Relative thermodynamic stabilities of the isomeric dihydrofurans and isomeric dihydropyrans. An experimental and DFT study

The relative thermodynamic stabilities of 2,5-dihydrofuran (1) and 2,3-dihydrofuran (2), and of 3,4-dihydro-6H-pyran (3) and 3,4-dihydro-2H-pyran (4), were determined at several temperatures by base-catalyzed equilibration in DMSO solution. For 1 → 2, = –15.4±0.1 kJ mol⁻¹, =–12.6±0.5 kJ mol⁻¹, and =9.5±1.3 J K⁻¹ mol⁻¹ at 298.15 K. The second-law reaction enthalpy agrees with literature data based on calorimetric enthalpies of hydrogenation of the isomeric forms in hexane. For 3 → 4, =–19.3±0.2 kJ mol⁻¹, = –18.9±1.1 kJ mol⁻¹ and =1.1±3.0 J K⁻¹ mol⁻¹ at 298.15 K: the experimental reaction enthalpy is in marked disagreement with literature data based on estimation. On the other hand, both of the experimental reaction enthalpies of the present study are in good agreement with DFT calculations using the B3LYP functional and 6-311+G(2d,p) basis set.     

Quantum Chemical Study of the Preferred Conformations,Molecular Geometries,and Relative Thermodynamic Stabilities of 2-Substituted 4-Methylene-1,3-Dioxolanes and 4-Methyl-1,3-Dioxoles

The preferred conformations, molecular geometries, and relative stabilities of carbon–carbon double-bond exo–endo isomeric 2-substituted 4-methylene-1,3-dioxolanes (a) and 4-methyl-1,3-dioxoles (b) have been studied by DFT calculations at the B3LYP/6-31G* level of theory. The main interest of this work was devoted to the contribution of alkoxy substituents on the relative thermodynamic stabilities of these isomeric unsaturated acetals. Comparison of the computational data with previous experimental findings shows both the enthalpies and entropies of the a b isomerization to be accurately predictable by the DFT calculations. Most importantly, the good agreement between experiment and theory proved also to be applicable to the previously observed unexpectedly large effect of 2-alkoxy substitution on the isomer equilibria.     

A theory for the construction of the irreducible representations of finite groups. II

The restriction on a method for computing irreducible representations of finite groups, requiring that in the irreducible representation to be constructed, at least one group element has at least one nondegenerate eigenvalue, is removed. The method is thus shown to be applicable to an arbitrary finite group and constitutes a practical algorithm for handling groups of order less than 400.     

Relative Stabilities and Molecular Structures of the Geometrical Isomers of α,α′-Dioxasubstituted Cycloalkylidenecycloalkanes. A DFT Study

The relative stabilities and molecular structures of the geometrical isomers of seven ,-dioxa derivatives of cycloalkylidenecycloalkanes with 3to 6-membered rings have been studied by DFT calculations at the B3LYP/6-31G* level of theory. In each case, the E form was calculated to have the lower total energy. The relative energy of the Z isomer proved to increase regularly with increasing sizes of the two heterocyclic rings, ranging from 1.1 to 13.8 kJ mol^–1 on going from the 3,3to the 6,6-membered rings. Intermediate values of the relative energy were calculated for the Z forms of compounds containing two dissimilar rings. The relative energy of the Z isomer was found to be proportional to d ^–9.3, where d = the distance separating the two O atoms of the Z compound. The molecular structures, electric dipole moments, and atomic charges on the O atoms are also discussed.     

