Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.     

A quantum-chemical study of dinitrogen reduction at mononuclear iron-sulfur complexes with hints to the mechanism of nitrogenase

The mechanism of biological dinitrogen reduction is still unsolved, and the structure of the biological reaction center, the FeMo cofactor with its seven iron atoms bridged by sulfur atoms, is too complicated for direct attack by current sophisticated quantum chemical methods. Therefore, iron-sulfur complexes with biologically compatible ligands are utilized as models for studying particular features of the reduction process: coordination energetics, thermodynamic stability of intermediates, relative stability of isomers of N2H2, end-on versus side-on binding of N2, and the role of states of different multiplicity at a single iron center. From the thermodynamical point of view, the crucial steps are dinitrogen binding and reduction to diazene, while especially the reduction of hydrazine to ammonia is not affected by the transition metal complex, because the complex-free reduction reaction is equally favored. Moreover, the abstraction of coordinated ammonia can be easily achieved and the complex is recovered for the next reduction cycle. Our results are discussed in the light of studies on various model systems in order to identify common features and to arrive at conclusions which are of importance for the biological mechanism.     

Synthesis of new isoxazoles derivatives attached to sugar moieties

This work reports the synthesis of isoxazoles linked to sugar derivatives in different positions of furanosidic rings, by intramolecular oxidative cyclization of α,β‐unsaturated oximes with iodine, potassium iodide and sodium hydrogen carbonate. These oximes were obtained from aldehyde‐sugar derivatives.     

Application of Discrete Wavelet Transform in the Analysis of Nonlinear Chemical System

Oscillations of species concentration are phenomena accompanying several types of electrochemical and purely chemical processes. Importance of analyzing of such processes results from both scientific and practical reasons. In the paper the authors deal with investigation of time dependent spectra of various stages of Belousov-Zhabotinsky type chemical oscillations. As the analytical tool the discrete wavelet transform is proposed.     

Zur Behandlung der Bindungsalternierung als Störung in der Hückelschen MO-Theorie

Zusammenfassung Es wird gezeigt, wie man den möglichen Einflu\ der Bindungsalternierung auf die Spektren ungesÄttigter organischer Moleküle störungstheoretisch im Rahmen der Hückelschen MO-Methode in einfacher Weise behandeln kann, wobei das Modell mit idealisierter Geometrie als nullte NÄherung dient und das Ausma\ der Bindungsalternierung als natürlicher Störparameter auftritt. An den diskutierten Beispielen (Polyene, Polymethine und zyklische Polyene als ModellfÄlle) erkennt man, da\ die Störung 1. Ordnung der langwelligsten Elektronenübergangsfrequenz entweder verschwindet oder einen innerhalb einer Reihe praktisch konstanten Wert liefert. Die bekannte Tatsache, da\ die im Rahmen der Hückel-Methode berechneten Frequenzen gegen die experimentellen aufgetragen i. a. Regressionsgeraden ergeben, die nicht durch den Nullpunkt gehen, lÄ\t sich so, jedenfalls z. T., verstehen. Besondere Beachtung findet die Diskussion der Konvergenz der Störungsentwicklung.

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It is shown how the possible effect of bond alternation on the spectra of unsaturated molecules can be accounted for in a simple way by a perturbation treatment in the framework of the Hückel MO-scheme. In zeroth approximation one assumes idealized geometry and the measure of bond alternation appears as a natural perturbation parameter. One sees from the examples discussed here in detail (polyenes, polymethines, and cyclic polyenes) that the 1^st order perturbation correction to the largest wave length absorption frequency either vanishes or is roughly constant within a series. The known fact that absorption frequencies calculated by the Hückel method versus the experimental ones can in general be fitted by a regression line that does not pass the origin, finds a partial explication. Special attention is given to the problem of convergency of the perturbation series.

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Résumé Il est demontré comment on peut tenir compte de l'influence possible de l'alternance des liaisons sur les spectres des molécules organiques non saturées. On commence par idéaliser la géométrie et fait intervenir une mesure de l'alternance comme parameter naturel de la perturbation. Les exemples étudiés en detail (les polyenes, les polymethines et les polyenes cycliques) suggèrent qu'il y a deux classes de molécules dont pour les unes il n'y a pas de correction de perturbation du premier ordre aux plus basses fréquences de transition electronique tandis que pour les autres ces corrections sont à peu près constantes pour une serie. Cela explique en partie le fait que les lignes de régression entre les fréquences calculées par la methode de Hückel et les valeurs experimentales correspondantes ne passent en general pas l'origine. Le problème de la convergence de la serie de perturbation est discuté en particulier.

