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.     

De novo design of a redox-active minimal rubredoxin mimic

Metal-binding sites in metalloproteins frequently occur at the interfaces of elements of secondary structure, which has enabled the retrostructural analysis of natural proteins and the de novo design of helical bundles that bind metal ion cofactors. However, the design of metalloproteins containing beta-structure is less well developed, despite the frequent occurrence of beta-conformations in natural metalloproteins. Here, we describe the design and construction of a beta-protein, RM1, that forms a stable, redox-active 4-Cys thiolate Fe(II/III) site analogous to the active site of rubredoxin. The protein folds into a beta-structure in the presence and absence of metal ions and binds Fe(II/III) to form a redox-active site that is stable to repeated cycles of oxidation and reduction, even in an aerobic environment.     

Optimal investment with two-factor uncertainty

This paper presents a real options model to value the option to invest in a project contingent on two stochastic factors. A general sensitivity analysis is conducted highlighting the importance of the variance and correlation between the two variables. A higher correlation is shown to increase always the values of the trigger, the active project and the option. The impact of uncertainty is more complex and depends on the assumption about which variables adjust and the correlation between the variables and the market.     

Reaction of N-(Benzyloxycarbonyl)aminobenzyl-phosphonous Acid with Ethyl Orthoformate

Reaction of N-(benzyloxycarbonyl)aminobenzylphosphonous acid with ethyl orthoformate afforded two major products diethyl N-(benzyloxycarbonyl)aminobenzylphosphhite and ethyl (diethoxymethyl)[N-(benzyloxy-carbonyl)aminobenzyl]phosphmate, a product of addition of phosphonous acid to orthoformate.     

The Dirichlet ring and unconditional bases in L 2[0, 2π]

It is observed that the Dirichlet ring admits a representation in an infinite-dimensional matrix algebra. The resulting matrices are subsequently used in the construction of nonorthogonal Riesz bases in a separable Hilbert space. This framework enables custom design of a plethora of bases with interesting features. Remarkably, the representation of signals in any one of these bases is numerically implementable via fast algorithms.