Die Berechnung von Einelektronen-Integralen in der SCF-Xα-SW-Methode: I. Die Normierung

A normalization of the wave functions by means of the theoretical exact Multiple-Scattering-(MS)-formalism is discussed within the framework of the SCF-X_{w7t2458r0417822n/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">}-SW-method. For the atomic and extramolecular regions the integrals of normalization can be easily determined and the results can be described by the corresponding electronic charges. The calculation of the integral of the interatomic region is problematic. The needful volume integration is only necessary to theGreen's functions of the wave functions and can be solved by means of the residual theory. The further analytical calculation of the surface integrals leads to a complicated formalism which can be numerically evaluated.

     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for w447641987403344/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">iterative evaluationw447641987403344/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Reaction of dibenzylphosphine oxide with α,β-unsaturated O-methyloximes

The reaction of dibenzylphosphine oxide with O-methyloximes of some w0557276558/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-unsaturated ketones results in the phosphorylation at the w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-carbon atom to form methoxyiminophosphine oxides, whereas the reaction of dibenzylphosphine oxide with O-methyloximes of w0557276558/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,w0557276558/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-unsaturated aldehydes affords aminodihydrophosphole oxides.     

The Comparison of the Orientation of Sodium 3-Hydroxy-2-Naphthalenecarboxylate in the Cavity of β-Cyclodextrin and Heptakis-(2,3,6-Tri-O-Methyl)-β-Cyclodextrin

Conformational analysis of inclusion complexes of sodium 3-hydroxy-2-naphthalenecarboxylate with w8k080n5454487v2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin and heptakis-(2,3,6-tri-o-methyl)-w8k080n5454487v2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin in D₂O was investigated by 1D and 2D ¹HNMR measurements. The results show that part of the naphthyl group of sodium 3-hydroxy-2-naphthalenecarboxylate is situated in the 2,3-OH side of the w8k080n5454487v2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin cavity asymmetrically while the whole naphthyl group is included in the heptakis-(2,3,6-tri-o-methyl)-w8k080n5454487v2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin cavity with the caboxylate and hydroxy group close to the 6-OCH₃ group.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy w8k/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">-equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

About a minimax theorem of Matthies,Strang and Christiansen

We give a new minisup theorem for noncompact strategy sets. Our result is of the type of the Matthies-Strang-Christiansen minimax theorem where the hyperplane should be replaced by any closed convex set. As an application, we derive a slight generalization of the Matthies-Strang-Christiansen minimax theorem.     

On the affinity of cytosine towards electrophiles

Ab initio SCF computations on the intrinsic preferences of the H⁺, CH ₃ ⁺ and C₂H ₅ ⁺ cations towards the two principal sites of protonation or alkylation on cytosine, N₃ or O₂, show that this preference undergoes a continuous modification with the increase in size and complexity of the cation. N₃ is the preferred site of fixation of H⁺, O₂ the preferred site of C₂H ₅ ⁺ , while CH ₃ ⁺ has no marked preference. The exchange repulsion term of the binding energy appears responsible for the preference of C₂H ₅ ⁺ for O₂.This work was supported by the Ligue Francaise contre le Cancer and the National Foundation for Cancer Research (USA)     

Atom-surface elastic scattering in the presence of laser radiation

A qualitative discussion on atom-surface elastic scattering taking place in the presence of laser radiation is given. It is suggested that appreciable effects of laser radiation on diffraction patterns may be expected if the laser radiation is capable of inducing electronic transitions in atoms with a large probability.Research sponsored by the Air Force Office of Scientific Research (AFSC), United States Air Force, under Contract No. F49620-78-C-0005, and the National Science Foundation under Grant No. CHE77-27826. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.Alfred P. Sloan Research Fellow, 1976–1980; Camille and Henry Dreyfus Teacher-Scholar, 1975–1980.     

Kinetics and mechanism of the hydrolysis of sodium carboxymethylcellulose (Na-CMC) by a cellulase complex

TheSomogyi-Nelson colorimetric method is applied in a new manner more suitable for evaluating the kinetics of the enzyme hydrolysis of sodium carboxymethylcellulose (Na-CMC) catalyzed by the cellulase complex. By means of selective inhibition of a chosen enzyme from the cellulase complex it became possible to trace the effect of the other enzymes included in its composition.

