Linear response coupled cluster singles and doubles approach with modified spectral resolution of the similarity transformed Hamiltonian

This paper discusses practical scheme for correcting the linear response coupled cluster with singles and doubles (CCSD) equations by shifting the poles corresponding to the equation-of-motion CCSD excitation energies by adding noniterative corrections due to triples. A simple criterion is derived for the excited states to be corrected in the spectral resolution of similarity transformed Hamiltonian on the CCSD level. Benchmark calculations were performed to compare the accuracies of static and dynamic polarizabilities obtained in this way with the CC3 and CCSDT counterparts.     

Tailoring Properties of Resol Resin-Derived Spherical Carbons for Adsorption of Phenol from Aqueous Solution

The polycondensation of resorcinol and formaldehyde in a water–ethanol mixture using the adapted Stöber method was used to obtain resol resins. An optimization of synthesis conditions and the use of an appropriate stabilizer (e.g., poly(vinyl alcohol)) resulted in spherical grains. The resins were carbonized in the temperature range of 600–1050 °C and then chemically activated in an aqueous HNO₃ solution, gaseous ammonia, or by an oxidation–reduction cycle (soaking in a HNO₃ solution followed by treatment with NH₃). The obtained carbons were characterized by XRD, the low-temperature adsorption of nitrogen, SEM, TGA, and XPS in order to determine degree of graphitization, porosity, shape and size of particles, and surface composition, respectively. Finally, the materials were tested in phenol adsorption. The pseudo-second order model perfectly described the adsorption kinetics. A clear correlation between the micropore volume and the adsorption capacity was found. The content of graphite domains also had a positive effect on the adsorption properties. On the other hand, the presence of heteroatoms, especially oxygen groups, resulted in the clogging of the pores and a decrease in the amount of adsorbed phenol.     

Highly recoverable pyridinium-tagged Hoveyda-Grubbs pre-catalyst for olefin metathesis. Design of the boomerang ligand toward the optimal compromise between activity and reusability

Whereas the boomerang ligand of Hoveyda-Grubbs pre-catalysts can be modified by attachment of a pyridinium tag to its benzylidene moiety, a precise adjustment of the length of the spacer allows the optimum balance to be reached between the activity of the catalyst and its recoverability, exceeding 98% after 6 catalytic runs in the best case.     

Novel Pirkle-type quinine 3,5-dinitrophenylcarbamate chiral stationary phase implementing click chemistry

A new Pirkle-anion exchange hybrid-type chiral stationary phase (CSP-1) has been synthesized by immobilizing 10,11-didehydroquinine 3,5-dinitrophenylcarbamate onto 3-azidopropyl silica gel using click chemistry (1,3-dipolar Huisgen cycloaddition). This chiral selector and CSP contain a strong π-accepting 3,5-dinitrophenyl residue besides the π-basic quinoline group and an ionizable tertiary amino group. In concert with ion pairing it offers π-donor-π-acceptor interactions resulting in an enhancement of the selectivity toward specific π-donating analytes such as aryloxypropionic acids and profens. A representative set of these analytes has been investigated under various chromatographic conditions (polar-organic, reversed- and normal-phase) leading to base-line enantioseparations with selectivity (α) values up to 1.8. Control experiments with related quinine tert-butylcarbamate phase grafted onto the surface either by thioether (Chiralpak QN-AX) or 1,2,3-triazole linker revealed the impact of the additional aromatic moiety in the chiral selector motif.     

Combinatorics of Generalized Bethe Equations

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over ${\mathbb{Z}^M}$ Z M , and on the other hand, they count integer points in certain M-dimensional polytopes.     

Classification of singular ℚ-homology planes. I. Structure and singularities

A ?-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for ?-homology planes with smooth locus of non-general type. We show, in particular, that if a ?-homology plane contains a non-quotient singularity, then it is a quotient of an affine cone over a projective curve by an action of a finite group respecting the set of lines through the vertex. In particular, it is contractible, has negative Kodaira dimension and only one singular point. We describe minimal normal completions of such planes.     

Evolution of curves on a surface driven by the geodesic curvature and external force

We study a flow of closed curves on a given graph surface driven by the geodesic curvature and external force. Using vertical projection of surface curves to the plane we show how the geodesic curvature-driven flow can be reduced to a solution of a fully nonlinear system of parabolic differential equations. We show that the flow of surface curves is gradient-like, i.e. there exists a Lyapunov functional nonincreasing along trajectories. Special attention is placed on the analysis of closed stationary surface curves. We present sufficient conditions for their dynamic stability. Several computational examples of evolution of surface curves driven by the geodesic curvature and external force on various surfaces are presented in this article. We also discuss a link between the geodesic flow and the edge detection problem arising from the image segmentation theory.