Vibrational Properties of LiGaO2 (II). Theoretical Model Considerations

On the basis of the correlation method and of a simplified version of the extended Keating model with bond-bending forces neglected sphalerite- and chalcopyrite-like modes can be identified in the lattice vibration spectrum of LiGaO₂. In agreement with recently published results for LiInTe₂ it is found that the Li O bond is considerably weaker than the Ga O bond.     

Neutron powder diffraction of metal-organic frameworks for hydrogen storage

We review recent structural studies that we have undertaken aimed at elucidating the fundamental properties of metal-organic framework materials and their interactions with hydrogen. We have shown that exposing coordinatively unsaturated metal centers can greatly enhance the hydrogen binding energy and that they result in a significant increase of the surface packing density of adsorbed hydrogen molecules on materials’ surface. We will review some of the structural aspects of these materials, especially the adsorbed hydrogen molecule surface packing density in one type of metal-organic framework, MOF-74, which can be packed even denser than that in solid hydrogen.      

Synthesis of Polymers Containing Potassium Acyltrifluoroborates (KATs) and Post-polymerization Ligation and Conjugation

We report the synthesis of monomers for atom-transfer radical polymerization (ATRP) and a reversible addition-fragmentation chain transfer (RAFT) agent bearing trifluoroborate iminiums (TIMs), which are quantitatively converted into potassium acyltrifluoroborates (KATs) after polymerization. The resulting KAT-containing polymers are suitable for rapid amide-forming ligations for both post-polymerization modification and polymer conjugation. The polymer conjugation occurs rapidly, even under dilute (micromolar) aqueous conditions at ambient temperatures, thereby enabling the synthesis of a variety of linear and star-shaped block copolymers. In addition, we applied post-polymerization modification to the covalent linking of a photocaged cyclic antibiotic (gramicidin S) to the side chains of the KAT-containing copolymer. Cellular assays revealed that the polymer–antibiotic conjugate is biocompatible and provides efficient light-controlled release of the antibiotic on demand.     

Ultraviolet reflectivity spectra of CuInSe2, CuInTe2 and CuGaTe2

Reflectivity spectra of CuInSe₂, CuInTe₂ and CuGaTe₂ are measured in the photon energy range from 2 to 9 eV. All compounds exhibit nearly the same reflectivity structures, and a comparison with measurements on the other Cu-III-VI₂ semiconductors shows that the band structures of all Cu-III-VI₂ compounds should be very similar except the energy range near the fundamental edge.     

Charge states of cobalt ions in nanostructured lithium cobaltite: X-ray absorption and photoelectron spectra

The charge states of ions in nanostructured lithium cobaltite prepared by severe plastic deformation under pressure have been determined using X-ray absorption spectroscopy and photoelectron spectroscopy, as well as calculations of the atomic multiplets with allowance for the charge transfer. It has been found that small deformations (pressures up to 5 GPa and angles of anvil rotation up to 30°) lead to the generation of lithium vacancies in the bulk of the nanostructured material and the formation of the Li₂O phase on the surface. The charge compensation occurs at the expense of holes in oxygen 2p states; the electronic configuration of cobalt ions is 3d ⁶ L, where L is a hole in oxygen 2p states. It has been shown that nanostructured lithium cobaltite belongs to the class of insulators with a negative charge transfer energy. An increase in the degree of deformation of lithium cobaltite (at a pressure up to 8 GPa) leads to the formation of Co²⁺ ions (with the electronic configuration 3d ⁷).     

Solvation of large dipoles

A model system consisting of one strongly polar molecule dissolved in a pool of 499 moderately polar particles is studied in a molecular dynamics experiment. A pair potential of Stockmayer type is used. The structure of the solution has been analysed in terms of g(R), f(R), h _Δ(R), h _D(R), g(R, x), and Voronoi polyhedra. Solvent-solvent spatial correlations are presented and compared to solute-solvent properties already discussed in part I. Voronoi polyhedra analysis is also used to define structural relaxation around solute or solvent particles unambiguously. The dynamics of the system is described by means of angular momentum, orientational, and velocity autocorrelation functions. The solute's influence on the dynamics of the solvent is analysed by a polyhedral decomposition of time correlation functions.     

Theorems of Stein-Rosenberg type. III. The singular case

In the theory of iterative methods, the classical Stein-Rosenberg theorem can be viewed as giving the simultaneous convergence (or divergence) of the extrapolated Jacobi (JOR) matrix J_ω and the successive overrelaxation (SOR) matrix

, in the case when the Jacobi matrix J₁ is nonnegative. As has been established recently by Buoni and Varga, necessary and sufficient conditions for the simultaneous convergence (or divergence) of J_ω and

have been established which do not depend on the assumption that J₁ is nonnegative. Our aim here is to extend these results to the singular case, using the notion of semiconvergence. In particular, for a real singular matrix A with nonpositive off-diagonal entries, we find conditions (Theorem 3.4) which imply that J_ω and

simultaneously semiconverge for all ω in the real interval [0,1).     

Preconditionings and splittings for rectangular systems

Summary Recently Eiermann, Marek, and Niethammer have shown how to applysemiiterative methods to a fixed point systemx=Tx+c which isinconsistent or in whichthe powers of the fixed point operator T have no limit, to obtain iterative methods which converge to some approximate solution to the fixed point system. In view of their results we consider here stipulations on apreconditioning QAx=Qb of the systemAx=b and, separately, on asplitting A=M–N which lead to fixed point systems such that, with the aid of a semiiterative method, the iterative scheme converges to a weighted Moore-Penrose solution to the systemAx=b. We show in several ways that to obtain a meaningful limit point from a semiiterative method requires less restrictions on the splittings or the reconditionings than those which have been required in the classical Picard iterative method (see, e.g., the works of Berman and Plemmons, Berman and Neumann, and Tanabe).We pay special attention to the case when the weighted Moore-Penrose solution which is sought is the minimal norm least squares solution toAx=b.Research supported by the Deutsche ForschungsgemeinschaftPartially supported by AFOSR research grant 88-0047