Design of Gaussian basis sets to the theoretical interpretation of IR-spectrum of hexaaquachromium (III) ion, tetraoxochromium (IV) ion, and tetraoxochromium (VI) ion

The Generator Coordinate Hartree-Fock (GCHF) method is employed to design 16s, 16s10p, 24s17p13d, 25s17p13d, and 26s17p Gaussian basis sets for the H ((2)S), O ((3)P), O(2-) ((1)S), Cr(3+) ((4)F), Cr(4+) ((3)F), and Cr(6+) ((1)S) atomic species. These basis sets are then contracted to (4s) for H ((2)S), (6s4p) for O ((3)P), and O(2-) ((1)S), (986p3d) for Cr(3+) ((4)F), (10s8p3d) for Cr(4+) ((3)F), and (13s7p) for Cr(6+) (1S) by a standard procedure. For evaluation of the quality of those basis sets in molecular calculations, we have accomplished studies of total and orbital (HOMO and HOMO-1) energies at the HF-Roothaan level for the molecular species of our interest. The results obtained with the contracted basis sets are compared to the values obtained with our extended basis sets and to the standard 6-311G basis set from literature. Finally, the contracted basis sets are enriched with polarization function and then utilized in the theoretical interpretation of IR-spectrum of hexaaquachromium (III) ion, [Cr(H(2)O)(6)](3+), tetraoxochromium (IV) ion, [CrO(4)](4-), and tetraoxochromium (VI) ion, [CrO(4)](2-). The respective theoretical harmonic frequencies and IR-intensities were computed at the density functional theory (DFT) level. In the DFT calculations we employed the Becke's 1988 functional using the LYP correlation functional. The comparison between the results obtained and the corresponding experimental values indicates a very good description of the IR-spectra of the molecular ions studied, and that the GCHF method is still a legitimate alternative for selection of Gaussian basis sets. (C) 2003 Elsevier B.V. All rights reserved.

Designing Gaussian basis sets to the theoretical study of the piezoelectric effect of perovskite (BaTiO3)

Gaussian basis sets (24s14p, 30s19p14d, and 33s21p14d for O (P-3), Ti (S-5), and Ba (S-1) atoms, respectively), are designed with the strategy of the Generator Coordinate Hartree-Fock method. The basis sets are then contracted to [6s4p], [10s5p4d], and [16s9p5d] to O, Ti, and Ba atoms, respectively, and used in calculations of total and orbital energies of (TiO+2)-Ti-1 and (BaO)-Ba-1 fragments for quality evaluation in molecular studies. For O atom, the [6s4p] basis set is enriched with d polarization function and used along with the [10s5p4d] and [16s9p5d] basis sets for the theoretical study of the piezoelectric effect of perovskite (BaTiO3). The results of this work evidence that the piezoelectric properties in BaTiO3 can be caused by electrostatic interactions. (C) 2003 Elsevier B.V. All rights reserved.

Gaussian basis sets by generator coordinate Hartree-Fock method to ab initio calculations of electron affinities of enolates

The Generator Coordinate Hartree-Fock (GCHF) method is employed to generate uncontracted 15s and 18s11p gaussian basis sets for the H, C and O atoms, respectively. These basis sets are then contracted to 3s and 4s H atom and 6s5p, for C and O atoms by a standard procedure. For quality evaluation of contracted basis sets in molecular calculations, we have accomplished calculations of total and orbital energies in the Hartree-Fock-Roothaaii (HFR) approach for CH, C(2) and CO molecules. The results obtained with the uncontracted basis sets are compared with values obtained with the standard D95, 6-311G basis sets and with values reported in the literature. The 4s and 6s5p basis sets are enriched with polarization and diffuse functions for atoms of the parent neutral systems and of the enolates anions (cycloheptanone enolate, 2,5-dimethyleyelopentanone enolate, 4-heptanone enolate, and di-isopropyl ketone enolate) from the literature, in order to assess their performance in ab initio molecular calculations, and applied for calculations of electron affinities of the enolates. The calculations were performed at the DFT (BLYP and B3LYP) and HF levels and compared with the corresponding experimental values and with those obtained by using other 6-3 1 + +G((*)) and 6-311 + +G((*)) basis sets from literature. For the enolates studied, the differences between the electron affinities obtained with GCHF basis sets, at the B3LYP level, and the experimental values are -0.001, -0,014, -0.001, and -0.001 eV. (C) 2002 Elsevier B.V. B.V. All rights reserved.

A pulsating Gaussian wave packet

A pulsating Gaussian wave packet for the harmonic oscillator is explicitly constructed. The mechanism for that behaviour is pointed out. © 1999 IOP Publishing Ltd.

