Ultrafast spectroscopy and computational study of the photochemistry of diphenylphosphoryl azide: direct spectroscopic observation of a singlet phosphorylnitrene

The photochemistry of diphenylphosphoryl azide was studied by femtosecond transient absorption spectroscopy, by chemical analysis of light-induced reaction products, and by RI-CC2/TZVP and TD-B3LYP/TZVP computational methods. Theoretical methods predicted two possible mechanisms for singlet diphenylphosphorylnitrene formation from the photoexcited phosphoryl azide. (i) Energy transfer from the (π,π*) singlet excited state, localized on a phenyl ring, to the azide moiety, thereby leading to the formation of the singlet excited azide, which subsequently loses molecular nitrogen to form the singlet diphenylphosphorylnitrene. (ii) Direct irradiation of the azide moiety to form an excited singlet state of the azide, which in turn loses molecular nitrogen to form the singlet diphenylphosphorylnitrene. Two transient species were observed upon ultrafast photolysis (260 nm) of diphenylphosphoryl azide. The first transient absorption, centered at 430 nm (lifetime (τ) ～ 28 ps), was assigned to a (π,π*) singlet S(1) excited state localized on a phenyl ring, and the second transient observed at 525 nm (τ ～ 480 ps) was assigned to singlet diphenylphosphorylnitrene. Experimental and computational results obtained from the study of diphenyl phosphoramidate, along with the results obtained with diphenylphosphoryl azide, supported the mechanism of energy transfer from the singlet excited phenyl ring to the azide moiety, followed by nitrogen extrusion to form the singlet phosphorylnitrene. Ultrafast time-resolved studies performed on diphenylphosphoryl azide with the singlet nitrene quencher, tris(trimethylsilyl)silane, confirmed the spectroscopic assignment of singlet diphenylphosphorylnitrene to the 525 nm absorption band.     

Efficient Approximation Algorithms for Tiling and Packing Problems with Rectangles

We provide improved approximation algorithms for several rectangle tiling and packing problems (RTILE, DRTILE, and d-RPACK) studied in the literature. Most of our algorithms are highly efficient since their running times are near-linear in the sparse input size rather than in the domain size. In addition, we improve the best known approximation ratios.     

Identities for minors of the Laplacian, resistance and distance matrices

It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D, up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q-analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse.     

Faster least squares approximation

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n >> d{n \gg d}. Then, existing exact methods find a solution vector in O(nd ²) time. We present two randomized algorithms that provide accurate relative-error approximations to the optimal value and the solution vector of a least squares approximation problem more rapidly than existing exact algorithms. Both of our algorithms preprocess the data with the Randomized Hadamard transform. One then uniformly randomly samples constraints and solves the smaller problem on those constraints, and the other performs a sparse random projection and solves the smaller problem on those projected coordinates. In both cases, solving the smaller problem provides relative-error approximations, and, if n is sufficiently larger than d, the approximate solution can be computed in O(nd ln d) time.     

Structural Elucidation and Position Identification of Cu(II) ion in Hexaaquazinc(diaquabismalonto)zincate: Single Crystal EPR and Optical Studies

Journal of Cluster Science - Single crystal electron paramagnetic resonance (EPR), powder X-ray diffraction (XRD), Fourier transform-infrared (FT-IR) and UV–Visible (UV–Vis)...     

Use of threshold activation technique in estimating energy distributions of accelerator produced neutrons

A study of effective implementation of threshold activation technique for neutron spectral analysis in the environment of an alpha-cyclotron target is presented. The activation data are analysed using LOUHI-82 code. Optimal choices of the regularization parameters of the code are studied and discussed. Energy distribution of neutrons emitted from thick targets of Be, C and Ta irradiated by 40–45 MeV alphas is discussed.     

On cardioactive steroids. Communication XV. A stereoselective synthesis of (21R)-21-methyldigitoxigenin,a fully active cardenolide with a wide margin of safety: A contribution to the topology of the Digitalis receptors

Two efficient preparations of the title compound, one from common C₁₉-steroids, the other frm digitoxigenin, are described. The less active minor epimer (21S)-methyldigitoxigenin was also obtained and characterized. The positive inotropic effects and margins of safety of the two C(21)-epimers (tested as glucosides) are discussed in terms of the topological properties of the Digitalis receptors.     

Calixarenes. II. The isolation and characterization of the calix[4]arene and the bishomooxacalix[4]arene from A p-t-butylphenol-formaldehyde condensation product

The base-catalyzed condensation of p-tbutylphenol and formaldehyde, which yields a cyclic octamer (I, n=8) as the major product, has been shown to also yield a cyclic tetramer (I, n=4) and a bischomooxa cyclic tetramer (II).     

High pressure pyrolysis of toluene. 2. Modeling benzyl decomposition and formation of soot precursors

The pyrolysis of toluene, the simplest methyl-substituted aromatic molecule, has been studied behind reflected shock waves using a single pulse shock tube. Part 1 in this two-part series focused on the high-pressure experimental results and the high-pressure limiting rate coefficients for the primary steps in toluene decomposition. The present work focuses on the modeling of benzyl decomposition and the growth of key soot precursors (C2H2, C4H2, C8H6, and indene) from toluene pyrolysis with 81 among the 262 reactions in the detailed toluene model representing the chemistry that describes the formation and decomposition of these species. Feasible pathways for benzyl decomposition as well as phenylacetylene and indene formation have been tested. The simulations also show very good agreement with the single pulse shock tube profiles for the growth of key soot precursors such as C2H2, C4H2, C8H6, and indene.