A Thermodynamic, 13C NMR,and 17O NMR Study of Isomeric 4,7-Dihydro-1,3-dioxepins and 4,5-Dihydro-1,3-dioxepins

The relative thermodynamic stabilities of 4,7-dihydro-1,3-dioxepin (4,6-dioxacycloheptene, 1a) and 4,5-dihydro-1,3-dioxepin (3,5-dioxacycloheptene, 1b), and of a number of their 2-substituted derivatives, have been determined by base-catalyzed chemical equilibration in DMSO solution. Without exception, the 4,5-dihydro isomer is the dominating species at thermodynamic equilibrium. The relative stability of the b form is promoted by the presence of a single alkyl group on C-2, whereas two alkyl groups on C-2 have an opposite effect. In general, the thermodynamic parameters H _m and _Sm , of isomerization vary unexpectedly with the pattern of substitution at C-2. These trends appear to be derived from significant substituent-induced conformational changes in the b isomer, as suggested by ¹³C and ¹⁷O NMR chemical shift data.     

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds: Unusual abundance of the [M + 1]+ ion and the effect of stereochemistry

Electron impact mass spectra of 2-(2-pyridyl)methylene-1,3-dicarbonyl compounds and related heteroaryl species have been investigated. In 3-(2-pyridyl)methylene-2,4-pentanedione, its 6′-methyl and 6′-methoxycarbonyl derivatives and in E- and Z-ethyl 3-oxo-2-(2-pyridyl)methylenebutanoates the base peak arises from the loss of methyl radical from the molecular ion to produce a 3-oxo-3H-indolizinium ion. A marked difference is observed in the behaviour of the geometric isomers of the keto esters. The diketones and E-keto ester carrying a 2-pyridyl substituent and ketone functionality on the same side of the carbon-carbon double bond exhibit an unusually high [M + 1]⁺/[M]^+˙ ratio (about 2.5) under normal ionization conditions (pressure 10–100 μPa). This abnormality is a function of pressure only and independent of temperature. In the case of the Z-keto ester, the corresponding malonate, 3- and 4-(2-pyridyl)methylene-2,4-pentanediones, and 2-furyl, 2-thienyl and phenyl diketone analogues, the ratio does not differ much from that due to the natural isotope abundance. Results for 1,1,1,5,5,5-hexadeuterio-2-(2-pyridyl)-methylene-2,4-pentanedione (strong M + 2 peak) suggest one mass unit transfer as an intermolecular proton shift from a methyl group to give a 3-hydroxy-3-methyl-3H-indolizinium ion. This real mass spectrometric phenomenon is a unique example of low pressure self-chemical ionization.     

Relative Stabilities and Molecular Structures of Isomeric Dihalobenzenes. A DFT Study

The molecular structures, total energies, and other computational data of benzene, and its monoand dihalogenated derivatives (halogen = F, Cl, Br) have been studied by DFT calculations. The main aim of the study was to estimate the relative stabilities (energies) of the ortho, meta, and para isomers of the six series of dihalobenzenes investigated. The computational data show that the ortho isomers always have the highest, and the meta isomers usually, but not always, the lowest total energies. Thus, 1,2-difluorobenzene is ca. 16.6 kJ mol^–1, and 1,4-difluorobenzene 2.5 kJ mol^–1 less stable than 1,3-difluorobenzene. Among the other isomeric dihalobenzenes, the differences in stability are less pronounced. For the dibromo-, dichloro-, and bromochlorobenzenes, the para compounds are calculated to be slightly (0.2–0.4 kJ mol^–1) more stable than their meta isomers. In addition to the thermochemical aspect of the study, the computational molecular structures of the halobenzenes are compared with available experimental data and discussed in terms of the substituent-induced deformation of the ideal geometry of the benzene ring. The computational electric dipole moments, especially for the fluorine-containing compounds, compare favorably with the respective experimental (gas-phase) values.     

