Self-consistent perturbation theory for conjugated molecules

Self-consistent bond polarizabilities are defined and computed for butadiene, benzene, naphthalene and anthracene. A self-consistent derivation of the bond order-bond length relationship is given and self-consistent formulae for force constants are obtained. Theoretical bond lengths for butadiene, naphthalene and anthracene are calculated in two ways; firstly by using the same values of _rs and _rs for all bonds and secondly by allowing these to vary with bond length. The agreement with experiment is very satisfactory although in some respects the first set of results is to be preferred. Force constants for ethylene and benzene are found which have the correct orders of magnitude although the detailed agreement is not always very good and the interaction force constant between meta bonds in benzene is predicted to have the wrong sign.

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Zusammenfassung Des polarisabilités de liaison self-consistantes sont définies et calculées pour le butadiène, le benzène, le naphtalène et l' anthracène. Une dérivation self-consistante de la relation entre l'indice de liaison et la longueur de liaison est obtenue, ainsi que des formules self-consistantes pour les constantes de force. Les longueurs théoriques des liaisons pour le butadiène, le naphtalène et l'anthracène sont calculées de deux manières: tout d'abord en utilisant les mêmes valeurs de _rs et _rs pour toutes les liaisons, puis en les faisant varier avec la longueur de la liaison. L'accord avec l'expérience est très satisfaisant, quoique, d'un certain point de vue, le premier groupe de résultats doit être préféré à l'autre. Les constantes de force calculées pour l'éthylène et le benzène ont un ordre de grandeur correct quoique dans le détail l'accord ne soit pas toujours très bon et que la constante de force d'interaction entre liaisons en méta du benzène soit obtenue avec le signe contraire.

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Résumé Es werden selbstkonsistente Bindungspolarisierbarkeiten definiert und für Butadiene, Benzol, Naphthalin und Anthrazen berechnet. Ebenso wird in diesem Rahmen eine Ableitung für eine Beziehung zwischen Bindungsordnung und Bindungslänge sowie ein Ausdruck für die Kraftkonstanten angegeben. Die Bindungslängen werden auf zwei Wegen berechnet: einerseits mit gleichen _rs und _rs für alle Bindungen und andererseits mit Werten, die von der Bindungslänge abhängen. Letztere ergeben sich in befriedigender Weise, während bei den Kraftkonstanten in bezug auf Einzelheiten Abweichungen zu verzeichnen sind.

     

The use of symmetry in direct Møller-Plesset second-order calculations

Summary An algorithm for utilising abelian point group symmetry in direct MP2 energy calculations is presented. This is based upon the direct MP2 method of Head-Gordon, Pople and Frisch. The method uses the petite atomic orbital integral list as in conventional transformations coupled with a symmetry adaption of the three quarter transformed integrals. Representative calculations for ethylene and benzene are presented which demonstrate the potential of the method.     

Spectrally Resolved Imaging of Cabot Rings and Howell-Jolly Bodies

The spectral characteristics of erythropoietic cellular inclusions stained by May-Grunwald Giemsa (MGG) were determined by spectrally resolved imaging. Multipixel spectra were obtained from Cabot rings and Howell-Jolly (HJ) bodies, displaying a range of wavelengths of transmitted light. The spectral characteristics of these inclusions were compared with those of isolated DNA, his-tones (type II) and arginine-rich histones (type VI), all stained by MGG. Results of single-cell spectroscopy show that the spectra of Cabot rings and HJ bodies share spectral characteristics with the type II and type VI histones. However, no resemblance was found between Cabot rings and DNA spectra. The spectral analysis of hetero-chromatin displayed a spectral pattern with characteristics of both DNA and histones, while the euchromatin showed a major contribution of the DNA component.     

An SCF and CI study of the properties of the HCl and CI2 molecules

The one-electron properties and polarizabilities of the HCl and Cl₂ molecules have been calculated using both SCF and CI wavefunctions. Agreement with experimental data, where such data exist, is found to be very good.     

A stereospecific total synthesis of (±)-epipentenomycin I, (±)-epipentenomycin II and (±)-epipentenomycin III

A highly efficient, stereospecific synthesis of the epimeric pentenomycins is reported utilizing the stereospecific addition of OsO₄ to substituted cyclopentenes.     

Wavelet compression of three-dimensional time-lapse biological image data.

The use of multifocal-plane, time-lapse recordings of living specimens has allowed investigators to visualize dynamic events both within ensembles of cells and individual cells. Recordings of such four-dimensional (4D) data from digital optical sectioning microscopy produce very large data sets. We describe a wavelet-based data compression algorithm that capitalizes on the inherent redunancies within multidimensional data to achieve higher compression levels than can be obtained from single images. The algorithm will permit remote users to roam through large 4D data sets using communication channels of modest bandwidth at high speed. This will allow animation to be used as a powerful aid to visualizing dynamic changes in three-dimensional structures.     

Time Frequency Representations of Almost Periodic Functions

In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl–Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L ₂(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L ₂(ℝ) representations and AP-representations.      

Nonlinear approximation using Gaussian kernels

It is well known that nonlinear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently by DeVore and Ron (in press) [2] for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function, the preferred kernel in machine learning and several engineering problems. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. At heart it employs the strategy for nonlinear approximation of DeVore-Ron, but it selects kernels by a method that is not straightforward. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We show that our algorithm is suitably optimal in the sense that it provides approximation rates similar to other established nonlinear methodologies like spline and wavelet approximations. As expected and desired, the approximation rates can be as high as needed and are essentially saturated only by the smoothness of the approximand.