Formulas for evaluation of expectation values of monoelectric operators with modified gaussian functions

Formulas are presented for the evaluation of the expectation values of various monoelectronic operators. The integrals are based on ?Hermite-Gausian”? or ?Modified Gaussian Functions”? and are expressed in suitable form for a computer programming. It is pointed out that the final expresions are simpler than the analogou omes obtained from the usual Gausian functions and can be written as linear combinations of a few baic integrals.     

Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions

Recurrence relations are derived for the evaluation of two-electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient ??(?). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.     

Ab initio calculation of some low-lying electronic excited states of methane

The energies of some low-lying electronic excited states of methane are calculated by using wave functions built up in terms of plane waves modulated by multicenter Gaussian factors. The wave functions of the various states are evaluated by a two steps iterative process. In the first step, each excited orbital is determined while keeping all other rigid; in the second, rearrangement effects are introduced. Final results are in good agreement with experimental data and allow to enhance an assignement hypothesis for the first electronic transitions.     

A numerical integration scheme for the evaluation of correlation energy functionals

A numerical integration scheme is presented for three-dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density-functional expression. The scheme is based on the choice of density-based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C₆₀ molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.     

X-ray diffraction study of the smectic mesophase of some azobenzene-containing polyacrylates

Abstract

An X-ray study is performed on powder specimens and on stretched oriented fibres of two liquid crystalline polyacrylates containing the azobenzene mesogenic unit with either a 4′-n-pentyloxy (sample 1–4) or 4′-n-hexyloxy (sample 1–5) substituent. The X-ray diffraction patterns of both samples showed the presence of a bilayer smectic C mesophase with the mesogneic groups tilted by an angle β ～ 45° (1–4) or β ～ 38° (1–5) with respect to the layer normal. The electron density profile p(z) along the direction normal to the smectic layers was calculated by Fourier inversion and possible structural models of the smectic mesophase are discussed. A partial interdigitation of the terminal alkyloxy substituents appears to occur.     

Resolving surface details with reflection and fluorescence video-confocal profilometry

Video-confocal profilometry has been exploited to characterize reflecting and non-reflecting surfaces in materials with tilted and corrugated areas. An alternative method based on fluorescence detection has been developed and tested to characterize metal surfaces modified by intense laser irradiation. Combined representations of surface topography have been obtained on the basis of both reflectance and fluorescence signals. A discussion of results and problems encountered in reflection and fluorescence based techniques is provided.     

Time-dependent heat capacity of water-lysozyme solution

Summary We report here the first observation of the time-dependent heat capacity of water-lysozyme solution. The observed increase of heat capacity in time occurs independently of the lysozyme concentration and thepH value of the solvent. The time necessary to attain the heat capacity equilibrium value and the amplitude of the effect are not well reproducible; the former tends to increase with temperature, while the amplitude decreases and practically disappears about 35°C. Evolution of a spatial order of the proteins in water and/or of water molecules interacting with the proteins is considered as a possible explanation for the results. The phenomenon promises to be an important tool to study the role of water in biological organization and activity.     

Sui diffeomorfismi di varietà isotopi all'identità

Riassunto Si considera il gruppoI(M) dei diffeomorfismi di una varietà differenziabileM che sono diffeotopi all'identità per una diffeotopia a supporto compatto. Viene dato (in maniera costruttiva) un insieme di generatori perI(M), costituito dai diffeomorfismi a supporto in uno degli aperti di un fissato ricoprimento. Conseguentemente si introduce una metrica suI(M) la quale induce una topologia che, pur essendo strettamente più fine dell'usuale topologiaC ^∞, rende ancoraI(M) gruppo topologico connesso.

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Summary LetM be a differentiable manifold. We prove that, iff is a diffeomorphism ofM ontoM which is isotopic to the identity by an isotopy having compact support thenf is a product of diffeomorphisms having a support of given size. As a consequence a distance δ on Diff₀ (M) is given such that it induces a topology stronger than the usualC ^∞-topology, even if it does not disconnect Diff₀ (M).

     

Characterization of a collinear double pulse laser-induced plasma at several ambient gas pressures by spectrally- and time-resolved imaging

A collinear double pulse laser-induced plasma was characterised by means of a spectrally and time resolved imaging technique. The beams of two Q-switched Nd:YAG lasers were focused on a brass target in a vacuum chamber to form the plasma. The plume emission intensity and spatial distribution were recorded with temporal resolution using an intensified CCD. Using a set of interference filters, we collected images of the emission from the major target components as well as from oxygen. Both the laser inter-pulse separation (in the range between 0 and 10 s) and the ambient air pressure value (in the range between 10⁵ and 10 Pa) were varied during the experiment. At atmospheric pressure, an enhancement of the line emission from the target elements was observed for delayed laser pulses compared to coincident pulses. However, this enhancement effect tends to fall at low pressure values, and a decrease of the signal is observed for pressures under about 10⁴ Pa. Moreover, it was observed that the evaluation of the enhancement factor strongly depends on the detector field of view. The propagation of the emitting plume was also studied at several pressures and inter-pulse delays.     

Integral cohomology of the Milnor fibre of the discriminant bundle associated with a finite Coxeter group

Let W be a finite Coxeter group generated by real reflections in a complex vector space. We compute the integral cohomology of the Milnor fibre of the discriminant bundle $\Delta :{\mathbb{C}}^n/W\to \mathbb{C}$, together with the action of the monodromy, for the whole list of exceptional groups. Here Δ is the map induced by the square of the polynomial defining the arrangement of reflection hyperplanes of W. The computation is equivalent to that of the cohomology, with suitable local coefficients, of the corresponding Artin group. These computations complete, for the exceptional cases, those performed by De Concini et al. for rational coefficients. To cite this article: F. Callegaro, M. Salvetti, C. R. Acad. Sci. Paris, Ser. I 339 (2004).