constructed as combined-permutation representations, the calculation of the respective cycle indices with chirality fittingness (CI-CFs) and the introduction of ligand-inventory functions are conducted to give generation functions for 3D-based enumerations (for PGs and RS-SIGs) and 2D-based enumerations (for SIGs and ISGs). The enumeration results are discussed by means of isomer-classification diagrams, in which equivalence classes under enantiomerism (for PGs), RS-stereoisomerism (for RS-SIGs), stereoisomerism (for SIGs), and isoskeletomerism (for ISGs) are illustrated schematically. The implicit connotations of the conventional terms “skeletal isomerism”, “positional isomerism”, and “constitutional isomerism” are discussed, where the effects of the concept of isoskeletomerism are emphasized.     

Antioxidant potential of non-oil seed legumes of Indonesian’s ethnobotanical extracts

This study investigated the in vitro antioxidant properties (DPPH, ABTS, CUPRAC and FRAP), total phenolic content and flavonoid content of extracts from three non-oil seed legumes (Phaseolus lunatus red and white, and Canavalia ensiformis), local edible seeds from Indonesia, obtained using different solvent system (distilled water, 70% ethanol, and 100% ethanol). The variety of legume was a major source of variation in the phenolic contents, flavonoid content and antioxidant activity. HPLC analysis of the non-oil seed legume extracts identified gallic acid, epicatechin and coumaric acid. Among the varieties of non-oil seed legume extracts, the phenolic content varied from 15.21–38.60 mg gallic acid equivalents/g dry weight and the flavonoid content was 11.73–24.61 mg catechin equivalents/g dry weight. The antioxidant activity of the extracts suppressed the reactive oxygen species (ROS) generation and cellular damage induced by UV-B in HaCaT cells. These results showed that antioxidant activity (1.83–19.42% of inhibition DPPH; 2.99–37.29% of inhibition ABTS; 0.20–2.47 µM CUPRAC value; and 0.96–1.10 µM of FRAP value) of extracts possessed strong radical scavenging activity as well as inhibited ROS generation in a dose-dependent manner without showing any cytotoxicity. Collectively, the data presented that antioxidant of the extracts have potent antioxidant activity and decreasing ROS generation in HaCaT cells. It can be intimately used as alternative criterion for antioxidant and antiradical activities that can be utilized as a functional food and nutraceutical ingredients.     

Reactions of Zincke’s salts with 2,3-dimethylbenzothiazolium iodide

Reactions of 1-(2,4-dinitrophenyl)pyridinium chloride and 2-(2,4-dinitrophenyl)isoquinolinium chloride with 2,3-dimethylbenzothiazolium iodide in hot pyridine allows introduction of an aryl residue into the thiazole ring via intermolecular transformation of the pyridine ring of Zincke’s salts with participation of the methyl group in position 2 of the benzothiazolium salt.     

Enhancement of polyaniline’s electrical conductivity by coagulation polymerization

An effective and simple method was developed to prepare highly conductive polyaniline by coagulation polymerization. Depending on the coagulation reaction between aniline salts and lauryl sulfonate (SDS), not only was the polymerization rate of aniline monomers greatly decreased but also the doping efficiency of hydrochloric acid was effectively increased. Low polymerization rate provided enough time for the conformation adjustment of polyaniline chains and the diffusion of doping agent. Meanwhile, the doping efficiency of hydrochloric acid on polyaniline chains was effectively increased due to its easy diffusion among many vacancies, which were generated when SDS separated in the process of polymerization. Therefore, the electrical conductivity of polyaniline prepared by coagulation polymerization was increased more than ten times than that of polyaniline, which was prepared by conventional methods. In addition, the important factors to influence the preparation, such as SDS concentration, hydrochloride acid (HCl) concentration, content of ammonium persulfate (APS), and polymerization time were also investigated. When the molar ratio (aniline:SDS:HCl :APS) was set to 1.69:0.46:15.38:1, the conductivity of polyaniline reached 24.39 S/cm.     

Selective Densitometric Analysis of Cephalosporins Using Dragendorff’s Reagent

A simple, selective, precise, and stability-indicating thin-layer chromatographic method has been developed and validated for analysis of the cephalosporins cefpodoxime proxetil, ceftriaxone sodium, ceftazidime pentahydrate, cefotaxime sodium, cefoperazone sodium, cefazolin sodium, and cefixime in the bulk drug and in pharmaceutical formulations. TLC was performed on aluminium sheets precoated with silica gel G 60F₂₅₄ as stationary phase. The mobile phases chosen for development gave compact spots for all the drugs (R _F values 0.43–0.60). The separated compounds were visualized as orange spots by spraying with Dragendorff’s reagent. Linear regression analysis data for the calibration plots revealed good linear relationships between response and amounts of the drugs with correlation coefficients ranging from 0.9977 to 0.9998 and determination coefficients ranging from 0.9954 to 0.9996 over the concentration ranges 5–25 μg per spot for cefpodoxime proxetil, ceftriaxone sodium, and ceftazidime pentahydrate and 10–50 μg per spot for cefotaxime sodium, cefoperazone sodium, cefazolin sodium, and cefixime. The method was validated for precision, recovery, and robustness. Limits of detection and quantitation for the drugs ranged from 0.35 to 2.48 and from 1.07 to 7.50 μg per spot, respectively. The method was successfully applied to analysis of the drugs in their pharmaceutical dosage forms with good precision and accuracy. The method can also be used as a stability-indicating assay.     

Copper-catalyzed trifluoromethylation of terminal alkynes using Umemoto’s reagent

A copper-catalyzed method for trifluoromethylation of terminal alkynes with Umemoto’s reagent has been developed. The reaction is conducted at room temperature and shows good tolerance to a variety of functional groups.