On clique relaxation models in network analysis

Increasing interest in studying community structures, or clusters in complex networks arising in various applications has led to a large and diverse body of literature introducing numerous graph-theoretic models relaxing certain characteristics of the classical clique concept. This paper analyzes the elementary clique-defining properties implicitly exploited in the available clique relaxation models and proposes a taxonomic framework that not only allows to classify the existing models in a systematic fashion, but also yields new clique relaxations of potential practical interest. Some basic structural properties of several of the considered models are identified that may facilitate the choice of methods for solving the corresponding optimization problems. In addition, bounds describing the cohesiveness properties of different clique relaxation structures are established, and practical implications of choosing one model over another are discussed.     

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.     

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.     

Complexation of calix[4]arenehydroxymethylphosphonic acids with amino acids. Binding constants determination of the complexes by HPLC method

Host–Guest complexation process of calixarenehydroxymethylphosphonic acids with 10 amino acids in solution H₂O/MeCN (99:1) had been studied. Binding constants of the inclusion complexes from the dependence between capacity factors of the Guest and the calixarene-Host concentration in the mobile phase had been calculated. It was shown the binding constants depend on the nature of the amino acid residue, conformation of the calixarene skeleton, quantity of phosphoryl groups at the upper rim. In accordance with molecular calculation the complexation is determined by the electrostatic interactions between the positively charged nitrogen atom of amino acid and the negatively charged oxygen atom of phosphonic group of calixarene molecule, hydrogen bonds, π–π, CH–π and solvatophobic, interactions.     

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.     

Conformational polymorphs of 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole

The dipharmacophore compound 3‐cyclopropyl‐5‐(3‐methyl‐[1,2,4]triazolo[4,3‐a]pyridin‐7‐yl)‐1,2,4‐oxadiazole, C₁₂H₁₁N₅O, was studied on the assumption of its potential biological activity. Two polymorphic forms differ in both their molecular and crystal structures. The monoclinic polymorphic form was crystallized from more volatile solvents and contains a conformer with a higher relative energy. The basic molecule forms an abundance of interactions with relatively close energies. The orthorhombic polymorph was crystallized very slowly from isoamyl alcohol and contains a conformer with a much lower energy. The basic molecule forms two strong interactions and a large number of weak interactions. Stacking interactions of the `head‐to‐head' type in the monoclinic structure and of the `head‐to‐tail' type in the orthorhombic structure proved to be the strongest and form stacked columns in the two polymorphs. The main structural motif of the monoclinic structure is a double column where two stacked columns interact through weak C—H…N hydrogen bonds and dispersive interactions. In the orthorhombic structure, a single stacked column is the main structural motif. Periodic calculations confirmed that the orthorhombic structure obtained by slow evaporation has a lower lattice energy (0.97 kcal mol^?1) compared to the monoclinic structure.     

Polymorphism of methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate: an experimental and theoretical study

Being a close analogue of amflutizole, methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate (C₁₁H₁₀N₂O₂S) was assumed to be capable of forming polymorphic structures. Noncentrosymmetric and centrosymmetric polymorphs have been obtained by crystallization from a series of more volatile solvents and from denser tetrachloromethane, respectively. Identical conformations of the molecule are found in both structures. The two polymorphs differ mainly in the intermolecular interactions formed by the amino group and in the type of stacking interactions between the π‐systems. The most effective method for revealing packing motifs in structures with intermolecular interactions of different types (hydrogen bonding, stacking, dispersion, etc.) is to study the pairwise interaction energies using quantum chemical calculations. Molecules form a column as the primary basic structural motif due to stacking interactions in both polymorphic structures under study. The character of a column (straight or zigzag) is determined by the orientations of the stacked molecules (in a `head‐to‐head' or `head‐to‐tail' manner). Columns bound by intermolecular N—H…O and N—H…N hydrogen bonds form a double column as the main structural motif in the noncentrosymmetric structure. Double columns in the noncentrosymmetric structure and columns in the centrosymmetric structure interact strongly within the ab crystallographic plane, forming a layer as a secondary basic structural motif. The noncentrosymmetric structure has a lower density and a lower (by 0.59 kJ mol^?1) lattice energy, calculated using periodic calculations, compared to the centrosymmetric structure.     

Halogen Bonding Between Anions: Association of Anion Radicals of Tetraiodo-p-benzoquinone with Iodide Anions

Halogen bonding between two negatively charged species, tetraiodo-p-benzoquinone anion radicals (I₄Q^−.) and iodide anions, was observed and characterized for the first time. X-ray structural and EPR/UV–Vis spectral studies revealed that the anion–anion bonding led to the formation of crystals comprising 2D layers of I₄Q^−. anion radicals linked by iodides and separated by Et₄N⁺ counter-ions. Computational analysis suggested that the seemingly antielectrostatic halogen bonds in these systems were formed via a combination of several factors. First, an attenuation of the interionic repulsion by the solvent facilitated close approach of the anions leading to their mutual polarization. This resulted in the appearance of positively charged areas (σ-holes) on the surface of the iodine substituents in I₄Q^−. responsible for the attractive interaction. Finally, the solid-state associations were also stabilized by multicenter (4:4) halogen bonding between I₄Q^−. and iodide.