Generalized exponential functions applied to atomic calculations

The use of a generalized exponential function r ^v?1 exp(?ζr ^μ ) as a radial basis function in atomic calculations is studied with our special interest in the variationally optimum value of the parameter μ, since special cases of μ = 1 and μ = 2 correspond respectively to the radial parts of commonly-used Slater-type and Gaussian-type functions. Roothaan-Hartree-Fock calculations are performed for ground-state neutral atoms with atomic number Z = 2–54, singly-charged cations with Z = 3–55, and anions with Z = 1–53 within the single-zeta (or minimal basis) framework. For all the species examined, the optimtum μ values are found to be smaller than unity and increase towards unity as the atomic number increases. The present results support the use of Slater-type functions when μ is restricted to be an integer, but suggest from the variational point of view that even the exponential decay of Slater-type functions is too “strong” within the single-zeta approximation.     

Study of the stress state of isotropic thick-walled shells of nonuniform structure

Scientific Research Institute of Applied Mathematics, Tbilisi University. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 37–44, May, 1991.     

Synthesis of dimethylditritiogermane Me<Subscript>2</Subscript>GeT<Subscript>2</Subscript>

A microsynthetic procedure for preparing tritium-labeled alkyl-substituted germanes is developed. The resulting dimethylditritiogermane can be used as a source of dimethylgermylium ions. The synthesis was performed by the reduction of dibromodimethylgermane with lithium tritide in presence of AlBr₃.     

Separation of piano keyboard vibrations into tonal and broadband components

A new method is presented for splitting musical notes into tonal and broadband components by removing the harmonic peaks from the spectra. This method was used to analyse the key vibrations of eight pianos (four grand and four upright). The broadband component of vibrations was found to be more intense in the upright pianos than in the grand pianos, while no such difference was found in the tonal component. As grands are considered to be superior to uprights, this suggests that it may be possible to improve upright pianos by reducing the strength of the broadband component of vibrations.     

Fluorescence anisotropy of acridinedione dyes in glycerol: Prolate model of ellipsoid

Time-dependent reorientations of resorcinol-based acridinidione (ADR) dyes in glycerol were studied using steady-state and time-resolved fluorescence studies. The difference between fluorescence anisotropy decays recorded at 460 nm when exciting at 250 nm and those obtained when exciting at 394 nm are reported. When exciting at 394 nm, the fluorescence anisotropy decay is bi-exponential, while on exciting at 250 nm a mono-exponential fluorescence anisotropy decay is observed. We interpret this in terms of different directions of the absorption dipole at 394 and 250 nm with the emission dipole respectively, which is experimentally validated and further analysed as a prolate model of ellipsoid.     

A density functional theory computational study of the role of ligand on the stability of CuI and CuII species associated with ATRP and SET‐LRP

Atom transfer radical polymerization (ATRP) and single electron‐transfer living radical polymerization (SET‐LRP) both utilize copper complexes of various oxidation states with N‐ligands to perform their respective activation and deactivation steps. Herein, we utilize DFT (B3YLP) methods to determine the preferred ligand‐binding geometries for Cu/N‐ligand complexes related to ATRP and SET‐LRP. We find that those ligands capable of achieving tetrahedral complexes with Cu^I and trigonal bipyramidal with axial halide complexes with [Cu^IIX]⁺ have higher energies of stabilization. We were able to correlate calculated preferential stabilization of [Cu^IIX]⁺ with those ligands that perform best in SET‐LRP. A crude calculation of energy of disproportionation revealed that the same preferential binding of [Cu^IIX]⁺ results in increased propensity for disproportionation. Finally, by examining the relative energies of the basic steps of ATRP and SET‐LRP, we were able to rationalize the transition from the ATRP mechanism to the SET‐LRP mechanism as we transition from typical nonpolar ATRP solvents to polar SET‐LRP solvents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4950–4964, 2007     

Phase transitions of liquid crystalline cyanoethyl cellulose solutions under static conditions and in shear field

Phase transitions in the systems cyanoethyl cellulose-DMF, cyanoethyl cellulose-DMAA, and cyanoethyl cellulose-(trifluoroacetic acid + methylene chloride) were studied by means of the cloud-point and polarization microscopy techniques, as well as with a photoelectric polarization unit and a modified plasticorder. It was shown that the LC phase appears at higher concentrations and lower temperatures as the polarity of solvent molecules increases. The shear deformation of cyanoethyl cellulose solutions in DMF and DMAA results in the expansion of the temperature-concentration region of existence of the LC phase. The effect of shear field on phase transitions in cyanoethyl cellulose solutions is nonmonotonic in character.