Integral algorithm and density matrix integration scheme for ab initio band structure calculations on polymeric systems

A new program for band structure calculations of periodic one-dimensional systems has been constructed. It is distinguishable from other codes by the efficient two-electron integral evaluation and the integration schemes of the density matrix in the first Brillouin zone. The computation of polymeric two-electron integrals is based on the McMurchie Davidson algorithm and builds batches of the different cell indices included in the polymeric system. Consequently it presents efficient scaling with respect to the number of unit cells taken into account. Our algorithm takes into account fully the polymeric symmetry rather than the molecular symmetry. A semidirect procedure where only exchange integrals are computed at each SCF cycle is proposed in order to maintain balance between computation time and disk space. In addition, the integration of the density matrix over a large number of cell indices can be performed by different methods, such as Gauss-Legendre, Clenshaw-Curtis, Filon, and Alaylioglu-Evans-Hyslop. This last scheme is able to obtain an accuracy of 10(-13) a.u. on each individual density matrix element for all cell indices with only 48 k-points.     

On the complex hybridization of orbitals of s and p type

The direction of valence is defined as the direction from the atomic nucleus to the center of gravity of the hybrid density. Complex mixing coefficients of the orbitals of pure angular momentum are introduced in the hybrid. This allows a considerable extension of the hybridization concept with regard to valence angles and equivalence restrictions. General expressions for the direction consines of valence and for bond angles are given, and applications are made to several molecules with bond angles of 90 degrees or less.

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Zusammenfassung Die Valenzrichtung eines Hybrids wird als die Richtung vom Atomkern zum Schwerpunkt der Elektronendichte difiniert. Dabei werden auch komplexe Koeffizienten für die atomaren Zustandsfunktionen zugelassen, wodurch eine erhebliche Erweiterung des Hybridisierungs-konzeptes im Hinblick auf Valenzwinkel und Nebenbedingungen infolge von Äquivalenz möglich ist. Allgemeine Ausdrücke für die Richtungskosinus und Bindungswinkel werden angegeben, ebenso einige Beispiele für Moleküle mit Winkeln unter 90.

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Résumé La direction de valence est définie comme la direction joignant le noyau atomique au centre de gravité de la densité de l'hybride. Des coefficients de mélange complexes sont introduits dans l'hybride pour les orbitales de moment angulaire pur. Ceci permet une extension considérable du concept d'hybridation en ce qui concerne les angles de valence et les restrictions d'équivalence. Des expressions générales pour les cosinus directeurs des directions de valence et pour les angles de liaison sont obtenues et appliquées á plusieurs molécules dont les angles de liaison sont au plus de 90.

     

Lifetime measurements of metastable states of Au,Bi, Cd,Mg, Pb,and Sr in an acetylene/air flame by laser-enhanced ionization spectrometry

The collisional dominated lifetimes of 9 metastable states of Au, Bi, Cd, Mg. Pb, and Sr in an acetylene/air flame have been measured by the step-wise delayed laser-enhanced ionization spectrometry technique. First, the dependency of the lifetime of the metastable 6p ^{2 3} P ₁ state in Pb upon both flame composition and height in the flame were studied. It was found that the lifetime was significantly shorter, both for lean as well as for rich flames, as compared to a stoichiometric composition. The lifetime was furthermore found to be dependent of the height in the flame with a maximum around 10 mm. The lifetimes were not significantly affected by the electron concentration in the flame. The lifetimes for the other metastable states were determined for one given flame composition ( 0.9 _stoich) and one given height (20 mm) only. The measured lifetimes were found to be between 5 ns and 3.1 s. The results show clearly that the lifetimes of metastable states are significantly shortened in the flame (as compared to natural lifetimes). The results also indicate that the metastable states which are of the same parity as the ground configuration (Au, Bi and Pb) in general have longer (collisional) lifetimes (85 ns to 3.1 s) than those which are forbidden to decay to the ground configuration only by violation of spin conservation (Cd, Mg and Sr) (5–33 ns).     

Introduction

The formalism for a configuration interaction approach is presented, in which explicit introduction of interelectronic coordinates into individual configurations is accomplished through the use of spherical Gaussian correlation factors. Formulas for all required matrix elements over these configurations are derived, and a computationally convenient algorithm to evaluate the matrix elements is presented. In addition, analysis of the form of the correlation factor shows that both angular and radial correlation can be obtained using spherical Gaussian correlation factors.     

Physical Properties of Biopolymers Assessed by Optical Tweezers: Analysis of Folding and Refolding of Bacterial Pili

Bacterial adhesion to surfaces mediated by specific adhesion organelles that promote infections, as exemplified by the pili of uropathogenic E. coli, is studied mostly at the level of cell–cell interactions and thereby reflects the averaged behavior of multiple pili. The role of pilus rod structure has therefore only been estimated from the outcome of experiments involving large numbers of organelles at the same time. It has, however, lately become clear that the biomechanical behavior of the pilus shafts play an important, albeit hitherto rather unrecognized, role in the adhesion process. For example, it has been observed that shafts from two different strains, even though they are similar in structure, result in large differences in the ability of the bacteria to adhere to their host tissue. However, in order to identify all properties of pilus structures that are of importance in the adhesion process, the biomechanical properties of pili must be assessed at the single‐molecule level. Due to the low range of forces of these structures, until recently it was not possible to obtain such information. However, with the development of force‐measuring optical tweezers (FMOT) with force resolution in the low piconewton range, it has lately become possible to assess forces mediated by individual pili on single living bacteria in real time. FMOT allows for a more or less detailed mapping of the biomechanical properties of individual pilus shafts, in particular those that are associated with their elongation and contraction under stress. This Mi‐ nireview presents the FMOT technique, the biological model system, and results from assessment of the biomechanical properties of bacterial pili. The information retrieved is also compared with that obtained by atomic force microscopy.     

Compounds labelled with short-lived beta(+)-emitting radionuclides and some applications in life sciences. The importance of time as a parameter.

Some examples of recent development of the synthesis of compounds labelled with short-lived beta(+)-emitting radionuclides will be discussed with an emphasis on the importance of time in selecting a synthetic strategy. Furthermore the use of such labelled compounds to monitor certain processes in areas within the field of analytical chemistry and in various applications in drug development will be presented.     

Formation Dynamics of Absorbing Layers in a Two‐Stage Atomizer

An experimental spatialresolution facility for recording the formation dynamics of absorbing layers in a twostage atomizer is described. An optical scheme with a convergent raying beam in the atomizer zone and a hollow cathode as a radiation source is considered. The dynamics of the absorptivity signal at evaporation of Rb, NaCl, and a standard sample CASS2 has been investigated under different operating conditions of the atomizer. It is shown that the proposed evaporation–condensation–atomization regime considerably lowers the spatial gradients of absorptivity and the level of nonselective absorption in recording the atomic absorption signal.     

Analytical applications of laser-enhanced lonization spectrometry in flames and furnaces

This paper is concerned with a critical analysis of the analytical performance of laser-enhanced ionization (LEI) spectrometry in flames and furnaces as an ultra-sensitive trace-element technique. Updated tables of LEI detection limits, both in flames and furnaces, are given. Special attention is paid to interference phenomena which are unique to the LEI technique. Ways of reducing their influence on the analytical signals are proposed. Finally, advantages and disadvantages of LEI spectrometry as a tool for ultra-sensitive trace element analysis are discussed.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria