Experimental and DFT studies of ethyl N′-3-(1H-imidazol-1-yl) propylcarbamoyl benzohydrazonate monohydrate

The Imidazole compound, Ethyl N′-3-(1H-imidazol-1-yl) propylcarbamoyl benzohydrazonate monohydrate, has been synthesized and characterized by IR, NMR, electronic spectroscopy, and X-ray single-crystal determination. Molecular geometry from X-ray experiment of the title compound in the ground state has been compared using the density functional method (B3LYP) with 6-31G+(d) basis set. To determine conformational flexibility, molecular energy profile of the title compound was obtained by DFT calculations with respect to two selected degrees of torsional freedom, which were varied from −180° to +180° in steps of 10°. Besides, molecular electrostatic potential (MEP), natural bond orbitals (NBO), frontier molecular orbitals (FMO), and thermodynamic properties were performed at B3LYP/6-31G+(d) level of theory.     

A new rational approximation technique based on transformational high dimensional model representation

In this work, a new rational approximation scheme, based on the recently developed Transformational High Dimensional Model Representation (THDMR) approximation method is developed. As an initial step to the construction of a rational approximation for multivariate functions via THDMR, this paper focuses on the general theoretical background of the method and gives explicit formulae for the computation of such approximants. The performance of the technique is shown by several examples both in univariate and bivariate cases.     

No fluctuation approximation in any desired precision for univariate function matrix representations

The operator involving problems are mostly handled by using the matrix representations of the operators over a finite set of appropriately chosen basis functions in a Hilbert space as long as the related problem permits. The algebraic operator which multiplies its operand by a function is the focus of this work. We deal with the univariate case for simplicity. We show that a rapidly converging scheme can be constructed by defining an appropriate fluctuation operator which projects, in fact, to the complement of the space spanned by appropriately chosen finite number of basis functions. What we obtain here can be used in efficient numerical integration also.     

Antimicrobial activity studies of mononuclear and binuclear mixed-ligand copper(II) complexes derived from Schiff base ligands and 1,10-phenanthroline

Mixed-ligand complexes of copper(II) with 1,10-phenanthroline and various Schiff bases have been prepared and characterized by elemental analysis, electronic and i.r. spectra, magnetic moment and molar conductance data. The Schiff base behave as bidentate ligands, and the mixed-ligand copper(II) complexes of the ligands HL1, HL2 and HL4 are binuclear. The conductivity data for all the complexes are consistent with those expected for an electrolyte. Antimicrobial activities of some of the ligands and complexes have been tested against Bacillus megaterium and Candida tropicalis. 1H and 13C n.m.r. spectra have been recorded in order to solve the solution structure of the ligands. Thermal properties of all complexes have been studied by the d.t.a. and t.g.a. techniques.     

Physical characterization of the polymorphic variations of magnesium stearate and magnesium palmitate hydrate species

The anhydrate, dihydrate, and trihydrate phases of chemically pure magnesium stearate and magnesium palmitate have been prepared and characterized as to their structural characteristics. The magnesium palmitate materials were obtained as significantly larger crystals than were the magnesium stearate materials, and the crystals of the dihydrate phase of either material were found to be the most fully developed. The crystal structures of all materials were judged to be very similar to each other, differing primarily in the magnitude of the long (001) crystal spacing. Thermal analysis studies revealed that the water of hydration contained within the dihydrate phases of either magnesium stearate or magnesium palmitate was more tightly bound than was the water of hydration within the corresponding trihydrate phases. These findings provide further support for the structural picture where the water contained in these lattice structures is present between the intermolecular planes.     

Incorporation of an Allene Unit into α‐Pinene via β‐Elimination

The two double‐bond isomers 3‐iodo‐2,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 6b ) and 3‐iodo‐4,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 11 ) were synthesized by reacting 2,6,6‐trimethylbicyclo[3.1.1]heptan‐3‐one ( 9 ) with hydrazine, followed by treatment with I₂ in the presence of Et₃N. Treatment of 11 with t‐BuOK as base in diglyme at 220° resulted in the formation of 9 and 6,6‐dimethyl‐4‐methylidenebicyclo[3.1.1]hept‐2‐ene ( 12 ). For the formation of 9 , the cyclic allene 7 is proposed as an intermediate. Treatment of the second isomer, 6b , with t‐BuOK at 170° gave rise to the diene 12 and the dimerization product 17 . The underlying mechanism of this transformation is discussed. On the basis of density‐functional‐theory (DFT) calculations on the allene 7 and the alkyne 15 , the formation of the latter as the intermediate was excluded.     

Evaluation of two-center overlap integrals using slater type orbitals in terms of bessel type orbitals

Using the definition of STOs in terms of BTOs, we have presented analytical formula for two-center overlap integrals. The obtained formula contains generalized binomial coefficients and Mulliken integrals A_k and B_k. Taking into account the recent advances on the efficient calculation of Mulliken integrals (Harris, Int. J. Quantum Chem., 100 (2004) 142), we have obtained many more satisfactory results for two-center overlap integrals, for arbitrary quantum numbers, scaling parameters, and location of atomic orbitals.PACS No: 31.15.+qAMS Subject Classification: 81V55, 81–08     

Constancy maximization based weight optimization in high dimensional model representation

This work focuses on the weight function optimization in high dimensional model representation (HDMR) via constancy maximization. There are a lot of circumstances where HDMR’s weight function becomes completely flexible in its factors. The univariate coordinate changes which can be constructed to produce nonnegative factors in the integrands of HDMR component, are perhaps the most important ones of these cases. Here, the weight function is considered as the square of a linear combination of certain basis functions spanning an appropriately chosen Hilbert space. Then, the coefficients of these linear combinations are determined to maximize the HDMR’s constant term contribution to the function. Although the resulting equations are nonlinear we could have been able to approximate the solutions by using recently proven fluctuationlessness theorem on matrix representations appearing in the equations.     

Some difference sequence spaces defined by a sequence of <Emphasis Type="Italic">ϕ</Emphasis> -functions

Abstract  In this paper, we introduce new difference sequence spaces combining with de la Vallee-Poussin mean using by a sequence of modulus functions and ϕ -functions. We also studied connections between statistically convergence related with this space. Keywords Difference sequence, Modulus function, ϕ -function, De la Vallee-Poussin means, Statistical convergence Mathematics Subject Classification (2000) 46A45, 40F05, 46A80