Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancing between all available processors/cores is obtained. A similar blocking technique can be used to exploit local cache memory of each processor to further speed up the process. Due to diversity of modern computer architectures, each of the algorithms described here may be the method of choice for a particular hardware and a given matrix size. All proposed block algorithms compute the eigenvalues with relative accuracy similar to the original non-blocked Jacobi algorithm.Comment: Submitted for publicatio

Novel Modifications of Parallel Jacobi Algorithms

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.Comment: Accepted for publication in Numerical Algorithm

Solvent and substituent effect on electronic spectra of N-(4-substitutedphenyl)-2,3-diphenylpropanamides

The UV absorption spectra (200-400 nm) of eleven N-(4-substituted phenyl)-2,3-diphenyl-propanamides 1 have been recorded in fourteen solvents of different polarity. A simple Hammett equation was used to study the effects of substituents on the UV spectra of compounds 1. The effects of solvent polarity and hydrogen bonding on the absorption spectra are interpreted by means of linear solvation energy relationships. The results show that the solvent effect on UV absorption spectra of the investigated amides are very complex and strongly depends on the nature of the substituents of the phenyl ring

Solvent and Structural Effects on the UV-Vis Absorption Spectra of Some 4,6-Disubstituted-3-Cyano-2-Pyridones

A series of 4,6-disubstituted-3-cyano-2-pyridones was synthesized and their UV-Vis absorption spectra were recorded in the region 200-600 nm in the set of selected solvents. The effects of solvent dipolarity/polarizability and solvent-solute hydrogen-bonding interactions on the spectral shifts were analyzed by means of the linear solvation energy relationship concept of Kamlet and Taft. The influence of solvents as well as substituents on the 2-pyridone/2-hydroxypyridine tautomeric equilibration was evaluated. The absorption band maximum of the 2-hydroxypyridine form is found to appear at a shorter wavelength than that of the 2-pyridone form in all investigated solvents. The replacement of the methyl and phenyl groups at position 6 of the pyridone ring, by a hydroxy group, significantly changes the solvatochromic behavior of the investigated pyridones

Supstituentima izazvana 13C- i 1H-NMR hemijska pomeranja N(1)-(4-supstituisani fenil)-3-cijano-4,6-dimetil-2-piridona

The 13C- and 1H-NMR chemical shifts of thirteen N(1)-(4-substituted phenyl)-3-cyano-4,6-dimethyl-2-pyridones were measured in deuterated dimethyl sulfoxide (DMSO-d6). The correlation analysis for the substituent-induced chemical shifts (SCS) with σp, inductive (σI) and different scale of resonance (σR) parameters were performed using the SSP (single substituent parameter), DSP (dual substituent parameter) and DSP-NLR (dual substituent parameter-non-linear resonance) methods. The results of the calculations concerning the polar and resonance effects satisfactorily describe the substituent effects at the carbon atoms of interest. The mode of transmission of the substituent effects, both inductive and resonance, in relation to the geometry of the investigated pyridones is discussed.13C- i 1H-NMR hemijska pomeranja trinaest N(1)-(4-supstituisani fenil)-3-cijano- -4,6-dimetil-2-piridona su određena u deuterisanom dimetilsulfoksidu (DMSO-d6). Korelaciona analiza hemijskih pomeranja pojedinih ugljenikovih atoma ispitivanih jedinjenja izazvana prisutnim supstituentima (SCS) sa σp, induktivnim (σI) i različitim rezonancionim (σR) konstantama je izvršena korišćenjem SSP (monoparametarska), DSP (dvoparametarska) i DSP-NLR (dvoparametarska nelinearna) metoda. Rezultati korelacionih analiza na zadovoljavajući način opisuju efekte supstituenata za posmatrane ugljenikove atome. Diskutovan je način prenošenja efekata supstituenata, induktivnih i rezonancionih, u odnosu na geometriju ispitivanih molekula

Azo-hydrazone tautomerism of aryl azo pyridone dyes

In the last three or four decades disperse dyes derived from pyridones (in particular azo pyridone dyes) have gained in importance, and are widely used in various fields. These compounds have excellent coloration properties, and are suitable for the dyeing of polyester fabrics. Basic features of these dyes are simplicity of their synthesis by diazotation and azo coupling. They generally have high molar extinction coefficient with medium to high light and wet fastness. The absorption maxima of these dyes show their visible absorption wavelength ranging from yellow to orange, which can be attributed to poorly delocalized electrons in the pyridone ring. However, there are several dyes with deep colors such as red or violet. Pyridone dyes with alkyl and aryl groups in ortho position to azo group show 2-pyridone/2-hydroxypyridine tautomerism, while those containing OH and NHR groups conjugated with the azo group show azo-hydrazone tautomerism. Determining azo-hydrazone tautomerism could be therefore interesting, since the tautomers have different physico-chemical properties and most importantly different coloration. The literature on azo-hydrazone tautomerism, determination of equilibrium position, and investigation of substituent and solvent influence on tautomerism has been summarized in the presented review. The general conclusion is that the equilibrium between two tautomers is influenced by the structure of the compounds and by the solvents used. The tautomeric behavior patterns of the arylazo pyridone dyes in the reviewed literature has been studied using various instrumental techniques, including FT-IR, UV-vis, and NMR spectroscopy. The quantum chemical calculations related to the azo-hydrazon tautomerism have also been included. A large number of pyridone dyes exist in hydrazone form in solid state, while in solvents there is a mixture of tautomers. In addition, the X-ray single-crystal diffraction data analysis of some commercial pyridone dyes has been discussed concluding that they all crystallize in the hydrazone form

