Rainbow Connection Number and Radius

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) ≤  r(r + 2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (K _1,n for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) ≤  rk. Hitherto, the only reported upper bound on the rainbow connection number of bridgeless graphs is 4n/5 ? 1, where n is order of the graph (Caro et al. in Electron J Comb 15(1):Research paper 57, 13, 2008). It is known that computing rc(G) is NP-Hard (Chakraborty and fischer in J Comb Optim 1–18, 2009). Here, we present a (r + 3)-factor approximation algorithm which runs in O(nm) time and a (d + 3)-factor approximation algorithm which runs in O(dm) time to rainbow colour any connected graph G on n vertices, with m edges, diameter d and radius r.     

Highly Emissive Luminogens Based on Imidazo[1,2‐a]pyridine for Electroluminescent Applications

A search for novel organic luminogens led us to design and synthesize some N‐fused imidazole derivatives based on imidazo[1,2‐a]pyridine as the core and arylamine and imidazole as the peripheral groups. The fluorophores were synthesized through a multicomponent cascade reaction (A³ coupling) of a heterocyclic azine with an aldehyde and alkyne, followed by Suzuki coupling and a multicomponent cyclization reaction. All of the compounds exhibited interesting photophysical responses, especially arylamine‐containing derivatives, which displayed strong positive solvatochromism in the emission spectra that indicated a more polar excited state owing to an efficient charge migration from the donor arylamine to the imidazo[1,2‐a]pyridine acceptor. The quantum yields ranged from 0.2 to 0.7 and depended on the substitution pattern, most notably that based on the donor group at the C2 position. Moreover, the influence of general and specific solvent effects on the photophysical properties of the fluorophores was discussed with four‐parameter Catalán and Kamlet–Taft solvent scales. The excellent thermal, electrochemical, and morphological stability of the compounds was explored by cyclic voltammetry, thermogravimetric analysis, and AFM methods. Furthermore, to understand the structure, bonding, and band gap of the molecules, DFT calculations were performed. The performance of the electroluminescence behavior of the imidazo[1,2‐a]pyridine derivative was investigated by fabricating a multilayer organic light‐emitting diode with a configuration of ITO/NPB (60 nm)/EML (40 nm)/BCP (15 nm)/Alq₃ (20 nm)/LiF (0.5 nm)/Al(100 nm) (ITO=indium tin oxide, EML=emissive layer, BCP=2,9‐dimethyl‐4,7‐diphenyl‐1,10‐phenanthroline, Alq₃=tris(8‐hydroxyquinolinato)aluminum), which exhibited white emission with a turn‐on voltage of 8 V and a brightness of 22 cd m^?2.     

Organic-soluble tri-, tetra-, and pentanuclear titanium(IV) phosphates

Bulky 2,6-disubstituted aryl esters of phosphoric acid, 2,6-dimethylphenyl phosphate (dmppH 2), and 2,6-diisopropylphenyl phosphate (dippH 2) react differently with Cp*TiCl 3 (Cp* = C 5Me 5) under identical reaction conditions. While dippH 2 and Cp*TiCl 3 react in THF at 25 degrees C to yield air-stable trinuclear titanophosphate cage [(Ti 3Cp*Cl(mu 2 -O)(dipp) 2(dippH) 4(THF)].(toluene) ( 1), the similar reaction involving dmppH 2 yields the tetranuclear titanophosphate [Ti 4Cl 2(mu 2 -O) 2(dmpp) 2(dmppH) 6(THF) 2].(toluene) 2 ( 2). Interestingly, the change of titanium source to Ti(O iPr) 4 in the reaction with dippH 2 produces a pentanuclear titanophosphate, [Ti 5(mu 3-O)(O iPr) 6((dipp) 6(THF)] ( 3). Compounds 1- 3 were the only products isolated as single crystals from the respective reaction mixtures in 59, 75, and 54% yield, respectively. The new clusters 1- 3 have been characterized by elemental analysis, IR and NMR ( (1)H and (31)P) spectroscopy, and single crystal X-ray diffraction studies. The structural elucidation reveals that in the reactions leading to 1 and 2, extensive Cp*-Ti bond cleavage occurs, leaving only one residual Cp*-ligand in cluster 1 and none in 2. Closer analysis of the structures of 1- 3 shows common structural features which in turn imply that the formation of all three products could have proceeded via a common Ti-O-Ti dimeric building block.     

Cooperative binding of phosphate anion and a neutral nitrogen donor to alkaline-Earth metal ions. Investigation of group 2 metal-organophosphate interaction in the absence and presence of 1,10-phenanthroline

