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).     

Stepwise hydration and multibody deprotonation with steep negative temperature dependence in the benzene.+ -water system

We studied the stepwise hydration and solvent-mediated deprotonation of the benzene*+ cation (Bz*+) and found several unusual features. The solvent binding energies DeltaH on-1,n for the reactions Bz*+(H2O)n-1 + H2O --> Bz*+(H2O)n are nearly constant at 9 +/- 1 kcal mol-1 for n = 1 to 8. We observed a remarkable sudden decrease in the entropy of association accompanying the formation of Bz*+(H2O)7 and Bz*+(H2O)8, indicating strong orientational restraint in the hydration shells of these clusters consistent with the formation of cagelike structures. We observed the size-dependent deprotonation of Bz*+ in a cooperative multibody process, where n H2O molecules (n >/= 4) can remove a proton from Bz*+ to form protonated water clusters. We measured, for the first time, the temperature dependence of such a process and found a negative temperature coefficient of a magnitude unprecedented in any chemical reaction, of the form k = AT-67+/- 4, or in an Arrhenius form having an activation energy of -34 +/- 1 kcal mol-1. The temperature effect may be explained by Bz*+ and four H2O molecules needing to be assembled from gas-phase components to form the reactive species. Such large temperature effects may be therefore general in solvent cluster-mediated reactions.     

SCF-π-electron calculations using orthogonalised atomic orbitals

Modifications of the SCF-LCAO-π-MO method analysed in the previous paper are described in which provision is made for the incorporation of Variable Bond Order and Variable Electronegativity procedures. A comparison is made with the results of other π-electron calculations and values are reported for twenty hydrocarbon systems.     

Clays as selective catalysts in organic synthesis

Suitably modified smectite clays can be very selective catalysts for a wide range of organic reactions. While it has long been known that such materials can act as Bronsted and Lewis acids, it has been shown recently that they are also effective Diels-Alder catalysts. A selection of illustrative reactions is given which emphasises their wide range of use, their selectivity, and the ease of work-up after reaction. In each case, mechanistic information is presented, e.g., on the site of reaction (whether interlayer or surface), rate determining steps, etc. The regiochemical consequences of the restricted reaction space are stressed.Based on material presented at the Fourth International Symposium on Inclusion Phenomena and the Third International Symposium on Cyclodextrins, Lancaster, U.K., 20–25 July 1986.     

Aggregation of iron colloids in estuaries: a heterogeneous kinetics study using continuous mixing of river and sea waters

The kinetics of iron colloid aggregation in estuaries have been simulated with a model estuary in which seawater is continuously pumped into a reservoir initially containing river water. Profiles of colloidal Fe concentration versus salinity produced in this apparatus closely resembled field data for actual estuaries. Synthetic Fe colloids prepared by peptising Fe(OH)₃ with humic acid and phosphate showed very similar kinetic behaviour. Aggregation rate was found to be almost independent of velocity shear rate, implying that most aggregations are induced by brownian interparticle collisions. A heterogeneous kinetic model is proposed to explain the kinetic behaviour of Fe colloids during seawater-induced aggregation. This model describes kinetic behaviour in terms of a log-normal distribution of rate constants characterised by a mean value k and a standard deviation γ. Experiments showed that k is linearly related to the rate constant for salinity increase during mixing. This coupling of salinity changes and aggregation rate leads to Fe-salinity profiles that are nearly independent of the rate of salinity change, but which are dependent on γ.     

Characterization of the oxidation products of styryl-substituted terthiophenes and sexithiophenes using electronic absorption spectroscopy and time-dependent DFT

The electronic absorption spectra of a series of alkoxy-styryl substituted terthiophenes, their corresponding sexithiophenes, and the oxidation products of both have been measured. The terthiophenes studied sigma-dimerize to sexithiophenes during the oxidation process and there is clear evidence of sexithiophene radical cations, dications, and pi-dimers in the electronic absorption spectra. The oxidation of concentrated solutions produces predominantly pi-dimer bands, as expected. The absorption spectrum of the styryl-functionalized sexithiophene dication without alkoxy substitution closely resembles that of unsubstituted sexithiophene, while alkoxy substitution induces changes in the wavelength of the dication band maximum and the overall band shape. Time-dependent density functional theory (TDDFT) calculations have shown that styryl-based molecular orbitals are important in the transitions of the neutral molecules as well as the charged species, the dication in particular. Kinetics analyses confirm the stabilization effect induced by the alkoxy substituents. The presence of a reversible pi-dimer equilibrium was verified by cyclic voltammetry. It is clear from the experimental observations and the theoretical calculations that both the styryl and alkoxy groups are influencing the electronic properties of this class of molecules.     

<Emphasis Type="Italic">Brønsted</Emphasis> Acids in Ionic Liquids: Fundamentals,Organic Reactions,and Comparisons

Summary. A background for studying acids in various solvents is developed, emphasizing the importance of knowing to what extent a solvent conducts electricity and is therefore ionized, the dissociation equilibria of common molecular solvents and the acidic and basic species generated by solvent leveling. Acidity measurements in the atypical solvent water are discussed and the common method of expressing acidity in other systems – by Hammett values – is introduced. Representative examples of reactions involving Br?nsted acids in ionic liquids are presented and attention paid to the questions of speciation and acidity values. It is found that the gas phase proton affinity of a base is often a better guide to the acidity of its conjugate acid in an ionic liquid than is the dissociation constant of the said acid in water.     

Effects of petroleum resins on asphaltene aggregation and water-in-oil emulsion formation

Asphaltenes from four crude oils were fractionated by precipitation in mixtures of heptane and toluene. Solubility profiles generated in the presence of resins (1:1 mass ratio) indicated the onset of asphaltene precipitation occurred at lower toluene volume fractions (0.1–0.2) than without resins. Small-angle neutron scattering (SANS) was performed on solutions of asphaltene fractions in mixtures of heptane and toluene with added resins to determine aggregate sizes. Water-in-oil emulsions of asphaltene–resin solutions were prepared and separated by a centrifuge method to determine the vol.% water resolved. In general, the addition of resins to asphaltenes reduced the aggregate size by disrupting the π–π and polar bonding interactions between asphaltene monomers. Interaction of resins with asphaltenic aggregates rendered the aggregates less interfacially active and thus reduced emulsion stability. The smallest aggregate sizes observed and the weakest emulsion stability at high resin to asphaltene (R/A) ratios presumably corresponded to asphaltenic monomers or small oligomers strongly interacting with resin molecules. It was often observed that, in the absence of resins, the more polar or higher molecular weight asphaltenes were insoluble in solutions of heptane and toluene. The addition of resins dissolved these insolubles and aggregate size by SANS increased until the solubility limit was reached. This corresponded approximately to the point of maximum emulsion stability. Asphaltene chemistry plays a vital role in dictating emulsion stability. The most polar species typically required significantly higher resin concentrations to disrupt asphaltene interactions and completely destabilize emulsions. Aggregation and film formation are likely driven by polar heteroatom interactions, such as hydrogen bonding, which allow asphaltenes to absorb, consolidate, and form cohesive films at the oil–water interface.     

A short,three-component total synthesis of 12-hydroxyeicosa-5,8,14(Z), 10(E)-tetraenoic acid (12-HETE) via the corresponding ketone

A highly effective synthesis of (±)-12-HETE (1) from the components 2, 3 and 6 is described which employs a new class of cuprate reagents.     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.