A Closed-Form Relation for Dimension-Dependent Two-Electron Matrix Elements of the Interelectronic Distance

The evaluation of matrix elements of two electron atoms is fundamental for the study of the electronic properties of those systems. We add to this knowledge by presenting an explicit expression for the matrix elements of the inverse of the interelectronic distance of two-electron atoms in any spatial dimension D. The basis functions used are the D-dependent hydrogenic wavefunctions {1s ²,2p ²,3d ²,4f ²,5g ²,...,21y ²,...}, extending and including, in this way, the results of the previous basis set {1s ²,2p ²,3d ²,4f ²}. The methodology used does not employ Fourier integral transforms as in previous works but hypergeometric transformation formulas.     

Structural studies of the carbon monoxide complex of [NiFe]hydrogenase from Desulfovibrio vulgaris Miyazaki F: suggestion for the initial activation site for dihydrogen

The carbon monoxide complex of [NiFe]hydrogenase from Desulfovibrio vulgaris Miyazaki F has been characterized by X-ray crystallography and absorption and resonance Raman spectroscopy. Nine crystal structures of the [NiFe]hydrogenase in the CO-bound and CO-liberated forms were determined at 1.2-1.4 A resolution. The exogenously added CO was assigned to be bound to the Ni atom at the Ni-Fe active site. The CO was not replaced with H(2) in the dark at 100 K, but was liberated by illumination with a strong white light. The Ni-C distances and Ni-C-O angles were about 1.77 A and 160 degrees, respectively, except for one case (1.72 A and 135 degrees ), in which an additional electron density peak between the CO and Sgamma(Cys546) was recognized. Distinct changes were observed in the electron density distribution of the Ni and Sgamma(Cys546) atoms between the CO-bound and CO-liberated structures for all the crystals tested. The novel structural features found near the Ni and Sgamma(Cys546) atoms suggest that these two atoms at the Ni-Fe active site play a role during the initial H(2)-binding process. Anaerobic addition of CO to dithionite-reduced [NiFe]hydrogenase led to a new absorption band at about 470 nm ( approximately 3000 M(-1)cm(-1)). Resonance Raman spectra (excitation at 476.5 nm) of the CO complex revealed CO-isotope-sensitive bands at 375/393 and 430 cm(-1) (368 and 413 cm(-1) for (13)C(18)O). The frequencies and relative intensities of the CO-related Raman bands indicated that the exogenous CO is bound to the Ni atom with a bent Ni-C-O structure in solution, in agreement with the refined structure determined by X-ray crystallography.     

Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals

BIT Numerical Mathematics - In this paper, we present a novel investigation of the so-called SAV approach, which is a framework to construct linearly implicit geometric numerical integrators for...     

Cooperative Competition Clustering for Gene Selection

Clustering analysis of data from DNA microarray hybridization studies is an essential task for identifying biologically relevant groups of genes. Attribute cluster algorithm (ACA) has provided an attractive way to group and select meaningful genes. However, ACA needs much prior knowledge about the genes to set the number of clusters. In practical applications, if the number of clusters is misspecified, the performance of the ACA will deteriorate rapidly. We propose the Cooperative Competition Cluster Algorithm (CCCA) in this paper. In the algorithm, we assume that both cooperation and competition exist simultaneously between clusters in the process of clustering. By using this principle of Cooperative Competition, the number of clusters can be found in the process of clustering. Experimental results on a synthetic and gene expression data are demonstrated. The results show that CCCA can choose the number of clusters automatically and get excellent performance with respect to other competing methods.     

Copper-mediated synthesis of N-acyl vinylogous carbamic acids and derivatives: synthesis of the antibiotic CJ-15,801

[reaction: see text] Copper(I)-mediated C-N bond formation has been employed to prepare both N-acyl vinylogous carbamic acids and ureas. The novel N-acyl vinylogous carbamic acid antibiotic, CJ-15,801, was synthesized using this methodology.     

Competitive potentiometric determination of binding constants between α-cyclodextrin and 1-alkanols

The binding constants of 1-alkanols with α-cyclodextrin (α-CD) were determined by indirect competitive potentiometry, although potentiometry is usually inapplicable to nonionic compounds. This novel method utilizes competitive binding of 1-alkanol and octyltrimethylammonium bromide (OTAB) to α-CD in aqueous media, where the concentration of free OTAB depending on the competitive binding is monitored with an OTAB-selective electrode. Therefore, the concentration of 1-alkanol is indirectly estimated from the observed electromotive force. The binding constants of 1-propapnol, 1-butanol, 1-hexanol, and 1-octanol with α-CD, obtained by this method, are close to the literature values. The implications and limitations of this indirect competitive potentiometry were discussed.     