Alkaline-earth metal phosphates containing nitrogen-donor ligands have been prepared by the reaction of alkaline-earth metal acetates M(OAc) 2. xH 2O (M = Mg, Ca, Sr, Ba) with 2,6-diisopropylphenyl phosphate (dippH 2) in the absence and presence of 1,10-phenanthroline (phen). Interaction of strontium or barium acetate with dippH 2 in methanol at room temperature leads to the isolation of ionic phosphates [{M 2(mu-H 2O) 4(H 2O) 10}{dipp} 2].4L [M = Sr, L = CH 3OH ( 1); M = Ba, L = H 2O ( 2)]. The addition of a bidentate nitrogen-donor phen to these reactions leads to the isolation of dinuclear metal phosphates [Mg(dipp)(phen)(CH 3OH) 2] 2 ( 3) and [M(dippH) 2(phen) 2(H 2O)] 2 [M = Ca ( 4), Sr ( 5), Ba ( 6)]. While ionic phosphates 1 and 2 are soluble in water, the predominately covalent dimeric compounds 3- 6 are insoluble in all common solvents including water. The new compounds have been characterized in the solid state by elemental analysis, IR, UV-vis, and emission spectroscopy, and single-crystal X-ray diffraction studies. The cationic part in 1 and 2 is a {M 2(mu-H 2O) 4(H 2O) 10} unit, where each metal ion is surrounded by four bridging and five terminal water molecules as ligands. The dipp anion does not directly bind to the metal ions but is extensively hydrogen-bonded to the cationic unit through the phosphate oxygen and water hydrogen atoms to result in an infinitely layered structure where the hydrophobic aryl group protrudes out of the hydrophilic layer formed by the cationic part and -PO 3 (2-) units. In contrast, compounds 3- 6 are discrete dimeric molecules built around a central M 2O 4P 2 eight-membered ring. While the dippH 2 ligand exists in a doubly deprotonated form in 3, two monodeprotonated dippH 2 ligands are present per metal ion in compounds 4- 6. While 3 prefers only one phen ligand in the metal coordination sphere, two phen ligands chelate each metal ion in 4- 6. The conformations of the eight-membered rings in 3- 6 vary significantly from each other depending on the size of the cation and the coordination number around the metal. Further, intermolecular hydrogen bonding involving the phenanthroline C-H linkages result, in a gridlike structure in 1, one-dimensional chains in isostructural 2 and 3, and a two-dimensional layer arrangement in 4. Compounds 3- 6 are the only examples of alkaline-earth metal phosphate complexes with neutral M-N donor bonds. The thermal behavior of compounds 1- 6 has been examined with the help of thermogravimetric analysis and differential scanning calorimetry and also by bulk thermolysis followed by powder X-ray diffraction measurements. While compounds 1 and 2 yield M 2P 2O 7, decomposition of 4- 6 results in the formation of M(PO 3) 2, consistent with the M-P ratio in the precursor complexes.     

A simple and efficient method for the synthesis of amidophenols using iodine as catalyst under neat condition

A convenient and efficient one-pot synthesis of substituted amidophenols using iodine as catalyst at room temperature under neat condition is described.     

Investigation on lithium ion conductivity and structural stability of yttrium-substituted Li<Subscript>7</Subscript>La<Subscript>3</Subscript>Zr<Subscript>2</Subscript>O<Subscript>12</Subscript>

Advanced Li-air battery architecture demands a high Li⁺ conductive solid electrolyte membrane that is electrochemically stable against metallic lithium and aqueous electrolyte. In this work, an investigation has been carried out on the microstructure, Li⁺ conduction behaviour and structural stability of Li₇La_3-x Y _x Zr₂O₁₂ (x = 0.125, 0.25 and 0.50) prepared by conventional solid-state reaction technique. The phase analysis of Li₇La_3-x Y _x Zr₂O₁₂ (x = 0.125, 0.25 and 0.50) sintered at 1200 °C by powder X-ray diffraction (PXRD) and Raman confirms the formation of high Li⁺ conductive cubic phase (\( Ia\overline{3}d \)) lithium garnets. Among the investigated lithium garnets, Li₇La_2.75Y_0.25Zr₂O₁₂ sintered at 1200 °C exhibits a maximized room temperature total (bulk + grain boundary) Li⁺ conductivity of 3.21 × 10^?4 S cm^?1 along with improved relative density of 96 %. The preliminary investigation on the structural stability of Li₇La_2.75Y_0.25Zr₂O₁₂ in the solutions of 1 M LiCl, dist. H₂O and 1 M LiOH at 30 °C/50 °C indicates that the Li₇La_2.75Y_0.25Zr₂O₁₂ is relatively stable against 1 M LiCl and dist. H₂O. Further electrochemical investigation is essential for practical application of Li₇La_2.75Y_0.25Zr₂O₁₂ as protective solid electrolyte membrane in aqueous Li-air battery.     

Facile one-pot synthesis of functionalized organophosphonate esters via ketone insertion into bulky arylphosphites

The reaction of phosphorus trichloride with 2,6-diisopropyl phenol in the presence of LiCl under reflux conditions for 24 h produces a mixture of (ArO)PCl₂ and (ArO)₂PCl (Ar = 2,6-iPr₂C₆H₃). The hydrolysis of the aryloxy compounds in acetone/H₂O results in the formation of two novel phosphonate ester derivatives [(ArO)P(O)(OH)(CMe₂OH)] (1) and [(ArO)₂P(O)(CMe₂OH)] (2), respectively in a moderate yield. The title compounds have presumably formed via acetone insertion to the P-H bonds of (ArO)P(O)(H)(OH) and (ArO)₂P(O)(H), respectively, in the presence of HCl produced during the hydrolysis. Compounds 1 and 2 have been characterized by elemental analysis, and ESI-mass, Infrared and NMR spectroscopic techniques. Further, solid state structures of 1 and 2 have been established by single crystals X-ray diffraction studies.     

CONFIRM: connecting fragments found in receptor molecules

A novel algorithm for the connecting of fragment molecules is presented and validated for a number of test systems. Within the CONFIRM (Connecting Fragments Found in Receptor Molecules) approach a pre-prepared library of bridges is searched to extract those which match a search criterion derived from known experimental or computational binding information about fragment molecules within a target binding site. The resulting bridge 'hits' are then connected, in an automated fashion, to the fragments and docked into the target receptor. Docking poses are assessed in terms of root-mean-squared deviation from the known positions of the fragment molecules, as well as docking score should known inhibitors be available. The creation of the bridge library, the full details and novelty of the CONFIRM algorithm, and the general applicability of this approach within the field of fragment-based de novo drug design are discussed.