Variational calculations for helium-like ions using generalized Kinoshita-type expansions

 Variational calculations are reported for the ground states of the helium atom and its isoelectronic ions H⁻, Li⁺, …, Ne⁸⁺. The calculations use generalized Kinoshita expansions with freely optimized, noninteger powers of the Hylleraas coordinates s and u. One hundred-term expansions of this type lead to better energies than any other expansions in the literature with comparable numbers of terms. Received: 4 September 2002 / Accepted: 14 October 2002 / Published online: 21 January 2003 Correspondence to: T. Koga e-mail: koga@mmm.muroran−it.ac.jp Acknowledgements. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. The final 100-term computations with real powers were performed at the Advanced Computational Research Laboratory of the University of New Brunswick.     

Polarizabilities and hyperpolarizabilities for the atoms Al, Si, P, S, Cl, and Ar: Coupled cluster calculations

Accurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the Al, Si, P, S, Cl, and Ar atoms. The finite-field computations use energies obtained with various ab initio methods including Moller-Plesset perturbation theory and the coupled cluster approach. Excellent agreement with experiment is found for argon. The experimental alpha for Al is likely to be in error. Only limited comparisons are possible for the other atoms because hyperpolarizabilities have not been reported previously for most of these atoms. Our recommended values of the mean dipole polarizability (in the order Al-Ar) are alpha/e(2)a(0) (2)E(h) (-1)=57.74, 37.17, 24.93, 19.37, 14.57, and 11.085 with an error estimate of +/-0.5%. The recommended values of the mean second dipole hyperpolarizability (in the order Al-Ar) are gamma/e(4)a(0) (4)E(h) (-3)=2.02 x 10(5), 4.31 x 10(4), 1.14 x 10(4), 6.51 x 10(3), 2.73 x 10(3), and 1.18 x 10(3) with an error estimate of +/-2%. Our recommended polarizability anisotropy values are Deltaalpha/e(2)a(0) (2)E(h) (-1)=-25.60, 8.41, -3.63, and 1.71 for Al, Si, S, and Cl respectively, with an error estimate of +/-1%. The recommended hyperpolarizability anisotropies are Deltagamma/e(4)a(0) (4)E(h) (-3)=-3.88 x 10(5), 4.16 x 10(4), -7.00 x 10(3), and 1.65 x 10(3) for Al, Si, S, and Cl, respectively, with an error estimate of +/-4%.     

Thermal properties of wholly aromatic polyamides

Various wholly aromatic polyamides based on m-and p-phenylene diamines and isophthaloyl and terephthaloyl chloride have been synthesized and their thermal properties and oxygen index values have been studied. The effect of different substituents on the aromatic ring of the diamine have been explored by comparing their differential thermal analysis (DTA) and thermogravimetric analysis (TGA) behavior, their relative char yields at 700°C, and their oxygen indices. The ? Cl, ? NO₂, and ? OH substituted polyamides have been found to produce the highest char yields. The high char yields are probably associated with crosslinking occurring at high temperatures. Attempts at correlating char yield with oxygen index indicated enhancement for the chlorosubstituted aramids.     

Basis set quality. II. Information theoretic appraisal of various s- orbitals

The expectation values 〈r^k〉 (?2 ? k ? 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree–Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21 , 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.     

Sampled-Data Nash Equilibria in Differential Games with Impulse Controls

Journal of Optimization Theory and Applications - We study a class of deterministic two-player nonzero-sum differential games where one player uses piecewise-continuous controls to affect the...     

Nonlinear pulse propagation in a single- and a few-cycle regimes with Raman response

The propagation equation for a single- and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single- and a 4-cycle pulse, at 0.8 μm wavelength, were studied numerically in one spatial dimension. It was shown that Raman term does influence the propagation characteristics of a single-as well as a few-cycle pulses by counteracting the self-steepening effect.     

11/9-mixed helices in the alpha/beta-peptides derived from alternating alpha- and beta-amino acids with proteinogenic side chains

alpha/beta-Hybrid peptides are prepared from amino acids with proteinogenic side chains on the basis of the concept of "alternating chirality", involving D-Phe and a beta3-hVal. Through the extensive NMR, CD, and MD studies, robust left-handed 11/9-mixed helices were identified in these peptides in CDCl3 solutions, wherein the 11/9-mixed helix was observed even in a small peptide with three residues.     

Synthesis and characterization of water-soluble and photostable L-DOPA dendrimers

A small drug molecule, L-DOPA, was converted into well-defined dendritic macromolecules. Their monodisperse nature was shown by NMR, MALDI-TOF-MS, and PAGE. A third-generation L-Dopa dendrimer contained 30 L-Dopa residues, which made up its core, branches, and periphery. Individual L-Dopa moieties in the dendrimer were connected to one another via hydrolyzable diester linkages. These Dopa dendrimers showed a 20-fold increase in aqueous solubility and enhanced photostability in solutions over L-Dopa under identical conditions.     

Nanocomposites based on vapor-grown carbon nanofibers and an epoxy: Functionalization, preparation and characterization

Vapor-grown carbon nanofibers (VGCNF) were functionalized with amine-containing pendants via a Friedel-Crafts acylation reaction with 4-(3-aminophenoxy)benzoic acid. The resulting H₂N-VGCNF was treated with epichlorohydrin, followed by sodium hydroxide solution to afford N,N-diglycidyl-modified VGCNF that is designated as epoxy-VGCNF. Subsequently, epoxy-VGCNF was dispersed in an epoxy resin (Epon 862) with the aid of acetone and sonication. After acetone had been removed under vacuum from the mixture, curing agent “W” was added to epoxy-VGCNF/Epon 862 mixture, which was then poured into molds and cured at 250 °F (121 °C) for 2 h and 350 °F (177 °C) for 2 h to form a series of epoxy/fVGCNF samples; fVGCNF designated for “functionalized VGCNF” was used to denote our belief that all epoxy functions have reacted in the resulting nanocomposites. The VGCNF content was increased from 0.10 to 10.0 wt%. For comparison purposes, the pristine VGCNF or pVGCNF (0.1-5.0 wt%) was also used in the in situ polymerization of Epon 862 and curing agent “W” to afford another series of epoxy/pVGCNF samples. The epoxy-VGCNF showed a better dispersion in the epoxy resin than pVGCNF according to SEM results. Both the tensile moduli and strengths of epoxy/fVGCNF nanocomposites are higher than those of epoxy/pVGCNF. The additive effect of VGCNF on glass-transition (T_g) was discussed in terms of thermal analysis results. The thermal stability of the nanocomposites was investigated by thermogravimetric analysis (TGA).