Linear viscoelastic models: Part I. Relaxation modulus and melt calibration

Constitutive models for the linear viscoelasticity of polymers are presented for the relation between the relaxation modulus and the molecular weight distribution (MWD). We also compute the MWD from a simulated relaxation modulus curve by first obtaining the rheologically effective distribution (RED) as a function of time, and converting this into the MWD by melt calibration; that is, the relation between timescale and the molecular weight. This procedure has similarities with the widely used universal calibration with solved polymers. The main principles of our technique are applied here to familiar relaxation modulus data, for which we present two models: (1) an analytical model derived from control theory, which is known capable of modelling partially observed system and (2) a practical characteristic model for obtaining usable results. No relaxation time or spectrum procedures are used to model the process of linear viscoelastic relaxation. The use of relative calculations and melt calibration dispenses with the need to know the real chain structures such as branching and entangled chain dynamics, and the model remains useful for future investigations of polymer chain structures and dynamics, such as using tube theory.     

Relative stabilities and molecular structures of the isomeric enol ethers and carboxylic esters derived from α‐acetyl‐γ‐butyrolactone and α‐acetyl‐δ‐valerolactone

Recently recorded ¹⁷O NMR spectra of compounds studied in a previous work (Taskinen E. Acta Chem. Scand. 1985; B39 : 489–494) dealing with the thermodynamics of isomerization of the enol ethers of α‐acetyl‐γ‐butyrolactone reveal an error in compound identification, caused by an unexpected isomerization reaction during the synthetic procedure. Thus, acid‐catalyzed treatment of the lactone with HC(OR)₃ in the respective alcohol ROH is shown to lead initially to the desired enol ethers which, however, are gradually isomerized to a mixture of the enol ethers and an ester of 2‐methyl‐4,5‐dihydrofuran‐3‐carboxylic acid. As a result, only one of the two isomeric compounds detected in the previous equilibration study was the expected enol ether (the thermodynamically more stable E isomer) of α‐acetyl‐γ‐butyrolactone, while the other, dominating species was the respective carboxylic ester. In the present work, the evidence provided by the ¹⁷O NMR spectra is presented, and the relative stabilities of the isomeric compounds are discussed on the basis of computational enthalpy data. The treatment is also extended to the respective isomeric compounds derived from α‐acetyl‐δ‐valerolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Transposition invariant string matching

Given strings A=a₁a₂…a_m and B=b₁b₂…b_n over an alphabet , where is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is , where A+t=(a₁+t)(a₂+t)…(a_m+t). We study the problem of computing the transposition invariant distance for various distance (and similarity) functions d, including Hamming distance, longest common subsequence (LCS), Levenshtein distance, and their versions where the exact matching condition is replaced by an approximate one. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance, and for some we achieve these upper bounds. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems, and its connection with multidimensional range-minimum search. As a byproduct, we give improved sparse dynamic programming algorithms to compute LCS and Levenshtein distance.     

Giant optical activity in quasi-two-dimensional planar nanostructures

We examine the spectral dependence in the visible frequency range of the polarization rotation of two-dimensional gratings consisting of chiral gold nanostructures with subwavelength features. The gratings, which do not diffract, are shown to exhibit giant specific rotation (approximately 10(4) degrees/mm) of polarization in direct transmission at normal incidence. The rotation is the same for light incident on the front and back sides of the sample. Such reciprocity indicates three dimensionality of the structure arising from the asymmetry of light-plasmon coupling at the air-metal and substrate-metal interfaces. The structures thus enable polarization control with quasi-two-dimensional planar objects. However, in contradiction with recently suggested interpretation of experiments on larger scale but otherwise similar structures, the observed polarization phenomena violate neither reciprocity nor time-reversal symmetry.     

An Isometric Approach to Generalized Stochastic Integrals

The possibility to extend the classical Ito's construction of stochastic integrals is studied. This construction can be applied to fractional Brownian motions with Hurst index H(0, 1/2). A change of variables formula for fractional Brownian motions in terms of the stochastic integrals is given.