Estimating the matrixp-norm

Summary The Hölderp-norm of anm×n matrix has no explicit representation unlessp=1,2 or . It is shown here that thep-norm can be estimated reliably inO(mn) operations. A generalization of the power method is used, with a starting vector determined by a technique with a condition estimation flavour. The algorithm nearly always computes ap-norm estimate correct to the specified accuracy, and the estimate is always within a factorn ^1–1/p of A _p . As a by-product, a new way is obtained to estimate the 2-norm of a rectangular matrix; this method is more general and produces better estimates in practice than a similar technique of Cline, Conn and Van Loan.     

Nonclassical titanocene silyl hydrides

The titanocene silyl hydride complexes [Ti(Cp)2(PMe3)(H)(SiR3)] [SiR3=SiMePhCl (6), SiPh2Cl (7), SiMeCl2 (8), SiCl3 (9)] were prepared by HSiR3 addition to [Ti(Cp)2(PMe3)2] and were studied by NMR and IR spectroscopy, X-ray diffraction (for 6, 8, and 9), and DFT calculations. Spectroscopic and structural data established that these complexes exhibit nonclassical Ti-H-Si-Cl interligand hypervalent interactions. In particular, the observation of silicon-hydride coupling constants J(Si,H) in 6-9 in the range 22-40 Hz, the signs of which we found to be negative for 8 and 9, is conclusive evidence of the presence of a direct Si-H bond. The analogous reaction of [Ti(Cp)2(PMe3)2] with HSi(OEt)3 does not afford the expected classical silyl hydride complex [Ti(Cp)2(PMe3)(H)[Si(OEt)3]], and instead NMR-silent titanium (apparently TiIII) complex(es) and the silane redistribution product Si(OEt)4 are formed. The structural data and DFT calculations for the compounds [Ti(Cp)2(PMe3)(H)(SiR3)] show that the strength of interligand hypervalent interactions in the chlorosilyl complexes decreases as the number of chloro groups on silicon increases. However, in the absence of an Si-bound electron-withdrawing group trans to the Si-H moiety, a silane sigma complex is formed, characterized by a long Ti-Si bond of 2.658 A and short Si-H contact of 1.840 A in the model complex [Ti(Cp)2(PMe3)(H)(SiMe3)]. Both the silane sigma complexes and silyl hydride complexes with interligand hypervalent interactions exhibit bond paths between the silicon and hydride atoms in Atoms in Molecules (AIM) studies. To date a classical titanocene phosphane silyl hydride complex without any Si-H interaction has not been observed, and therefore titanocene silyl hydrides are, depending on the nature of the R groups on Si, either silane sigma complexes or compounds with an interligand hypervalent interaction.     

Mild and efficient Cs2CO3-promoted synthesis of phosphonates

A mild and convenient synthesis for phosphonates using cesium carbonate (Cs₂CO₃), tetrabutylammonium iodide (TBAI) and DMF was developed at room temperature. Numerous dialkyl phosphites were screened using a diverse array of alkyl halides and these reaction conditions were found to be highly efficient producing various phosphonates exclusively in moderate to high yields.     

Assay development and high-throughput screening of caspases in microfluidic format

Caspase proteases are familiar targets in drug discovery. A common format for screening to identify caspase inhibitors employs fluorogenic or colorimetric tetra-peptide substrates in 96, 384, or 1536 -well microtiter plates. The primary motivation for increasing the number of wells per plate is to reduce the reagent cost per test and increase the throughput of HTS operations. There are significant challenges, however, to moving into or beyond the 1536-well format, such as submicroliter liquid handling, liquid evaporation, increased surface area-to-volume ratios, and the potential for artifacts and interference from small air-borne particles such as lint. Therefore, HTS scientists remain keenly interested in technologies that offer alternatives to the ever-shrinking microtiter plate well. Microfluidic assay technology represents an attractive option that, in theory, consumes only subnanoliter volumes of reagents per test. We have successfully employed a microfluidic assay technology in fluorogenic screening assays for several caspase isoforms utilizing the Caliper Technologies Labchip platform. Caspase-3 is used as a representative case to describe microfluidic assay development and initial high-throughput screening results. In addition, microfluidic screening and plate-based screening are compared in terms of reagent consumption, data quality, and ease of operation.     

Influence of dipolar interactions on radical pair recombination reactions subject to weak magnetic fields

Monte Carlo simulations of the effects of weak magnetic fields on the recombination of interacting radical pairs undergoing free diffusion in solution have been performed, with the aim of determining the influence on the low field effect of the magnetic dipolar coupling between the radicals. The suppression of singlet-triplet interconversion in the radical pair by the dipolar interaction is found to be pronounced at magnetic field strengths comparable to the hyperfine interactions in the radicals, to the extent that the low field effect is completely abolished. The averaging of the dipolar coupling by the translational diffusion of the radicals around one another is relatively efficient in the presence of strong magnetic fields but becomes ineffective in weak applied fields where the strength of the dipolar interaction is independent of the orientation of the inter-radical vector. Low field effects are only likely to be observed if the motion of the radical pair is restricted in some way so as to increase the likelihood that, having separated to the large distance required for the dipolar interaction to have a negligible effect, the radicals subsequently encounter and have the opportunity to recombine.     

Theoretical study of the electronic spectroscopy of CO adsorbed on Pt(111)

The excited states of CO adsorbed on the Pt(111) surface are studied using a time-dependent density functional theory formalism. To reduce the computational cost, electronic excitations are computed within a reduced single excitation space. Using cluster models of the surface, excitation energies are computed for CO in the on-top, threefold, and bridge binding sites. On adsorption, there is a lowering of the 5sigma orbital energy. This leads to a large blueshift in the 5sigma- -> pi(CO*) excitation energy for all adsorption sites. The 1pi and 4sigma orbital energies are lowered to a lesser extent, and smaller shifts in the corresponding excitation energies are predicted. For the larger clusters, pi* excitations at lower energies are observed. These transitions correspond to excitations to virtual orbitals of pi* character which lie below the pi* orbitals of gas phase CO. These orbitals are associated predominantly with the metal atoms of the cluster. The excitation energies are also found to be sensitive to changes in the adsorption geometry. The electronic spectrum of CO on Pt(111) is simulated and the assignment of the bands observed in experimental electron energy loss spectroscopy discussed.     

Deactivation of vibrationally excited ozone by O(3P) atoms

Using laser-induced fluorescence of ozone (to measure the rate of disappearance of O₃²) and NO₂ titration (to determine O atom concentrations), we have determined bimolecular rate constants for the deactivation by O(³P atoms) of ozone in excited stretching and bending modes. These experiments do not distinguish between deactivation by (a) the exchange of vibrational and translational energy or (b) the chemical reaction O₃ + O → 2O₂. If the non-reactive pathway (a) is assumed to dominate, then O(³P) is 150 times more effective than O₂ in deactivating O²₃. If chemical reaction (b) is dominant, the bimolecular rate constant for O²₃ + O(³P) is larger by a factor of 150–1500 than that for ground-state ozone.