Proof of the Fukui conjecture via resolution of singularities and related methods. II $$^{\star}$$

The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism. Dedicated to the memory of Prof. Kenichi Fukui (1918–1998).     

Synthesis,Redox Properties,and Electronic Spectra of Sterically Crowded Triarylphosphines Conjugated with Electron Acceptors

Abstract

Synthesis, redox properties, and electronic spectra of the sterically crowded triarylphosphines conjugated with π-electron systems, especially electron acceptors such as carbonyl group, are briefly reviewed. The sterically crowded triarylphosphines conjugated with various π-electron systems were synthesized from the common synthetic intermediate, (bromoaryl)phosphine, by conventional manner. The sterically crowded triarylphosphines conjugated with the electron acceptors exhibit visible absorption and fluorescence with large Stokes shift. Large solvent effect, redshift in polar solvent, and good correlation with the difference of the oxidation potential of the phosphine moiety and the reduction potential of the acceptor moiety suggest polar excited state resulting from HOMO-LUMO transition.     

Hydrogen bonding in macrocyclic receptor systems

Abstract

The interactions of macrocyclic polyethers with alkali and alkaline earth cations have been well studied and much about their chemistry is now well understood. Less well examined or comprehended are hydrogen bond interactions. A combination of ion selective electrode binding constant determination techniques and fast atom bombardment mass spectrometry are brought to bear on this problem. It is found that all-oxygen crown ethers and their derivatives exhibit quite different complexation behaviour with ammonium salts than do their various azacrown counterparts.     

Quantum Chemical Insight of the Dimetallic Sulfide Endohedral Fullerene Sc2S@C70: Does It Possess the Conventional D5h Cage?

Like C₆₀, C₇₀ is one of the most representative fullerenes in fullerene science. Even though there are 8149 C₇₀ isomers, only two of them have been found before: the conventional D_5h and an isolated pentagon rule (IPR)‐violating C_2v(7854). Through the use of quantum chemical methods, we report a new unconventional C₇₀ isomer, C₂(7892), which survives in the form of dimetallic sulfide endohedral fullerene Sc₂S@C₇₀. Compared with the IPR‐obeying C₇₀ and the C_2v(7854) fullerene with three pairs of pentagon adjacencies, the C₂(7892) cage violates the isolated pentagon rule and has two pairs of pentagon adjacencies. In Sc₂S@C₂(7892)‐C₇₀, two scandium atoms coordinate with two pentalene motifs, respectively, presenting two equivalent Sc? S bonds. The strong coordination interaction, along with the electron transfer from the Sc₂S cluster to the fullerene cage, results in the stabilization of the non‐IPR endohedral fullerene. The electronic structure of Sc₂S@C₇₀ can be formally described as [Sc₂S]⁴⁺@[C₇₀]^4?; however, a substantial overlap between the metallic orbitals and cage orbitals has also been found. Electrochemical properties and electronic absorption, infrared, and ¹³C NMR spectra of Sc₂S@C₇₀ have been calculated theoretically.     

High-Performance Liquid Chromatographic Characterization of the Role of Inorganic Pyrophosphatase in Regulating the Reaction of Uridine 5′-Triphosphate with Glucose 1-Monophosphate

Abstract

Inorganic pyrophosphatase (EC 3. 6. 1. 1) drived the reaction of uridine 5′-triphosphate with glucose 1-monophosphate in the direction of uridine 5′-diphosphoglucose formation.     

UV dose measurements of photosensitive dermatosis patients by polycrystalline GaN-based portable self-data-acquisition UV monitors

We have developed a UV monitor with polycrystalline (poly-) gallium nitride (GaN) UV sensors and evaluated its performance from the viewpoint of its effectiveness for use with photosensitive dermatosis patients. The poly-GaN UV sensor is sensitive to UV light from 280 to 410 nm even without optical filters. The UV monitor is a portable self-data-acquisition instrument with a minimum detection level (defined as average UV intensity over 290 to 400 nm) of 2 microW/cm2 and can store UV dose data for 128 days. It allows easy measurement of four orders of magnitude of ambient UV intensity and dose from indoor light to direct solar radiation in summer. Trial use of the UV monitor by five xeroderma pigmentosum patients started in June 2000 and was carried out for 1 year. It was demonstrated that the UV monitor was useful in improving their quality of life.     

Photoinduced chemical reactions on natural single crystals and synthesized crystallites of mercury(II) sulfide in aqueous solution containing naturally occurring amino acids

Photoirradiation at >300 nm of aqueous suspensions of several natural crystal specimens and synthesized crystallites of mercury(II) sulfide (HgS) induced deaminocyclization of optically active or racemic lysine into pipecolinic acid (PCA) under deaerated conditions. This is the first example, to the best of our knowledge, of photoinduced chemical reactions of natural biological compounds over natural minerals. It was found that the natural HgS crystals had activity higher than those of synthesized ones but lower than those of other sulfides of transition metals, e.g., CdS and ZnS, belonging to the same II-IV chalcogenides. In almost all of the photoreactions, decompostion of HgS occurred to liberate hydrogen sulfide (H(2)S) and Hg(2+), and the latter seemed to have undergone in-situ reductive deposition on HgS as Hg(0) after a certain induction period (24-70 h) during the photoirradiation, as indicated by the darkened color of the suspensions. The formation of PCA, presumably through combination of oxidation of lysine and reduction of an intermediate, cyclic Schiff base, could also be seen after a certain induction time of the Hg(0) formation. This was supported by the fact that the addition of small amount of Hg(2+) (0.5 wt % of HgS) increased the PCA yield by almost 2-fold. We also tried to elucidate certain aspects of the plausible stereochemical reactions in relation to the chiral crystal structure of HgS. Although, in some experiments, slight enantiomeric excess of the product PCA was observed, the excess was below or equal to the experimental error and no other supporting analytical data could not be obtained; we cannot conclude the enantiomeric photoproduction of PCA by the natural chiral HgS specimen.     

New Proof of the Fukui Conjecture by the Functional Asymptotic Linearity Theorem

The present article provides a new proof of the Fukui conjecture concerning the additivity problem of the zero-point vibrational energies of hydrocarbons. This conjecture played a prominent role in the initial development of the repeat space theory (RST), and continues to be of vital significance in the recent development of the theory of the generalized repeat space X _r (q,d). The new proof of the Fukui conjecture has been given here by establishing the functional version of the Asymptotic Linearity Theorem (ALT), the Functional ALT. This enhanced version of the ALT directly implies the validity of the Fukui conjecture; it easily unifies, in a broad perspective, a variety of additivity phenomena in physico-chemical network systems having many identical moieties, and efficiently solves some interpretational problems of the empirical additivity formulae from experimental chemistry. The proof of the functional version of the ALT is based on a new method transferable to the extended theoretical framework of the generalized repeat space X _r (q,d).