Polarizable biphenyl polysiloxane stationary phase for capillary column gas chromatography

A crosslinkable biphenylmethylpolysiloxane stationary phase was synthesized for capillary column gas chromatography and compared with methyl, phenyl, and cyanopropyl polysiloxane stationary phases for the separation of isomeric polycyclic aromatic compounds. While the new phase gave similar separations of nonpolar isomers when compared to the nonpolar phases, separations of polar isomers were greatly improved because of the induced polarity of the biphenyl group of the stationary phase by the solute molecules. This polarizable stationary phase offers a unique selectivity which is not available in other stationary phases.     

Titanocene(III)-promoted Reformatsky additions

[reaction: see text] A novel method for the promotion of Reformatsky-like reactions is presented. The technique employs titanocene(III) chloride as a mild and homogeneous single-electron reductant. The reactions are rapid, operationally simple, and compatible with a wide range of functionalities. These additions are also anti diastereoselective.     

An analysis of the composite step biconjugate gradient method

Summary The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2×2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal matrix generated by the underlying Lanczos process. We also prove a best approximation result for the method. Some numerical illustrations showing the effect of roundoff error are given.The work of this author was supported by the Office of Naval Research under contract N00014-89J-1440.The work of this author was supported by the Office of Naval Research under contracts N00014-90-J-1695 and N00014-92-J-1890, the Department of Energy under, contract DE-FG03-87ER25307, the National Science Foundation under contracts ASC 90-03002 and ASC 92-01266, and the Army Research Office under contract DAAL03-91-G-0150. Part of this work was completed during a visit to the Computer Science Dept. The Chinese University of Hong Kong.     

Addendum to "a note on the zeros of solutions of w″+P(z)w=0 where P is a polynomial

In the original paper [1], it was shown that the zeros of solutions of w″ + P(z)w = 0, where P(z) is a polynomial of degree n ≥ 1, must approach certain rays. This was proved by first obtaining asymptotic formulas for a fundamental set of solutions in sectors, and then using them to derive estimates on the rate at which the nearby zeros approach the ray. The estimates derived in [1] for the rate of approach were rough estimates which were sufficient to prove the main result but simple enough to avoid unnecessary complications in the proof. The present note is intended to give the best estimate which can be derived from the asymptotic formulas for the rate of approach of the zeros. The main reason for deriving these estimates is that they show that for many equations (e.g., the Titchmarsh equation) the rate of approach is actually much faster than that indicated by the rough estimate in [1]. In fact, we show that the estimate dramatically improves whenever P(z) has the property that the translate P(z ? c) which eliminates the term of degree n ? 1 also eliminates the term of degree n ? 2.     

Why does perfluorination render bicyclo[2.2.0]hex-1(4)-ene stable toward dimerization? Calculations provide the answers

B3LYP calculations with two different basis sets have been performed to understand why bicyclo[2.2.0]hex-1(4)-ene (1a) undergoes dimerization with DeltaH(++) = 11.5 kcal/mol, but dimerization of perfluorobicyclo[2.2.0]hex-1(4)-ene (1b) has never been observed. The former reaction is computed to be exothermic by 37.2 kcal/mol, whereas the latter is calculated to be endothermic by 7.4 kcal/mol. The 44.6 kcal/mol difference between the enthalpies of these two reactions can be dissected into contributions of 24.5 kcal/mol for the difference between the enthalpies for forming diradical intermediates 2a and 2b and 20.1 kcal/mol for cyclization of 2a and 2b to, respectively, 3a and 3b. The latter enthalpy difference is largely attributable to repulsions between the endo-fluorines in the dimer, although the exo-fluorines also are found to contribute. The former enthalpy difference is attributable to the difference between the dissociation enthalpies of the pi bonds in 1a and 1b, which is shown to amount to 16 +/- 1 kcal/mol. About 25% of the stronger pi bond in fluoroalkene 1b is found to be due to hyperconjugation of the eight C-F bonds in 1b with the filled pi orbital. However, the major contributor to the stronger pi bond in 1b is shown to be the unfavorable interaction that results when a pyramidalized radical center is syn to a C-F bond. Both of these effects, which contribute to the greater strength of the pi bond in 1b, relative to that in 1a, are analyzed and discussed.