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Kinetik und Mechanismus der Hydrolyse von Natriumcarboxymethylcellulose (Na-CMC) durch einen Cellulase-Komplex

Zusammenfassung Die kolorimetrische Methode nachSomogyi undNelson wird nach einem neuen Verfahren zur Verfolgung der Kinetik der hydrolytischen Spaltung von Natriumcarboxymethylcellulose (Na-CMC), katalysiert durch den Cellulase-Komplex, angewandt. Durch selektive Inhibierung eines bestimmten Enzyms des Cellulase-Komplexes kann man die Wirkung der anderen zu seiner gesamten Zusammensetzung gehörenden Enzyme verfolgen.

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Symbols Used E enzyme (Ew3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">—cellulase;Ew3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">—exo-cellobiohydrolase;Ew3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">—w3508h3735x70768/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-glucosidase) - [E] _w weight concentration of enzymeE - S substrate (Na-CMC—sodium carboxymethylcellulose) - [S]₀ weight concentration of substrateS - I inhibitor (Iw3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">—lactose;Iw3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">—calcium chloride;Iw3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">—condurrite-B-epoxide) - P product (Pw3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">—oligosaccharides;Pw3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">—cellobiose;Pw3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">—D-glucose) - P _{w3508h3735x70768/xxlarge8733.gif" alt="prop" align="MIDDLE" BORDER="0">} end product (K _{w3508h3735x70768/xxlarge8733.gif" alt="prop" align="MIDDLE" BORDER="0">} ^{w3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">} , K _{w3508h3735x70768/xxlarge8733.gif" alt="prop" align="MIDDLE" BORDER="0">} ^{w3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">} , K _{w3508h3735x70768/xxlarge8733.gif" alt="prop" align="MIDDLE" BORDER="0">} ^{w3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">} ) - DP degree of polymerization - DS degree of substitution - ES enzyme-substrate complex (Ew3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0"> S, Ew3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0"> S, Ew3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0"> S) - EP enzyme-product complex (Ew3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0"> Pw3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">, Ew3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0"> Pw3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">) - EI enzyme-inhibitor complex (Ew3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0"> Iw3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">, Ew3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0"> Iw3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">, Ew3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0"> Iw3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">) - M _s molecular mass of substrateS - K _s substrate constant (K _s ^{w3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">} , K _s ^{w3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">} , K _s ^{w3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">} ) - K _I inhibitor constant (K _I ^{w3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">} , K _I ^{w3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">} , K _I ^{w3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">} ) - K _m Michaelis-Menten constant - k ₊₁,k ₊₂ (k ₊₂ ^{w3508h3735x70768/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">} ,k ₊₂ ^{w3508h3735x70768/xxlarge8243.gif" alt="Prime" align="MIDDLE" BORDER="0">} ,k ₊₂ ^{w3508h3735x70768/xxlarge8244.gif" alt="tprime" align="MIDDLE" BORDER="0">} ) forward rate constants - k _–1 reverse rate constant - w3508h3735x70768/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₀ initial rate of reaction - V maximal reaction rate - w3508h3735x70768/xxlarge916.gif" alt="Delta" align="BASELINE" BORDER="0">A change in absorbance - w3508h3735x70768/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0"> molar absorption coefficient - w3508h3735x70768/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0"> wavelength Herrn Prof. Dr.Hans Tuppy zum 60. Geburtstag herzlichst gewidmet.     

Photochemically induced fluorescence investigation of aβ-cyclodextrin: Azure A inclusion complex and determination of analytical parameters

The photooxidation of Azure A and fluorescence properties of Azure A and its photoproduct have been investigated in aqueous media and in the presence ofw330h5325n6/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (w330h5325n6/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD). The fluorescence intensity of the complex formed between the photoproduct and w330h5325n6/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD was found to be three times higher than that of the uncomplexed Azure A photoproduct. A complex formation constant of 110±40 M^–1 was calculated using the Benesi-Hildebrand treatment of the fluorescence emission data. Although the stoichiometry of the Azure A photoproduct: w330h5325n6/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD complex was found to be 1: 1, it seems that the Azure A structure is only partially included. Calibration graphs were plotted for the free Azure A photoproduct and the photogenerated product included in w330h5325n6/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD. The analytical parameters and quantification limits were determined.