Synthesis, structure and solvatochromic properties of 3-cyano--4,6-diphenyl-5-(3- and 4-substituted phenylazo)-2-pyridones

Abstract: A series of some new pyridone arylazo dyes was synthesized from the corresponding diazonium salts and 3-cyano-4,6-diphenyl-2-pyridone using the classical reaction for the synthesis of the azo compounds. The structures of these dyes were confirmed by UV–Vis, FT-IR and 1 H-NMR spectroscopic techniques. The solvatochromism of the dyes was evaluated with respect to visible absorption properties in various solvents. The effects of solvent dipolarity/polarizability and solvent/solute hydrogen bonding interactions were analyzed by means of the linear solvation energy relationship concept proposed by Kamlet and Taft. The 2-pyridone/2-hydroxypiridine tautomeric equilibration was found to depend on the substituents as well as on the solvents

Synthesis, structure and solvatochromic properties of some novel 5-arylazo-6-hydroxy-4-(4-methoxyphenyl)-3-cyano-2-pyridone dyes: Hydrazone-azo tautomeric analysis

A series of eleven new 5-arylazo-6-hydroxy-4-(4-methoxyphenyl)-3-cyano-2-pyridone dyes was synthesized and their absorption spectra were recorded in twenty solvents in the range 300-600 nm. Different solvent parameters, such as microscopic solvent polarity, E-T(N), relative permittivity, epsilon(r), refractive index, n, the Kamlet-Taft and the Catalan parameters were used for the evaluation of the solute-solvent interactions and the solvatochromic shifts of the UV-vis absorption maxima of the hydrazone tautomeric form of the investigated arylazo pyridone dyes. The Catalan solvent scales are found to be the most suitable for describing the solvatochromic behavior of the dyes

N-(substituted phenyl)-2-chloroacetamides: LSER and LFER study

The UV absorption spectra of twelve N-(substituted phenyl)-2-chloroacetamides were recorded in eighteen solvents. The effect of specific and non-specific solvent-solute interactions on the absorption maxima shifts was evaluated by using the Kamlet-Taft solvent parameter set, i.e. applying linear solvation energy relationships (LSER) principles. Optimized geometries and experimental results were interpreted by using DFT (B3LYP/6-311+G(d,p) method) and time-dependent density functional (TD-DFT) method. Overall electron density in both ground and excited state was obtained by the use of Quantum Theory of Atoms in Molecules, i.e. Bader's analysis. It was found that both solvent and substituents cause appropriate change of the extent of conjugation in the molecules that further affect their intra-molecular charge transfer (ICT) character. Linear free energy relationships (LFERs) were applied to the substituent-induced NMR chemical shifts (SCS) using single substituent parameter (SSP) and dual substituent parameter (DSP) model. Transmission mode of the electronic effects of substituent was discussed according to the results of theoretical calculations and results of LFER correlations. Comparative analysis of presented results with the ones published for structurally similar series of amide which contained cyano group, instead chlorine, provides additional information on the impact of present group to the properties of investigated compound

Solvatochromism and azo-hydrazo tautomerism of novel arylazo pyridone dyes: Experimental and quantum chemical study

The state of the tautomeric equilibria of eleven arylazo pyridone dyes was evaluated from UV-Vis absorption spectra with the aid of the quantum mechanical modeling. NMR analysis and theoretical calculations, by using PCM/omega B97X-D/6-311G(d,p) method, confirmed that prepared compounds exist mainly in Hydrazo form. Internal hydrogen bonding in Hydrazo tautomer, analyzed by AIM topological analysis and total electron density at the bond critical point (BCP), confirmed a presence of strong hydrogen bond which contributes to higher stability of Hydrazo form. Linear solvation energy relationships (LSERs) rationalized solvent influence on solvatochromism of all compounds in Hydrazo form and K-T by using Kamlet-Taft model. Linear free energy relationships (LFERs) were applied to the substituent-inducedNMR chemical shifts (SCS) using SSP (single substituent parameter) and DSP (dual substituent parameter) model. Density plots over the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO) energy surface provide information on the charge transfer during excitation. The molecular electrostatic potential (MEP) surface map was plotted over the optimized geometry of the molecules in order to visualize electron density distribution and explain origin of solvent/solute interactions