On a Polynomial Fractional Formulation for Independence Number of a Graph

In this paper we characterize the local maxima of a continuous global optimization formulation for finding the independence number of a graph. Classical Karush-Kuhn-Tucker conditions and simple combinatorial arguments are found sufficient to deduce several interesting properties of the local and global maxima. These properties can be utilized in developing new approaches to the maximum independent set problem.     

2,3,4,5,6‐Penta­nitro­aniline 1,2‐dichloro­ethane disolvate: `push–pull' deformation of aromatic rings by intra­molecular charge transfer

The title compound, C₆H₂N₆O₁₀·2C₂H₄Cl₂, forms layered stacks of penta­nitro­aniline mol­ecules, which possess twofold symmetry. The voids between these stacks are occupied by dichloro­ethane mol­ecules, which reside near a 2/m symmetry element and display pseudo‐inversion symmetry. The C atoms in one of the two solvent mol­ecules are threefold disordered. In the penta­nitro­aniline mol­ecule, considerable distortion of the benzenoid ring, coupled with the short C—N(H₂) bond and out‐of‐plane NO₂ twistings, point to significant intra­molecular `push–pull' charge transfer at the amino‐ and nitro‐substituted (ortho and para) positions, as theoretically quantified by natural bond orbital analysis of the π‐electron density.     

Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly

Nanoscale uniform films containing gold nanoparticle and polyelectrolyte multilayer structures were fabricated by the using spin-assembly or spin-assisted layer-by-layer (SA-LbL) deposition technique. These SA-LbL films with a general formula [Au/(PAH-PSS)nPAH]m possessed a well-organized microstructure with uniform surface morphology and high surface quality at a large scale (tens of micrometers across). Plasmon resonance peaks from isolated nanoparticles and interparticle interactions were revealed in the UV-visible extinction spectra of the SA-LbL films. All films showed the strong extinction peak in the region of 510-550 nm, which is due to the plasmon resonance of the individual gold nanoparticles redshifted because of a local dielectric environment. For films with sufficient density of gold nanoparticles within the layers, the second strong peak was consistently observed between 620 and 660 nm, which is the collective plasmon resonance from intralayer interparticle coupling. Finally, we suggested that, for certain film designs, interlayer interparticle resonance might be revealed as an independent contribution at 800 nm in UV-visible spectra. The observation of independent and concurrent individual, intralayer, and interlayer plasmon resonances can be critical for sensing applications, which involve monitoring of optomechanical properties of ultrathin optically active compliant membranes.     

Photochemical structuring and fixing of structures in binary polymer brush layers via 2pi+2pi photodimerization

Binary polymer brushes grafted to Si wafers were prepared from hydrophilic and hydrophobic polymer components, which allow switching the surface properties (as revealed by contact angles) by exposure to varying solvents. The hydrophilic component was poly-2-vinylpyridine; the hydrophobic component was a copolymer of styrene and 2-(4-vinylphenyl)indene containing the photodimerizable phenylindene chromophore. The brushes were prepared via thermal and via photochemical grafting-to methods, which led to distinct layer thicknesses. Structural patterns differing in surface properties were produced and fixed via crosslinking the hydrophobic component by 2pi+2pi photodimerization of phenylindene moieties. The patterns were visually observable.     

Alkylation of 3‐Phenyl‐1H‐pyrazolo[4,3‐c] quinoline: Theoretical Analysis of Regioselectivity

The interaction of 3‐phenyl‐1H‐pyrazolo[4.3‐c]quinoline with alkylating agents in the presence of NaH leads mainly to N1‐substituted derivatives. The regioselectivity of the reaction has been studied using AM1 semi‐empirical calculations in the isolated molecule approximation.     

Experimental and Computational Probes of the Nature of Halogen Bonding: Complexes of Bromine‐Containing Molecules with Bromide Anions

The nature of halogen bonding is examined via experimental and computational characterizations of a series of associates between electrophilic bromocarbons R? Br (R? Br=CBr₃F, CBr₃NO₂, CBr₃COCBr₃, CBr₃CONH₂, CBr₃CN, etc.) and bromide anions. The [R? Br, Br^?] complexes show intense absorption bands in the 200–350 nm range which follow the same Mulliken correlation as those observed for the charge‐transfer associates of bromide anions with common organic π‐acceptors. For a wide range of the associates, intermolecular R? Br???Br^? separations decrease and intramolecular C? Br bond lengths increase proportionally to the Br^?→R? Br charge transfer; and the energies of R? Br???Br^? bonds are correlated with the linear combination of orbital (charge‐transfer) and electrostatic interactions. On the whole, spectral, structural and thermodynamic characteristics of the [R? Br, Br^?] complexes indicate that besides electrostatics, the orbital (charge‐transfer) interactions play a vital role in the R? Br???Br^? halogen bonding. This indicates that in addition to controlling the geometries of supramolecular assemblies, halogen bonding leads to electronic coupling between interacting species, and thus affects reactivity of halogenated molecules, as well as conducting and magnetic properties of their solid‐state materials.     

Synthesis,antiradical, and antimicrobial activities of new pteridine-2,4,7-trione derivatives

The synthesis of 6-(2-hydroxy-2-aryl (heteryl)ethyl)-1-methylpteridine-2,4,7(1H,3H,8H)-triones by the reduction of the corresponding ketones and the peculiarities of conversion of the synthesized alcohols to (E)-1-methyl-6-(2-aryl (heteryl)ethenyl)pteridine-2,4,7(1H,3H,8H)-triones was reported. The mechanism of monomolecular elimination that occurred in the presence of hydrogen halides was discussed, namely, the competitive formation of an energy-efficient conjugated system by deprotonation of a stable benzyl-type carbocation. Alternative synthesis methods of pteridine-2,4,7(1H,3H,8H)-triones were developed. Abovementioned approach involved [4+2]-cyclocondensation of 1-methyl-5,6-diaminouracil to 2-oxo-4-R-but-3-enoic acids and Knoevenagel condensation of 1,6-dimethylpteridine-2,4,7(1H,3H,8H)-trione with aromatic aldehydes. The antiradical, antimicrobial, and antifungal activities were studied for the synthesized compounds.     

Sulfonimidamides and Imidosulfuric Diamides: Compounds from an Underexplored Part of Biologically Relevant Chemical Space

Two novel solid reagents—1-sulfonimidoyl- and 1-sulfamimidoyl-3-methylimidazolium derivatives—for the synthesis of sulfonimidamides and imidosulfuric diamides, respectively, were developed. It is shown that these reagents are very effective in substitution reactions with various N- and O-nucleophiles; therefore, they significantly extend the accessibility to the chemical space covered by organosulfur(VI) compounds with S=N bonds. In addition, previously unknown imidosulfuric diamides with free imino nitrogen groups were prepared, and their physical and chemical properties were characterized (including molecular geometry, pK_a, Log P, microsomal stability, and reactivity towards typical electrophiles). Similar to other organosulfur(VI) derivatives with S=N bonds, these compounds can be considered as promising bioisosteres of amides, ureas, or sulfonamides.