Boundary triplets and generalized resolvents of isometric operators in a Pontryagin space

The notions of the boundary triplet of an isometric operator V in the Pontryagin space and the corresponding function Weyl are introduced. Proper extensions of the isometric operator V, their spectra, and canonical and generalized resolvents of the operator V are described.     

Modulation of excited-state intramolecular proton transfer by viscosity in protic media

3-Hydroxyquinolones undergo excited-state intramolecular proton transfer (ESIPT), resulting in a dual emission highly sensitive to H-bonding perturbations. Here, we report on the strong effect of viscosity on the dual emission of 2-(2-thienyl)-3-hydroxyquinolone in protic solvents. An increase in viscosity significantly decreases the formation of the ESIPT product, thus changing dramatically the ratio of the two emission bands. Time-resolved studies suggest the presence of solvated species characterized by decay times close to the solvent relaxation times in viscous media. The intramolecular H bond in this species is probably disrupted by the solvent, and therefore, its ESIPT requires a reorganization of the solvation shell for restoring this intramolecular H bond. Thus, the ESIPT reaction of this dye and its dual emission depend on solvent relaxation rates and, therefore, on viscosity. The present results suggest a new physical principle for the fluorescence ratiometric measurement of local viscosity.     

An investigation into the initial degradation steps of four major dye chromophores: study of their one-electron oxidation and reduction by EPR, ENDOR, cyclic voltammetry, and theoretical calculations

The degradation of dyes is frequently initiated by one-electron oxidation or reduction; however, relatively little is known about the initially formed radicals. Acid Green 25 (AG25), Crystal Violet (CVI), Methylene Blue (MB), and Acid Orange 7 (AO7), representing paradigms of four types of commercial organic dyes, were therefore investigated in terms of their redox behavior. Their redox potentials in MeCN and buffered aqueous solutions were determined by cyclic voltammetry. The structures of the one-electron reduced and oxidized dyes were established by EPR spectroscopy and by theoretical calculations on the density functional level of theory.     

An efficient method for the transformation of 5-ylidenerhodanines into 2,3,5-trisubstituted-4-thiazolidinones

The use of 3-substituted-2-mercaptoacrylic acids, synthesized via hydrolysis of 5-ylidenerhodanines for the preparation of 2,3,5-trisubstituted-4-thiazolidinones via a new variant of the one-pot, three-component reaction has been studied.     

Rapid Ti(Oi-Pr)4 facilitated synthesis of α,α,α-trisubstituted primary amines by the addition of Grignard reagents to nitriles under microwave heating conditions

A series of carbinamines (α,α,α-trisubstituted amines) have been prepared in a simple and efficient one-pot procedure by the addition of Grignard reagents to a series of aliphatic, aromatic and heteroaromatic nitriles. The resulting magnesium imines are subsequently converted to the desired amine after treatment with Ti(Oi-Pr)₄ and additional microwave heating. Key to this procedure is the use of microwave heating for both steps of the reaction protocol, which significantly improves both reaction yields and reduces reaction times. In general, the Grignard addition reaction is complete within 5-10 min at 100 °C followed by conversion with Ti(Oi-Pr)₄ and additional microwave heating to give the target amines in good yields.     

Single-pulse multiphoton fabrication of high aspect ratio structures with sub-micron features using vortex beams

Single ultra-short pulses from Gaussian and vortex beams have been used for the fabrication of complex micro-structures via multi-photon polymerization. The complexity of the resultant micro-structures stems from the modification of both transverse intensity and phase profiles of these single pulses to create modulated scaffolds and hollow cylinders. Experimental results are compared to theoretical models, and good agreement is shown.     

Efficient implementation of the analytic second derivatives of Hartree–Fock and hybrid DFT energies: a detailed analysis of different approximations

In this paper, various implementations of the analytic Hartree–Fock and hybrid density functional energy second derivatives are studied. An approximation-free four-centre implementation is presented, and its accuracy is rigorously analysed in terms of self-consistent field (SCF), coupled-perturbed SCF (CP-SCF) convergence and prescreening criteria. The CP-SCF residual norm convergence threshold turns out to be the most important of these. Final choices of convergence thresholds are made such that an accuracy of the vibrational frequencies of better than 5 cm^?1 compared to the numerical noise-free results is obtained, even for the highly sensitive low frequencies (<100–200 cm^?1). The effects of the choice of numerical grid for density functional exchange–correlation integrations are studied and various weight derivative schemes are analysed in detail. In the second step of the work, approximations are introduced in order to speed up the computation without compromising its accuracy. To this end, the accuracy and efficiency of the resolution of identity approximation for the Coulomb terms and the semi-numerical chain of spheres approximation to the exchange terms are carefully analysed. It is shown that the largest performance improvements are realised if either Hartree–Fock exchange is absent (pure density functionals) and otherwise, if the exchange terms in the CP-SCF step of the calculation are approximated by the COSX method in conjunction with a small integration grid. Default values for all the involved truncation parameters are suggested. For vancomycine (176 atoms and 3593 basis functions), the RIJCOSX Hessian calculation with the B3LYP functional and the def2-TZVP basis set takes ～3 days using 16 Intel® Xeon® 2.60GHz processors with the COSX algorithm having a net parallelisation scaling of 11.9 which is at least ～20 times faster than the calculation without the RIJCOSX approximation.     

Ultrametricity and metric betweenness in tangent spaces to metric spaces

The paper deals with pretangent spaces to general metric spaces. An ultrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.