Oblong Mean Prime Labeling of Some Snake Graphs

A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. The graph for which every edge(uv),the labels assigned to u and v are oblong numbers and for each vertex of degree at least 2, the g c d of the labels of the incident edges is 1. Here we characterize some snake graphs for oblong mean prime labeling

Square Sum Difference Product Prime Labeling of Some Tree Graphs

Square sum difference product prime labeling of a graph is the labeling of the vertices with {0,1,2---------,p-1} and the edges with absolute difference of the sum of the squares of the labels of the incident vertices and product of the labels of the incident vertices. The greatest common incidence number of a vertex (gcin) of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is one, then the graph admits square sum difference product prime labeling. In this paper we investigate some tree graphs for square sum difference product prime labeling

Hexagonal Difference Prime Labeling of Some Path Graphs

Hexagonal difference prime labeling of vertices of a graph is the labeling of the vertices of the graph with hexagonal numbers and the edges with absolute value of the difference of the labels of the incident vertices. The greatest common incidence number (gcin) of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits hexagonal difference prime labeling.  Here we identify some path related graphs for hexagonal difference prime labeling

Some Results on Reciprocal Subtangent in the Context of Weighted Models

Recently, reciprocal subtangent has been used as a useful tool to describe the behaviour of a density curve. Motivated by this, in the present article we extend the concept to the weighted models. Characterization results are proved for models viz. gamma, Rayleigh, equilibrium, residual lifetime, and proportional hazards. An identity under weighted distribution is also obtained when the reciprocal subtangent takes the form of a general class of distributions. Finally, an extension of reciprocal subtangent for the weighted models in the bivariate and multivariate cases are introduced and proved some useful resultsCochin University of Science and TechnologyCommunications in Statistics—Theory and Methods, 41: 1397–1410, 201

Directing group assisted meta-hydroxylation by C-H activation

meta-Hydroxylated cores are ubiquitous in natural products. Herein, we disclose the first template assisted meta-hydroxylation reaction. Experimental and in silico studies helped us to gain valuable mechanistic insights, including the role of the hexafluoroisopropanol (HFIP) solvent, during C-H hydroxylation. The reactive intermediates, prior to the C-H activation, have been detected by spectroscopic techniques. Additionally, the C-O bond formation has been extended to meta-acetoxylation. The preparation of a phase II quinone reductase activity inducer and a resveratrol precursor illustrated the synthetic significance of the present strategy

Intramolecular interactions between chalcogen atoms: organoseleniums derived from 1-bromo-4-tert-butyl-2,6-di(formyl)benzene

The synthesis and characterization of a series of low-valent organoselenium compounds derived from 1-bromo-4-tert-butyl-2,6-di(formyl)benzene (22) is described. The synthesis of diselenide 25 was achieved by the lithiation route whereas bis(4-tert-butyl-2,6-di(formyl)phenyl) diselenide (26) was synthesized by treating 22 with disodium diselenide. A series of monoselenides (27, 28, and 29) was obtained by facile nucleophilic substitution of bromine in 22, using the corresponding selenolates as nucleophiles. The halogenation reactions of bis(4-tert-butyl-2,6-di(formyl)phenyl) diselenide (26) did not afford the corresponding selenenyl halides but resulted in the isolation of an unexpected cyclic selenenate ester 34 as a product. The selenide 32 was synthesized by the treatment of dimethoxymethyl diselenide with trilithiated 2-bromo-5-tert-butyl-N,N'-di(phenyl)isophthalamide. The existence of potential Se···O intramolecular nonbonding interactions was examined by IR, 1H, and 77Se NMR spectroscopy, X-ray crystallography, and computational studies. The X-ray crystal structures of 26 and 27, having two ortho formyl groups, reveal the absence of any Se···O interactions. However, the Se···O interactions were observed in the selenenate ester 34 where one of the formyl groups has been utilized for the selenenate ring formation. The crystal structures of 26 and 27 exhibited intermolecular short-range C-H···Se interactions (hydrogen bonding). Although there are four heteroatoms in carbamoyl moieties ortho to selenium capable of forming a five-membered ring on intramolecular coordination, no such intramolecular Se···X (X=N, O) interaction was observed in the crystal structure of 32. The density functional theory calculations at the B3LYP/6-31G∗ level predicted that for all the diformyl systems (47a-c, 48a-c), the anti,anti conformer (when both formyl oxygen atoms point away from the selenium) is more stable. This preference was found to be reversed in the monoformyl-substituted systems (50a,b, 51a,b), where the syn conformer (when formyl oxygen is near the selenium) is energetically more favorable than the anti conformer

