Perfect divisibility and 2-divisibility

A graph G is said to be 2-divisible if for all (nonempty) induced subgraphs H of G, can be partitioned into two sets such that and . (Here denotes the clique number of G, the number of vertices in a largest clique of G). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, can be partitioned into two sets such that is perfect and . We prove that if a graph is -free, then it is 2-divisible. We also prove that if a graph is bull-free and either odd-hole-free or P₅-free, then it is perfectly divisible.     

Hyperpolarizability,Hirshfeld, and density functional theory computations of a nonlinear optical picrate

bis(2-nitroaniline) picrate (BNP) single crystals was grown by slow evaporation growth technique using mixed solvent system with methanol–acetone (1:1, v/v) at a constant temperature, and the structure was interpreted by single crystal X-ray, Power Diffraction (XRD) analysis. Inter- and intramolecular hydrogen bonding interactions were interpreted, and crystal cohesion was architectured by N-H···O, O-H···O, C-H···N, H···H, O···O, and π···π staking interactions. All intermolecular interactions occurring in the crystal lattice were calculated using fingerprint analysis. Interaction strengths were graphically illustrated by the Hirshfeld surface analysis. The band gap energy of BNP was estimated by the application of the Kubelka–Munk algorithm. Nonlinear optical behavior was confirmed by the Kurtz–Perry technique. Optimized geometry was derived by the density functional theory calculations. The first-order molecular hyperpolarizability (β) and excited state energies were estimated by the time-dependent density functional theory analysis.     

Thiol‐Directed Synthesis of Highly Fluorescent Gold Clusters and Their Conversion into Stable Imaging Nanoprobes

Fluorescent gold clusters (FGCs) with tunable emission from blue to red and quantum yields in the range of 6–17 % have been synthesized by simple modification of the conditions used for the synthesis of gold nanoparticles, namely by replacing the stronger reducing agent with a controlled amount of thiol. Various functional FGCs with hydrodynamic diameters of 5–12 nm have been successfully synthesized and used as cell labels. The results of our investigations strongly indicate that FGCs composed of Au⁰ are more stable imaging probes than commonly reported red/NIR‐emitting FGCs with a composition of Au⁰/Au^I, as this combination rapidly transforms into nonfluorescent large clusters on exposure to light. The FGC‐based nanoprobes reported herein exhibit stable fluorescence upon continuous light exposure and can be used as imaging probes with low cytotoxicity.     

Practical asymmetric synthesis of β-hydroxy γ-amino acids via complimentary aldol reactions

Orthogonally protected chiral β-hydroxy-γ-amino acids can be accessed in >100 g quantities from readily available starting materials and reagents in three to four steps. These chiral synthons contain two adjacent stereocenters along with suitably protected functional groups (O-TBS, N-Boc) for downstream reactivity. Implementation of two existing aldol technologies allows rapid access to all possible stereoisomers of 1. The guiding principles during reaction optimization were reaction scalability and operational efficiency. Conversion of the amino acids to a variety of chiral building blocks in one to two steps demonstrates their synthetic utility.     

Weinreb amide based building blocks for convenient access to 1,1-diarylethenes and isocombretastatin analogues

A successful strategy based on the synthetic equivalent containing Weinreb amide functionality for the convenient access to 1,1-diarylethenes in general and for the isocombretastatin analogues in particular has been developed from the commercially available glyoxalic acid. The convenience with which the structural variations can be made in assembling the aryl residues shows generality associated with the developed strategy. The intermediates also provide access to 1,2,2-triarylethanones, represented by the synthesis of advanced intermediate of tamoxifen.     

On the electron-induced isotope fractionation in low temperature (32)O(2)/(36)O(2) ices--ozone as a case study

The formation of six ozone isotopomers and isotopologues, (16)O(16)O(16)O, (18)O(18)O(18)O, (16)O(16)O(18)O, (18)O(18)O(16)O, (16)O(18)O(16)O, and (18)O(16)O(18)O, has been studied in electron-irradiated solid oxygen (16)O(2) and (18)O(2) (1?∶?1) ices at 11 K. Significant isotope effects were found to exist which involved enrichment of (18)O-bearing ozone molecules. The heavy (18)O(18)O(18)O species is formed with a factor of about six higher than the corresponding (16)O(16)O(16)O isotopologue. Likewise, the heavy (18)O(18)O(16)O species is formed with abundances of a factor of three higher than the lighter (16)O(16)O(18)O counterpart. No isotope effect was observed in the production of (16)O(18)O(16)O versus(18)O(16)O(18)O. Such studies on the formation of distinct ozone isotopomers and isotopologues involving non-thermal, non-equilibrium chemistry by irradiation of oxygen ices with high energy electrons, as present in the magnetosphere of the giant planets Jupiter and Saturn, may suggest that similar mechanisms may contribute to the (18)O enrichment on the icy satellites of Jupiter and Saturn such as Ganymede, Rhea, and Dione. In such a Solar System environment, energetic particles from the magnetospheres of the giant planets may induce non-equilibrium reactions of suprathermal and/or electronically excited atoms under conditions, which are quite distinct from isotopic enrichments found in classical, thermal gas phase reactions.     

Morphological study into the temperature dependence of solid ammonia under astrochemical conditions using vacuum ultraviolet and Fourier-transform infrared spectroscopy

The authors present the results of a morphological study of solid ammonia using both Fourier-transform infrared and vacuum ultraviolet (VUV) spectroscopy. Dramatic changes in the VUV and infrared spectra at temperatures between 65 and 85 K provide a deeper insight into the structure of ammonia ice particularly with the observation of an exciton transition at 194 nm (6.39 eV) in the VUV spectrum, revealing a structure that is composed of crystallites. A complementary structure is observed in the IR spectrum at 1100 cm(-1) which is assigned to the symmetric deformation of ammonia molecules at the surfaces of the crystallites. Such spectral signatures may be used to identify the environment within which the ammonia ice is formed and provide a new route for obtaining information on the physical and chemical conditions occurring within the interstellar medium, on the surfaces of planetary bodies, and in Kuiper belt objects.