Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Experimental and theoretical studies of the quenching of Li(3p,4p) by N2

Quenching mechanisms of the Li3p and Li4p states in collision with the nitrogen molecule are studied by laser-induced fluorescence spectroscopy and by a quantum chemical calculation. The Li3p state is observed to be efficiently quenched to the Li3s state detected as intense 3s-->2p emission. The Li4p state is efficiently quenched to the Li4s and Li3d states detected as 4s-2p and 3d-2p emissions, respectively. The potential-energy surfaces for the Li(2s-4p)N2 states show a large number of conical intersections and avoided crossings resulting from the couplings between the ionic [Li+(N2)-] and covalent configurations. There are a large number of stable excited states, and we give here the spectroscopic constants for the lowest two stable isomers correlating to Li2p+N2.     

Mechanism and nanosize products of the sol-gel reaction using diphenylsilanediol and 3-methacryloxypropyltrimethoxysilane as precursors

We use a first-principles calculation and small-angle neutron scattering (SANS) to investigate the mechanism and the nanosize products of the sol-gel reaction with diphenylsilanediol (DPD) and 3-methacryloxypropyltrimethoxysilane (MEMO) precursors in synthesizing a hybrid waveguide material. It is predicted that switching between a DPD hydroxyl and a MEMO methoxy with a reaction rate of 6.8 x 10(-6) s(-1) at 300 K is the fastest process for the first reaction step, thus generating diphenylmethoxysilanol (DPM) and 3-methacryloxypropyldimethoxysilanol (MEDO) as products. However, we determine that this reaction pathway could be modified by the presence of the H2O released from a catalyst such as Ba(OH)2.H2O. Next, switching between the DPM hydroxyl and the MEDO methoxy is followed to generate diphenyldimethoxysilane (DPDM) and 3-methacryloxypropylmethoxysilanediol (MEMDO). However, condensation between a MEMDO hydroxyl and a DPDM methoxy is found to be most favorable for the third reaction step, which generates the DPDM-MEMDO dimer and CH3OH molecule as products. In a similar fashion, a DPDM methoxy of the DPDM-MEMDO dimer can condense with a MEMDO hydroxyl of the second DPDM-MEMDO dimer to increase the chain, but its reaction rate of 2.8 x 10(-11) s(-1) is predicted to be about 5 times smaller than that between a DPDM methoxy and a MEMDO hydroxyl. This implies that the reaction rate for the larger nanostructures becomes smaller. Additionally, our SANS measurements determine that the final products from our sol-gel reaction are on the nanometer scale, at sizes from 1.76 to 2.36 nm.     

Dynamic kinetic resolution of atropisomeric amides

[reaction: see text] Using L-proline as catalyst in the asymmetric aldol reaction and a series of benzamides and naphthamides, we have accomplished a dynamic kinetic resolution that simultaneously establishes the stereochemistry of the atropisomeric amide's chiral axis and a stereogenic center. The enantioselectivities ranged from 82% to 95% and the diastereoselectivities from 2.1:1 to 7.0:1.     

The Predissociation of the 1(3)Sigma(-)(g) State of (7)Li(2)

The predissociation of the 1(3)Sigma(-)(g) v >/= 10 levels of (7)Li(2) has been observed by pulsed and continuous-wave perturbation-facilitated optical-optical double-resonance spectroscopy (PFOODR). Our ab initio calculation shows that the inner wall of the 1(3)Sigma(-)(g) potential intersects the 1(3)Pi(g) repulsive potential at internuclear distance R = 2.00 ?. The predissociation is due to a DeltaS = 0, DeltaLambda = +/-1 rotational-electronic interaction with the repulsive 1(3)Pi(g) state. Copyright 2001 Academic Press.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

Divergent strategy for the synthesis of bottlebrush polymers via postpolymerization modification of macromonomer

A simple and divergent synthetic strategy of bottlebrush polymers (BBPs) is presented, consisting of postpolymerization modification of a macromonomer and grafting-through polymerization. Beginning with a single macromonomer, its direct modification could build a library of macromonomers with an identical chain length, thus guaranteeing the precision in the synthesis of BBPs. In this study, a newly designed norbornenyl-terminated poly(methyl acrylate) (NB-PMA) is proposed as a chemically robust template. Ti-mediated transesterification of NB-PMA successfully produces structurally diverse polyacrylates while maintaining the terminal norbornenyl group intact. All macromonomers obtained from transesterification possess a good grafting-through ring-opening metathesis polymerization reactivity, furnishing homo, random, and block BBPs in a controllable manner. Moreover, atomic force microscopy analysis supports the controlled side-chain length distribution in the resulting BBPs.     

Highly concentrated catalytic asymmetric allylation of ketones

[reaction: see text] We report the catalytic asymmetric allylation of ketones under highly concentrated reaction conditions with a catalyst generated from titanium tetraisopropoxide and BINOL (1:2 ratio) in the presence of isopropanol. This catalyst promotes the addition of tetraallylstannane to a variety of ketones to produce tertiary homoallylic alcohols in excellent yield (80-99%) with high enantioselectivities (79-95%). The resulting homoallylic alcohols can also be epoxidized in situ using tert-butyl hydroperoxide (TBHP) to afford cyclic epoxy alcohols in high yield (84-87%).     

Oxaaza macrocycles constructed on poly(ethylenimine) through Ni(II)-template cyclization and their metal binding

Polymeric oxaaza macrocycles (PEI-OAM) are constructed on poly(ethylenimine) (PEI) by Ni(II)-template alkylation of PEI with diethyleneglycol ditosylate. The K_f values for Ni(II), Cu(II), and Zn(II) complexes of PEI–OAM are measured at pH 3.5–10 at 25°C. At pH 7, log K_f values for these complexes are 9–15, indicating that the polymeric oxaaza macrocycles can readily reduce concentrations of these metal ions below ppb level. Metal binding ability of nonpolymeric oxaaza macrocyclic compounds reported in the literature decreases rapidly as pH is lowered below 7, whereas that of PEI–OAM decreases to lesser extents. This is attributed to the electrostatic effects exerted by the ammonium ions of PEI backbone. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 527–532, 1997.