Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals

The authors propose a new algorithm, "local K" (LK), for fast evaluation of the exchange Fock matrix in case the Cholesky decomposition of the electron repulsion integrals is used. The novelty lies in the fact that rigorous upper bounds to the contribution from each occupied orbital to the exchange Fock matrix are employed. By formulating these inequalities in terms of localized orbitals, the scaling of computing the exchange Fock matrix is reduced from quartic to quadratic with only negligible prescreening overhead and strict error control. Compared to the unscreened Cholesky algorithm, the computational saving is substantial for systems of medium and large sizes. By virtue of its general formulation, the LK algorithm can be used also within the class of methods that employ auxiliary basis set expansions for representing the electron repulsion integrals.     

Crystallization kinetics study on higher homologues of benzylidene aniline compounds: impact of phase variant on nucleation process

A systematic kinetic study leading to the crystallization process from the kinetophases (which occur prior to crystal phase) smectic B, crystal G and smectic F is performed on representative compounds of the homologous series p -phenylbenzylidene-p′-alkylanilines (PBnA) and p-n -alkoxybenzylidene-p′-alkylanilines (nO.m) these compounds are p-phenylbenzylidene-p′-nonylaniline (PB9A), p -phenylbenzylidene-p′-tetradecylaniline (PB14A), p-n -pentadecyloxybenzylidene p′-tetradecylaniline (15O.14) and p-n -octadecyloxybenzylidene-p′-nonylaniline (18O.9). The molecular mechanism and dimensionality in crystal growth from the kineto phases are computed from the Avrami equation, while the characteristic crystalline time (t ^*) at each crystallization temperature is deduced from the individual plots of log t vs. Δ H. The low magnitudes of the dimensionality parameter n infers the occurrence of diffusion-controlled transformations leading to the formation of plates or needles of finite size possessing impinged edges. The degree of variation in the value of n at each crystallization temperature also reveals the existence of an independent nucleation mechanism for any individual member of the series. The influence of the terminal alkyl chain lengths on the rate of crystallization is determined from a comparative study with the reported analogous compounds.     

A Mössbauer spectroscopic study of salt lake sediments from Qaidam basin

Mössbauer spectroscopy, X-ray diffractometry and chemical fractionation have been used to study the clay smaples in sediments of Charhan playa and Qinghai lake. The spectral components of the Mossbauer spectra of the samples are attributed to Fe²⁺ ions in chlorite and siderite, Fe³⁺ ions in clay minerals and hematite, and partly in amorphous ferric hydroxides. The essential difference in the mineral composition of the sediments of both lakes is the presence of siderite in the samples of Char han playa, whereas it is absent in the samples of Qinghai lake. The fraction of the amorphous ferric hydroxides is higher in the sediments of Qinghai lake. Total Fe²⁺/Fe³⁺ ratios increase with sediment depth of Charhan playa, whereas these ratios are altogether smaller and run through a maximum at a certain depth for Qinghai lake.     

Elastic electron scattering from 40Ar

Cross sections for elastic electron scattering from ⁴⁰Ar have been measured for the momentum transfer range from 0.59 to 1.31 fm^?1. We have analyzed with the Fourier-Bessel ansatz our data as well as the data of former experiments. The rms charge radius we have found is 3.423(14) fm. The results are in excellent agreement with latest muonic data. Furthermore, we have reanalyzed former ⁴⁰Ca data and have discussed the ⁴⁰Ca- ⁴⁰Ar charge distribution.     

Optical clock distribution with a compact free space interconnect system

Optical clock signal distribution has been widely discussed to be an attractive way to reduce the clock skew in high-speed digital systems. For short interconnect lengths, especially for chip level clock distribution, free space systems using diffractive optical elements (DOEs) have specific advantages. The optoelectronic pathway described in this paper consists of a GaAs laser diode, a microetched silicon mirror, a faceted diffractive element and four silicon photodiodes hybridized to a (dummy) silicon chip. The key element of the clock distribution demonstrator is the diffractive element which matches setup requirements like compactness, off-axis geometry and use of an unshaped laser beam. The whole setup meets the demands of alignment accuracy in an excellent way. This is achieved by the very good imaging characteristic of the DOE and by an alignment technique based on precision mounting of micromachined silicon components. The system was tested with clock rates up to 2.5 GHz, the cut-off frequency is 350 MHz.     

Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations

This paper is concerned with the asymptotic behaviour and the stability of a class of linear neutral delay difference equations with variable coefficients and constant delays. Via an appropriate solution of the so-called generalized characteristic equation, an asymptotic criterion and a stability result are established.     

De novo sequencing of proteolytic peptides by a combination of C-terminal derivatization and nano-electrospray/ collision-induced dissociation mass spectrometry

A series of synthetic peptides (3-15 residues), C-terminally derivatized with 4-aminonaphthalenesulfonic acid (ansa), have been analyzed on a hybrid magnetic sector-orthogonal acceleration time-of-flight tandem mass spectrometer, fitted with a nano-electrospray (nano-ES) interface. Deprotonated molecules generated by negative-ion ES were subjected to collision-induced dissociation (CID) using either methane or xenon as the collision gas, at a collision energy of 400 eV (laboratory frame of reference). As a consequence of charge localization on the sulfonate group, only C-terminal fragment ions were formed, presumably by charge-remote fragmentation mechanisms. Interpretable CID spectra were obtained from fmol amounts of the small peptides (up to 6 residues), whereas low pmol amounts were required for the larger peptides. CID spectra were also recorded of derivatized, previously noncharacterised peptides obtained by proteolysis of cytosolic hamster liver aldehyde dehydrogenase. Interpretation of these CID spectra was based on rules established for the fragmentation of the synthetic peptides. This study shows that derivatization with ansa may be useful in the de novo sequencing of peptides.     

Study of the ion exchange equilibrium of Cl−, NO_3^{ - } , and SO_4^{{2 - }} ions on the AMX membrane

Equilibrium between the ion exchange membrane and solutions of anions at various valences has been the subject of this investigation. Competitive ion exchange reactions were studied on a strong base anion exchange membrane AMX manufactured by Tokuyama, commercialized by Eurodia, involving Cl^?, $ {\text NO}_3^{ - } $ and $ {\text SO}_4^{{2 - }} $ ions. Solution concentrations studied were 0.05 and 0.1 M for all the systems reported. Experiments were performed with sodium as the counter ion, and the temperature was kept constant (T?=?298 K). Ionic exchange isotherms for the binary systems— $ {{\text Cl}^{ - }}/{\text NO}_3^{ - } $ , $ {{\text Cl}^{ - }}/{\text SO}_4^{{2 - }} $ , and $ {\text NO}_3^{ - }/{\text SO}_4^{{2 - }} $ —were established. The obtained results show that the sulfate was the most strongly sorbed, and the selectivity order is $ {\text SO}_4^{{2 - }} > {\text NO}_3^{ - } > {{\text Cl}^{ - }} $ at 0.05 M and $ {\text NO}_3^{ - } > {\text SO}_4^{{2 - }} > {{\text Cl}^{ - }} $ at 0.1 M under the experimental conditions. Selectivity coefficients $ K_{{{{{\text Cl} }^{ - }}}}^{{{\text NO}_3^{ - }}} $ , $ K_{{2{{{\text Cl} }^{ - }}}}^{{{\text SO}_4^{{2 - }}}} $ , and $ K_{{2{\text NO}_3^{ - }}}^{{{\text SO}_4^{{2 - }}}} $ for the three binary systems were determined. All the results given by this membrane were compared with those obtained, in the same conditions, with the RPA membrane (produced by RHONE POULENC). Ternary equilibrium data were taken for $ {{\text Cl}^{ - }}/{\text NO}_3^{ - }/{\text SO}_4^{{2 - }} $ . The prediction of the ternary system based only on the binary data was consistent with the experimental data obtained for this system. The good agreement between the experimental and the predicted data showed that the proposed framework can be considered as an effective method to predict many ternary systems from binary systems.