Consecutive processes in the photolysis of dimethyl-s-tetrazine molecules in the vapor phase

Experimental studies of the variation of the fluorescence yield and photochemical product yield are presented for dimethyl-s-tetrazine (DMT) at 0.6 Torr and 300 K. Results are also reported for the variation of these yields upon adding argon buffer gas. The fluorescence yield decreases with increasing excitation energy (0 to 4200 cm^?1 vibrational energy excess in the first excited singlet state) but the decrease is insufficient to account for the corresponding increase in product yield. Added gas (600 Torr argon) quenches the photochemistry but not the fluorescence. The results imply that the photo-dissociation involves a bottleneck (B) in the non-radiative singlet decay. The molecules in B can be relaxed by collisions, relax to photostable DMT molecules without collisions, or undergo photodissociation.     

A modified Hückel method for calculating ring current contributions to the diamagnetic susceptibilities of conjugated hydrocarbons

SCF calculations of the ring current contributions to the diamagnetic susceptibilities of certain conjugated hydrocarbons are compared with the Hückel values. It is shown that discrepancies arise because of the inherent inability of the Hückel formalism to allow for two-electron terms in the Hamiltonian. A modified Hückel scheme is proposed which rectifies this omission while still retaining the fundamental simplicity of the theory.

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Zusammenfassung Der Anteil des Ringstroms an der diamagnetischen Suszeptibilität konjugierter Kohlenwasserstoffe wurde mit der SCF-MO-Methode berechnet und mit den mittels Hückelmethode erhaltenen verglichen. Es wird gezeigt, daß die Unterschiede daher rühren, daß im Hückelformalismus die Zweielektronenterme des Hamiltonoperators nicht richtig berücksichtigt sind. Ein modifiziertes Hückelschema, das diese Terme berücksichtigt, aber die fundamentale Einfachheit der Theorie beibehält, wird angegeben.

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Résumé La contribution des courants cycliques à la susceptibilité diamagnétique des hydrocarbures conjugués est calculée par la méthode SCF-MO et comparée avec les valeurs obtenues par la méthode de Hückel. On montre que les désaccords proviennent de l'inaptitude propre au formalisme de Hückel de tenir compte des termes biélectroniques contenus dans l'hamiltonien. On propose une méthode de Hückel modifiée qui corrige cette omission tout en conservant la simplicité de la théorie.

     

Design, total synthesis, and evaluation of C13-C14 cyclopropane analogues of (+)-discodermolide

[structure: see text] The design, total synthesis, and biological evaluation of two C13-C14-cyclopropyl analogues [(+)-1 and (+)-2] of (+)-discodermolide have been achieved. Key features of the syntheses include highly stereoselective, hydroxyl-directed cyclopropanations of vinyl iodides and higher order cuprate-mediated cross-coupling reactions between cyclopropyl iodides and alkyl iodides. Biological evaluation revealed that neither orientation of the cyclopropyl methylene completely substitutes for the C14 methyl found in (+)-discodermolide (3).     

Proteins and polymers

Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native state structures and is not incompatible with the existence of structured building blocks such as alpha helices and beta strands. We present a discussion on how the notion of the thickness of a polymer chain, besides being useful in describing a chain molecule in the continuum limit, plays a vital role in interpolating between conventional polymer physics and the phase of matter associated with protein structures.     

Electrochemical Redundant Microsensor Arrays for Glucose Monitoring with Patterned Polymer Films

Redundant microsensor arrays for glucose sensing were fabricated using photopolymerization of poly(ethylene glycol) diacrylate (PEG‐DA) with 2‐hydroxy‐2‐methyl phenyl‐propanone as photoinitiator to encapsulate the enzyme glucose oxidase. Silicon micro fabrication technologies were used to fabricate microelectrode sensor arrays on flexible polyimide sheets. These microarray sensors were individually addressable as observed using square‐wave voltammetry. Redox polymer, poly[4‐vinylpyridine Os(bipyridine)₂Cl]‐co‐ethylamine, was first immobilized on the electrode surface and then glucose oxidase was entrapped in PEG‐DA hydrogels. The redox polymer was found to exchange electrons with glucose oxidase in biocompatible PEG‐DA hydrogels. The entrapped glucose oxidase was found to respond linearly to glucose in solution (0–20 mM) as determined using square‐wave voltammetry.     

Some numerical results on best uniform rational approximation ofx α on [0,1]

Let be a positive number, and letE _n,n (x ;[0,1]) denote the error of best uniform rational approximation from _n,n tox on the interval [0,1]. We rigorously determined the numbers {E _n,n (x ;[0,1])} _n ^=1/30 for six values of in the interval (0, 1), where these numbers were calculated with a precision of at least 200 significant digits. For each of these six values of , Richardson's extrapolation was applied to the products to obtain estimates of

On the construction of multivariate (pre)wavelets

A new approach for the construction of wavelets and prewavelets onR ^d from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL ₂(R ^d ) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution.     

Asymptotics for the zeros and poles of normalized Pad\'{e} approximants to{\rm e}^{z}

Summary. With denoting the -th partial sum of ${\rm e}^{z}$, the exact rate of convergence of the zeros of the normalized partial sums, , to the Szeg\"o curve was recently studied by Carpenter et al. (1991), where is defined by Here, the above results are generalized to the convergence of the zeros and poles of certain sequences of normalized Pad\'{e} approximants to , where is the associated Pad\'{e} rational approximation to . Received February 2, 1994