Electronic Structure and Size of TiO2 Nanoparticles of Controlled Size Prepared by Aerosol Methods

Summary.  A complete characterization of nanostructures has to deal both with electronic structure and dimensions. Here we present the characterization of TiO₂ nanoparticles of controlled size prepared by aerosol methods. The electronic structure of these nanoparticles was probed by X-ray absorption spectroscopy (XAS), the particle size by atomic force microscopy (AFM). XAS spectra show that the particles crystallize in the anatase phase upon heating at 500°C, whereas further annealing at 700°C give crystallites of 70% anatase and 30% rutile phases. Raising the temperature to 900°C results in a complete transformation of the particles to rutile. AFM images reveal that the mean size of the anatase particles formed upon heating at 500°C is 30 nm, whereas for the rutile particles formed upon annealing at 900°C 90 nm were found. The results obtained by these techniques agree with XRD data. Received October 5, 2001. Accepted (revised) December 6, 2001     

An analysis of the effect of rounding errors on the flow of control in numerical processes

Rounding errors may change the flow of control in numerical computing processes by leading to changes in some branching decisions of the process. In this paper some general topological and measure theoretical results associated with this effect of rounding errors are derived. The approach is based on a model of numerical computation related to program schemes. Each computing process specified by the model computes a partial functionR ⁿ R ^m using rational operations and simple tests on real numbers. The topological structure of input point sets inR ⁿ on which the computation follows the same execution path is studied. We also investigate input points, called sensitive, on which rounding errors may change the execution path followed. Conditions concerning computing processes are given which guarantee that the Lebesgue measure of sensitive points approaches zero (i.e. the probability of a branching error gets arbitrarily small) as the precision of the arithmetic increases. Most numerical processes used in practice are easily seen to satisfy these conditions.     

Indolizine derivatives. VII. indolizines via cyclizations of 2-(2-Pyridyl)methylene-1,3-diketones and −1,3-Keto esters

The reaction of 3-(2-pyridyl)methylene-2,4-pentanedione with acetic anhydride gives at 60° 1-(1-acetoxy-3-methyl-2-indolizinyl)ethanone ( 3a ) or, in the presence of 2,4-pentanedione, 3-(2-acetyl-3-methyl-7-indolizinyI)-2,4-pentanedione ( 7a ) in good yield. In refluxing acetic anhydride, 1-(3-methyl-2-indolizinyl)ethanone ( 4a ) is the main product. In refluxing dimethyl sulfoxide the cycloaddition product, 3-[2-acetyl-3-(2-pyridyl)-l-indolizinyl)]-2,4-pentanedione ( 6 ), is obtained. Ethyl 2-(2-pyridyl)methylene-3-oxobutanoate and ethyl 2-(2-pyridyl)methylene-3-oxo-3-phenylpropanoate behave analogously. The stereochemistry of the keto esters has a marked influence on the course of cyclization. The mechanisms are discussed.     

Electron‐Beam Manipulation of Silicon Impurities in Single‐Walled Carbon Nanotubes

The recent discovery that impurity atoms in crystals can be manipulated with focused electron irradiation has opened novel perspectives for top‐down atomic engineering. These achievements have been enabled by advances not only in electron optics and microscope stability but also in the preparation of suitable materials with impurity elements incorporated via ion and electron‐beam irradiation or chemical means. Here it is shown that silicon heteroatoms introduced via plasma irradiation into the lattice of single‐walled carbon nanotubes (SWCNTs) can be manipulated using a focused 55–60 keV electron probe aimed at neighboring carbon sites. Moving the silicon atom mainly along the longitudinal axis of large 2.7 nm diameter tubes, more than 90 controlled lattice jumps are recorded and the relevant displacement cross sections are estimated. Molecular dynamics simulations show that even in 2 nm diameter SWCNTs, the threshold energies for out‐of‐plane dynamics are different than in graphene, and depend on the orientation of the silicon‐carbon bond with respect to the electron beam as well as the local bonding of the displaced carbon atom and its neighbors. Atomic‐level engineering of SWCNTs where the electron wave functions are more strictly confined than in 2D materials may enable the fabrication of tunable electronic resonators and other devices.     

Replicated Polymer Light Guide Interconnector with Depth Modified Surface Relief Grating Couplers

Planar light guide plate with one in-coupling and N out-coupling surface relief gratings is designed to perform as optical backplane broadcasting system for board-to-board connections. The performance of the element is analyzed theoretically with rigorous electromagnetic theory and results are confirmed experimentally. In addition, optical backplane elements have been replicated using conventional injection molding and UV-replication techniques.