An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

Parameterization of peptide 13C carbonyl chemical shielding anisotropy in molecular dynamics simulations.

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.     

Theoretical study of [F−; e+] and [CN−; e+]

Ab initio calculations are presented for the [F^?; e⁺] and [CN^?; e⁺] complexes. Positron affinities of 4.99 and 3.79 eV are obtained for F^? and CN^?, respectively. The excitation energies to the low-lying excited states of the positron complexes are also calculated.     

Effect of film thickness and supercooling on the performance of cholesteryl cinnamate liquid crystal capillary columns

Improved separations of the isomers of olefinic aliphatic insect pheromones were obtained on cholesteryl cinnamate glass capillary columns by operating in the supercooled temperature range of the liquid crystal. Capillary columns were prepared with varying film thickness of the stationary phase; choice of the correct film thickness ensured optimum retention for a wide range of compounds within the most effective temperature range of the liquid crystal. The deactivation procedures described made the liquid crystal columns suitable for separation of the geometric isomers of polar and nonpolar compounds.     

Complex formation constants for the aqueous copper(I)-acetonitrile system by a simple general method

A simple spectrophotometric method for the evaluation of formation constants for aqueous copper(I) has been developed, based on the kinetics of reduction of Co(III)(NH(3))(5)X complexes. The method has been applied to the aqueous copper(I)-acetonitrile system to determine the successive formation constants beta(1), beta(2), and beta(3) as 4.3 x 10(2) M(-)(1), 1.0 x 10(4) M(-)(2), and 2.0 x 10(4) M(-)(3), respectively, in 0.14 M NaClO(4)/HClO(4) at 21 +/- 1 degrees C.     

Acrylonitrile polymerization by Cy3PCuMe and (Bipy)2FeEt2

Cy(3)PCuMe (1) undergoes reversible ligand redistribution at low temperature in solution to form the tight ion pair [Cu(PCy(3))(2)][CuMe(2)] (3). The structure of 3 was assigned on the basis of (i) the stoichiometry of the 1 = 3 equilibrium, (ii) the observation of a triplet for the PCy(3) C1 (13)C NMR resonance due to virtual coupling to two (31)P nuclei, and (iii) reverse synthesis of 1 by combining separately generated Cu(PCy(3))(2)(+) and CuMe(2)(-) ions. Complex 1 and [Cu(PCy(3))(2)][PF(6)] (5) coordinate additional PCy(3) to form (Cy(3)P)(2)CuMe and [Cu(PCy(3))(3)][PF(6)], respectively, while 3 does not. Complex 1, free PCy(3), and (bipy)(2)FeEt(2) (2) each initiate the polymerization of acrylonitrile. In each case, the polyacrylonitrile contains branches that are characteristic of an anionic polymerization mechanism. The major initiator in acrylonitrile polymerization by 1 is PCy(3), which is liberated from 1. A transient iron hydride complex is proposed to initiate acrylonitrile polymerization by 2.     

The use of Hückel theory charge densities and localization energies for the prediction of kinetic and thermodynamic factors involved in an assumed model for the hydrohalogenation of 1,3-butadiene,isoprene and chloroprene

It is assumed that the first step in the hydrohalogenation of a diene under conditions such that an ionic mechanism is operative involves the formation of a linear carbonium ion via attachment of a proton to the 1-position and that the second step involves addition of the halide ion to either the 2- or 4-positions. If it is also assumed that hyperconjugation plays some non-negligible role in the carbonium ion intermediate, then it turns out that the use of Hückel theory charge densities and localization energies predict (1) that the 1,2-product is kinetically favored in the cases of butadiene and isoprene, (2) that the 1,4-product is kinetically favored in the case of chloroprene, and (3) that the 1,4-product is thermodynamically favored in all of the above systems. All of these predictions appear to be in agreement with available experimental results.

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Zusammenfassung Bei der Addition von Halogenwasserstoffen an die hier untersuchten Diene wird im Reaktions-ablauf ein lineares Carbeniumion angenommen. Das Proton wird in 1-Stellung addiert und in einem zweiten Schritt wird das Halogenion in 2- oder 4-Stellung angelagert. Weiter wird angenommen, daß Hyperkonjugation beim intermediären Carbeniumion eine Rolle spielt. Aus den mit der Hückel-theorie ermittelten Ladungsverteilungen und Lokalisierungsenergien läßt sich dann voraussagen, daß (1) das 1,2-Produkt bei Butadien und Isopren, (2) das 1,4-Produkt bei Chloropren kinetisch und (3) das 1,4-Produkt in allen Fällen thermodynamisch bevorzugt ist. Diese Voraussagen scheinen mit den bekannten experimentellen Resultaten übereinzustimmen.

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Résumé On admet que l'hydrohalogénation d'un diène dans des conditions où prévaut un mécanisme ionique comporte comme première étape la formation d'un ion carbonium linéaire par addition d'un proton à la position 1 et comme seconde étape l'addition de l'ion halogène à l'une des positions 2 ou 4. Si l'on admet par ailleurs que l'hyperconjuguaison joue un rôle non négligeable dans l'intermédiaire carbonium, l'emploi de la théorie de Hückel permet de prédire à l'aide des densités de charge et des énergies de localisation (1) que le produit 1,2 est favorable du point de vue cinétique dans les cas du butadiène et de l'isoprène (2) que le produit 1,4 est favorable du point de vue cinétique dans le cas du chloroprène et (3) que le produit 1,4 est favorable du point de vue thermodynamique dans tous ces systèmes. Toutes ces prédictions sont apparemment en accord avec les résultats expérimentaux disponibles.