On Gevrais classes of certain self-adjoint differential operators with degeneration

Classical spaces of ultradifferentiable functions on [–1,1] are compared with the Gevrais classes of a self-adjoint differential operator whose eigenfunctions are orthogonal Jacobi polynomials.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1622–1626, 1993.     

Towards an understanding of many-particle effects in hydrophobic association in methane solutions

This paper applies the multiscale coarse-graining method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] to analyze many-body effects in concentrated methane solutions. Pairwise decompositions of N-particle solute-solute potentials of mean force (PMFs), and the respective solvent cavity potentials, enthalpic, entropic, and heat capacity of hydrophobic association, are calculated directly from unconstrained molecular-dynamics simulations of methane solutions at different molar fractions, with the highest being 0.055. The many-body effects in hydrophobic hydration are further studied using N-methane PMFs, which are explicitly dependent on solvent coordinates.     

Particle-based multiscale coarse graining with density-dependent potentials: application to molecular crystals (hexahydro-1,3,5-trinitro-s-triazine)

We describe the development of isotropic particle-based coarse-grain models for crystalline hexahydro-1,3,5-trinitro-s-triazine (RDX). The coarse graining employs the recently proposed multiscale coarse-graining (MS-CG) method, which is a particle-based force-matching approach for deriving free-energy effective interaction potentials. Though one-site and four-site coarse-grain (CG) models were parameterized from atomistic simulations of non-ordered (molten and ambient temperature amorphous) systems, the focus of the paper is a detailed study of the one-site model with a brief recourse to the four-site model. To improve the ability of the one-site model to be applied to crystalline phases at various pressures, it was found necessary to include explicit dependence on a particle density, and a new theory of local density-dependent MS-CG potentials is subsequently presented. The density-dependency is implemented through interpolation of MS-CG force fields derived at a preselected set of reference densities. The computationally economical procedure for obtaining the reference force fields starting from the interaction at ambient density is also described. The one-site MS-CG model adequately describes the atomistic lattice structure of α-RDX at ambient and high pressures, elastic and vibrational properties, pressure-volume curve up to P = 10 GPa, and the melting temperature. In the molten state, the model reproduces the correct pair structure at different pressures as well as higher order correlations. The potential of the MS-CG model is further evaluated in simulations of shocked crystalline RDX.     

Using force-matching to reveal essential differences between density functionals in ab initio molecular dynamics simulations

The exchange-correlation (XC) functional and value of the electronic fictitious mass μ can be two major sources of systematic errors in ab initio Car-Parrinello Molecular Dynamics (CPMD) simulations, and have a significant impact on the structural and dynamic properties of condensed-phase systems. In this work, an attempt is made to identify the origin of differences in liquid water properties generated from CPMD simulations run with the BLYP and HCTH∕120 XC functionals and two different values of μ (representative of "small" and "large" limits) by analyzing the effective pairwise atom-atom interactions. The force-matching (FM) algorithm is used to map CPMD interactions into non-polarizable, empirical potentials defined by bonded interactions, pairwise short-ranged interactions in numerical form, and Coulombic interactions via atomic partial charges. The effective interaction models are derived for the BLYP XC functional with μ=340 a.u. and μ=1100 a.u. (BLYP-340 and BLYP-1100 simulations) and the HCTH∕120 XC functional with μ=340 a.u. (HCTH-340 simulation). The BLYP-340 simulation results in overstructured water with slow dynamics. In contrast, the BLYP-1100 and HCTH-340 simulations both produce radial distribution functions (indicative of structure) that are in reasonably good agreement with experiment. It is shown that the main difference between the BLYP-340 and HCTH-340 effective potentials arises in the short-ranged nonbonded interactions (in hydrogen bonding regions), while the difference between the BLYP-340 and BLYP-1100 interactions is mainly in the long-ranged electrostatic components. Collectively, these results demonstrate how the FM method can be used to further characterize various simulation ensembles (e.g., density-functional theory via CPMD). An analytical representation of each effective interaction water model, which is easy to implement, is presented.     

Electronic structure of Ti<Subscript>4</Subscript>Fe<Subscript>2</Subscript>O as determined from <Emphasis Type="Italic">ab initio</Emphasis> calculations and X-ray spectroscopy studies

The TiL _α, FeL _α and OK _α ultrasoft X-ray emission bands obtained in experiment reflect, respectively, the energy distribution of mainly the Ti3d, Fe3d and O2p electronic states in Ti₄Fe₂O compound, which is an efficient hydrogen absorber for energy cells. Full and partial densities of electronic states for all atoms constituting the indicated oxide were calculated by a modified method of associated plane waves (APW) using the WIEN2k software package. The APW calculation data for Ti₄Fe₂O compound as well as superposition of TiL _α, FeL _α and OK _α ultrasoft X-ray emission bands on a single energy scale indicate that O2p states in the oxide are localized mainly near the bottom of the valence band, the major contribution near the ceiling of the valence band belonging to Fe3d and Ti3d states. According to the APW calculation, the major contribution to the bottom of Ti₄Fe₂O conduction band is made by Fe3d* and Ti3d* states. The APW data for Ti₄Fe₂O are supported by the cluster calculation performed for this compound using a FEFF82 software package.     

Halochromism of thiophene-containing analogs of chalcones and their derivatives

The formation of hydroxy-, acyloxy-, chloro-, and tetrachlorophosphoroxycarbonium ions was established on the basis of the electronic absorption spectra of thiophene-containing analogs of chalcones and their derivatives in concentrated sulfuric acid, in dilute solutions of sulfuric acid in acetic and trichloroacetic anhydrides, and in acetonitrile benzene, dichloroethane, and nitromethane in the presence of phosphorous pentachloride.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1361–1364, October, 1971.     

Infrared spectra of chalcone homologs containing a pyrrole nucleus

The IR-spectra of 29 chalcone homologs containing a pyrrole nucleus were recorded in the solid phase, and in some cases in carbon tetrachloride solutions of varying concentrations. All the compounds studied formed intermolecular hydrogen bonds; and, when the carbonyl group was located close to the pyrrole ring (propenones-1), intramolecular hydrogen bonds were also formed. According to the distribution of substituents about the aliphatic double bond, all the ketones studied were trans-isomers; and, according to the relative distribution of carbonyl and vinyl groups, they had an s-cis-conformation. In the propenone-1 series there was a satisfactory correlation between v _C=O and Hammett's -parameters. The corresponding frequencies were investigated.     

Systematic coarse-graining of nanoparticle interactions in molecular dynamics simulation

A recently developed multiscale coarse-graining procedure [Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469] is extended to derive coarse-grained models for nanoparticles. The methodology is applied to C(60) and to carbonaceous nanoparticles produced in combustion environments. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom MD simulations. The CG models are shown to reproduce accurately the structural properties of the nanoparticle systems studied, while allowing for MD simulations of much larger self-assembled nanoparticle systems.     

Synthesis of chalcone analogs containing a pyrrole ring

Crotonaldehyde-type condensation in alkaline medium of 2-acetylpyrrole or pyrrole-2-aldehyde with aromatic or heterocyclic aldehydes and methyl ketones gives a number of hitherto undescribed pyrrole analogs of chalcone, and their 2, 4-dinitrophenylhydrazones are prepared.