Controlling chemistry with cations: photochemistry within zeolites

The alkali ions present in the supercages of zeolites X and Y interact with included guest molecules through quadrupolar (cation-π), and dipolar (cation-carbonyl) interactions. The presence of such interactions can be inferred through solid-state NMR spectra of the guest molecules. Alkali ions, as illustrated in this article, can be exploited to control the photochemical and photophysical behaviors of the guest molecules. For example, molecules that rarely phosphoresce can be induced to do so within heavy cation-exchanged zeolites. The nature (electronic configuration) of the lowest triplet state of carbonyl compounds can be altered with the help of light alkali metal ions. This state switch (nΠ*-ΠΠ*) helps to bring out reactivity that normally remains dormant. Selectivity obtained during the singlet oxygen oxidation of olefins within zeolites illustrates the remarkable control that can be exerted on photoreactions with the help of a confined medium that also has active sites. The reaction cavities of zeolites, like enzymes, are not only well-defined and confined, but also have active sites that closely guide the reactant molecule from start to finish. The examples provided here illustrate that zeolites are far more useful than simple shape-selective catalysts

Isomeric ruthenium terpyridine complexes [Ru(trpy)(L)Cl](n+) containing the unsymmetrically bidentate acceptor L=3-amino-6-(3,5-dimethylpyrazol-1-yl)-1,2,4,5-tetrazine. Synthesis, structures, electrochemistry, spectroscopy and DFT calculations

The isomeric title complexes were obtained in almost equimolar ratio from the reaction of Ru(trpy)Cl-3 and L. Crystal structure analyses of the perchlorate hemihydrates, electrochemical and spectroscopic (NMR, UV/VIS, EPR) studies, supported by DFT calculations, reveal distinct differences between the isomeric redox series [1](n+) (tetrazine-N-t trans to Cl) and [2](n+) (pyrazolyl-N-p trans to Cl; n = 0, 1, 2). The latter system with the pi acceptors trpy and tetrazine in the equatorial plane and the pyrazolyl and chloride donors in the axial positions exhibits facilitated oxidation, lower energy MLCT transitions, more balanced chelate coordination, and a higher g anisotropy in the oxidised (Ru-III) state. According to partially resolved EPR spectra of one-electron reduced neutral compounds 1 and 2 they have the unpaired electron predominantly in the tetrazine ring of L

Mixed-valent metals bridged by a radical ligand: Fact or fiction based on structure-oxidation state correlations

Electron-rich Ru(acaC)(2) (acac(-) = 2,4-pentanedionato) binds to the pi electron-deficient bis-chelate ligands L, L = 2,2'-azobispyridine (abpy) or azobis(5-chloropyrimidine) (abcp), with considerable transfer of negative charge. The compounds studied, (abpy)Ru(acac)(2) (1), meso-(mu-abpy)[Ru(acaC)(2)](2) (2), rac-(mu-abpy)[Ru(acac)(2)](2) (3), and (mu-abcp)[Ru(acac)(2)](2) (4), were calculated by DFT to assess the degree of this metal-to-ligand electron shift. The calculated and experimental structures of 2 and 3 both yield about 1.35 angstrom for the length of the central N-N bond which suggests a monoanion character of the bridging ligand. The NBO analysis confirms this interpretation, and TD-DFT calculations reproduce the observed intense long-wavelength absorptions. While mononuclear 1 is calculated with a lower net ruthenium-to-abpy charge shift as illustrated by the computed 1.30 angstrom for d(N-N), compound 4 with the stronger pi accepting abcp bridge is calculated with a slightly lengthened N-N distance relative to that of 2. The formulation of the dinuclear systems with monoanionic bridging ligands implies an obviously valence-averaged (RuRuII)-Ru-III mixed-valent state for the neutral molecules. Mixed valency in conjunction with an anion radical bridging ligand had been discussed before in the discussion of MLCT excited states of symmetrically dinuclear coordination compounds. Whereas 1 still exhibits a conventional electrochemical and spectroelectrochemical behavior with metal centered oxidation and two ligand-based one-electron reduction waves, the two one-electron oxidation and two one-electron reduction processes for each of the dinuclear compounds Ru-2.5(L*(-))Ru-2.5 reveal more unusual features via EPR and UV-vis-NIR spectroelectrochemistry. In spite of intense near-infrared absorptions, the EPR results show that the first reduction leads to Ru-II(L*(-))Ru-II species, with an increased metal contribution for system 4*(-). The second reduction to Ru-II(L2-)Ru-II causes the disappearance of the NIR band. One-electron oxidation of the Ru-2.5(L*(-)) Ru-2.5 species produces a metal-centered spin for which the alternatives Ru-III(L-0)Ru-II or Ru-III(L*(-))Ru-III can be formulated: The absence of NIR bands as common for mixed-valent species with intervalence charge transfer (IVCT) absorption favors the second alternative. The second one-electron oxidation is likely to produce a dication with Ru-III(L-0)Ru-III formulation. The usefulness and limitations of the increasingly popular structure/oxidation state correlations for complexes with noninnocent ligands is being discussed