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Der Verfasser möchte an dieser Stelle Herrn Prof. Dr. W. A. Bingel herzlich für sein Interesse an dieser Arbeit danken. Dank gebührt ferner den Mitgliedern des Laboratoire de Chimie Quantique in Paris, mit denen der Verfasser Gelegenheit hatte, wÄhrend eines Besuches in Paris über das Thema dieses Artikels zu diskutieren. Dieser Besuch wurde im Rahmen des Nato research grant Nr. 223 möglich gemacht.Die erforderlichen numerischen Rechnungen wurden auf der Göttinger IBM 7040 durchgeführt.     

New derivation and a k-particle generalization of SCF-type theories

A hierarchy of necessary conditions that an exact density matrix of a pure state or an ensemble has to satisfy is derived, namely the hermiticity of certain operators F^(k). For k = 1 this reduces to the well-known Hartree-Fock condition. It is then shown that the kth set of conditions is equivalent to stationarity of the energy with respect to unitary k-particle transformations. k-Particle generalizations of Hartree-Fock theory are then discussed both in the spirit of k-particle pseudoeigenvalue equations and in the framework of a Newton–Raphson-type constructive scheme.     

Soluble Extracellular Polymeric Substances Produced by Parachlorella kessleri and Chlorella vulgaris: Biochemical Characterization and Assessment of Their Cadmium and Lead Sorption Abilities

In the present study, the potential of lead and cadmium removal by the extracellular polymeric substances (EPS) produced from Parachlorella kessleri and Chlorella vulgaris were investigated. Carbohydrates were the dominant components of EPS from both analyzed species. The contents of reducing sugars, uronic acids, and amino acids were higher in EPS synthesized by C. vulgaris than in EPS from P. kessleri. The analysis of the monosaccharide composition showed the presence of rhamnose, mannose and galactose in the EPS obtained from both species. The ICP-OES (inductively coupled plasma optical emission spectrometry) analyses demonstrated that C. vulgaris EPS showed higher sorption capacity in comparison to P. kessleri EPS. The sorption capacity of C. vulgaris EPS increased with the increase in the amount of metal ions. P. kessleri EPS had a maximum sorption capacity in the presence of 100 mg/L of metal ions. The FTIR analysis demonstrated that the carboxyl, hydroxyl, and carbonyl groups of EPS play a key role in the interactions with metal ions. The present study showed C. vulgaris EPS can be used as a biosorbent in bioremediation processes due to its biochemical composition, the presence of significant amounts of negatively charged uronic acids, and higher sorption capacity.     

Effect of Phenolic Compounds from Cymbopogon citratus (DC) Stapf. Leaves on Micellar Solubility of Cholesterol

Dyslipidemias are one of the risk factors for cardiovascular diseases, the leading cause of death and hospitalization worldwide. One way to control cholesterol levels is to control the exogenous cholesterol intake in the body. Natural polyphenolic compounds, namely theaflavins from plant extracts such as black tea, showed the ability to inhibit the formation of the micellar structure, essential for the absorption of cholesterol in the intestine. There are several methodologies to determine this effect, many of which are expensive and time-consuming. Due to these facts, the main purposes of this work were to optimize an inexpensive colorimetric method to study, in vitro, the micellar solubility of cholesterol and applied it to plant extracts. In this work, Cymbopogon citratus leaf extracts, its phenolic fractions, and flavonoids were evaluated. The non-delipidified infusion (CcI) obtained a maximum percentage of micelle destruction of 59.22% for a concentration of 50 μg/mL and the delipidified infusion (CcdI) obtained a maximum percentage of micelle destruction of 58.01% for a concentration of 200 μg/mL. In the case of the fraction of phenolic acids (CcPAs), 23.85% of maximum micellar destruction was recorded for the concentration of 100 μg/mL, while for the fraction of flavonoids (CcF), the micellar destruction was 92.74% at 1 μg/mL, and for the tannin fraction (CcT) of 99.45% at 25 μg/mL. Luteolin presented a percentage of micelle destruction of 94.83% in the concentration of 1 ng/mL, followed by luteolin-7-O-glucoside with 93.71% and luteo-lin-6-C-glucoside with 91.26% at the concentrations of 25 ng/mL and 50 ng/mL, respectively. These results suggest the capability of polyphenols from Cymbopogon citratus to prevent the cholesterol absorption in the gut by micellar destruction, and its contribution for cholesterol-lowering activity.