Proofs of macrocyclization of gable porphyrins as mimics of photosynthetic light-harvesting complexes

Porphyrin macrocycles composed of five and six units of m-gable imidazolylporphyrinatozinc (1-Zn) were synthesized by self-assembled cyclization followed by ring-closing metathesis linkings. Each porphyrin macrocycle was isolated by GPC chromatography, and their molecular weights were determined by MALDI-TOF mass spectroscopy. These structures represent mimics of light-harvesting complexes in photosynthetic bacteria. [structure: see text]     

Reaction of 2-methoxy-3H-azepine with NBS: efficient synthesis of 2-substituted 2H-azepines

[reaction: see text] The reaction of 2-methoxy-3H-azepines, in the presence or absence of a nucleophile, with N-bromosuccinimide (NBS) gave a regioselective 1,4-adduct from which the corresponding 2H-azepine derivatives were formed via base-promoted hydrogen bromide elimination, generally in moderate to quantitative yield. Competitive formation of 4-bromo-2-methoxy-3H-azepine by electrophilic substitutuion or 3H-azepin-2-yl 2H-azepin-2-yl ether by transetherification was minimized at lower reaction temperatures. Quantitative substitution of 2-(2',4',6'-trichlorophenoxy)-2H-azepine derivatives, formed in moderate yield from the respective 3H-azepine and NBS in the presence of 2,4,6-trichlorophenol (TCP), by various nucleophiles gave the corresponding 2-substituted 2H-azepine. Among these nucleophiles were alkanethiol and alkylamine that are not tolerated in the reaction of 3H-azepine and NBS.     

Improved modification for the density-functional theory calculation of thermodynamic properties for C-H-O composite compounds

A three-parametric modification equation and the least-squares approach are adopted to calibrating hybrid density-functional theory energies of C(1)-C(10) straight-chain aldehydes, alcohols, and alkoxides to accurate enthalpies of formation DeltaH(f) and Gibbs free energies of formation DeltaG(f), respectively. All calculated energies of the C-H-O composite compounds were obtained based on B3LYP6-311++G(3df,2pd) single-point energies and the related thermal corrections of B3LYP6-31G(d,p) optimized geometries. This investigation revealed that all compounds had 0.05% average absolute relative error (ARE) for the atomization energies, with mean value of absolute error (MAE) of just 2.1 kJ/mol (0.5 kcal/mol) for the DeltaH(f) and 2.4 kJ/mol (0.6 kcal/mol) for the DeltaG(f) of formation.     

Selenium dioxide oxidations of dialkyl-3H-azepines: the first synthesis of 2-azatropone from oxidation of 2, 5-Di-tert-butyl-3H-azepine

Oxidation reactions of 2,5- and 3,6-di-tert-butyl-3H-azepines (1 and 2) with selenium dioxide (SeO(2)) were performed. The oxidation of 1 with SeO(2) gave 3-tert-butyl-7,7-dimethyl-4-oxo-octa-2,5-dienal 3 in 36% yield, 4-tert-butyl-5-(3,3-dimethyl-2-oxo-butylidene)-1, 5-dihydro-pyrrol-2-one 4 in 13% yield, 2, 6-di-tert-butyl-2-pyridinecarbaldehyde 5 in 12% yield, and 4, 7-di-tert-butyl-2H-azepin-2-one (2-azatropone) 6 in 6% yield, respectively. Oxidation of 2 with SeO(2) gave 2, 2-dimethyl-1-[2-(5-tert-butyl)-pyridyl]propanol 7 in 55% yield, and 3,6-di-tert-butyl-2H-azepine 8 in 5% yield, respectively. We found that selenium dioxide oxidation of 1 affords 4-oxo-octa-2,5-dienal 3 by a new ring cleavage reaction of 1, and we described the first synthesis of 2-azatropone 6 from this oxidation of 1. In the case of 2, pyridylpropanol 7 was obtained as the major product. We now report in detail result of these oxidation reactions, which have led to the synthesis of a novel azatropone derivative.