Deformed Gaussian orthogonal ensemble and the statistical fluctuations in the spectra of the quartic oscillator

The nearest-neighbor spacing distributions proposed by four models, namely, the Berry-Robnik, Caurier-Grammaticos-Ramani, Lenz-Haake, and the deformed Gaussian orthogonal ensemble, as well as the ansatz by Brody, are applied to the transition between chaos and order that occurs in the isotropic quartic oscillator. The advantages and disadvantages of these five descriptions are discussed. In addition, the results of a simple extension of the expression for the Dyson-Mehta statistic Δ3 are compared with those of a more popular one, usually associated with the Berry-Robnik formalism. ©1999 The American Physical Society.

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Migração 3-D Kirchhoff-Gaussian-Beam (KGB) pré-empilhamento no domínio da profundidade

O Feixe Gaussiano (FG) é uma solução assintótica da equação da elastodinâmica na vizinhança paraxial de um raio central, a qual se aproxima melhor do campo de ondas do que a aproximação de ordem zero da Teoria do Raio. A regularidade do FG na descrição do campo de ondas, assim como a sua elevada precisão em algumas regiões singulares do meio de propagação, proporciona uma forte alternativa na solução de problemas de modelagem e imageamento sísmicos. Nesta Tese, apresenta-se um novo procedimento de migração sísmica pré-empilhamento em profundidade com amplitudes verdadeiras, que combina a flexibilidade da migração tipo Kirchhoff e a robustez da migração baseada na utilização de Feixes Gaussianos para a representação do campo de ondas. O algoritmo de migração proposto é constituído por dois processos de empilhamento: o primeiro é o empilhamento de feixes (“beam stack”) aplicado a subconjuntos de dados sísmicos multiplicados por uma função peso definida de modo que o operador de empilhamento tenha a mesma forma da integral de superposição de Feixes Gaussianos; o segundo empilhamento corresponde à migração Kirchhoff tendo como entrada os dados resultantes do primeiro empilhamento. Pelo exposto justifica-se a denominação migração Kirchhoff-Gaussian-Beam (KGB). As principais características que diferenciam a migração KGB, durante a realização do primeiro empilhamento, de outros métodos de migração que também utilizam a teoria dos Feixes Gaussianos, são o uso da primeira zona de Fresnel projetada para limitar a largura do feixe e a utilização, no empilhamento do feixe, de uma aproximação de segunda ordem do tempo de trânsito de reflexão. Como exemplos são apresentadas aplicações a dados sintéticos para modelos bidimensionais (2-D) e tridimensionais (3-D), correspondentes aos modelos Marmousi e domo de sal da SEG/EAGE, respectivamente.

Análise do efeito da discretização do modelo de velocidades nas migrações Kirchhoff e Kirchhoff-Gaussian- Beam 2D pré-empilhamento em profundidade

O Feixe Gaussiano (FG) é uma solução assintótica da equação da elastodinâmica na vizinhança paraxial de um raio central, a qual se aproxima melhor do campo de ondas do que a aproximação de ordem zero da Teoria do Raio. A regularidade do FG na descrição do campo de ondas, assim como a sua elevada precisão em algumas regiões singulares do meio de propagação, proporciona uma forte alternativa no imageamento sísmicos. Nesta dissertação, apresenta-se um novo procedimento de migração sísmica pré-empilhamento em profundidade com amplitudes verdadeiras, que combina a flexibilidade da migração tipo Kirchhoff e a robustez da migração baseada na utilização de Feixes Gaussianos para a representação do campo de ondas. O algoritmo de migração proposto é constituído por dois processos de empilhamento: o primeiro é o empilhamento de feixes (“beam stack”) aplicado a subconjuntos de dados sísmicos multiplicados por uma função peso definida de modo que o operador de empilhamento tenha a mesma forma da integral de superposição de Feixes Gaussianos; o segundo empilhamento corresponde à migração Kirchhoff tendo como entrada os dados resultantes do primeiro empilhamento. Pelo exposto justifica-se a denominação migração Kirchhoff-Gaussian-Beam (KGB).Afim de comparar os métodos Kirchhoff e KGB com respeito à sensibilidade em relação ao comprimento da discretização, aplicamos no conjunto de dados conhecido como Marmousi 2-D quatro grids de velocidade, ou seja, 60m, 80m 100m e 150m. Como resultado, temos que ambos os métodos apresentam uma imagem muito melhor para o menor intervalo de discretização da malha de velocidade. O espectro de amplitude das seções migradas nos fornece o conteúdo de frequência espacial das seções das imagens obtidas.

Filmes finos híbridos orgânicos-inorgânicos para fotônica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de temperatura de plasma de álcool através de espectroscopia de emissão natural radical C2*

Non-intrusive methods of diagnosis, such as spectral analysis of the radiation emitted by the system, have been used as a viable alternative for determining the temperature of combustion systems. Among them, the determination of temperature by natural emission spectroscopy has the advantage of requiring relatively simple experimental devices. Once Chemiluminescent species are formed directly in the excited state, the collection and recording of radiation emission spectrum is enough to determine the temperature (CARINHANA, 2008). In this study we used the process of making direct comparisons between the experimental spectra obtained in the laboratory from the plasma of alcohol, and the theoretical spectra plotted from a computer program developed at the IEAv. The objective was to establish a fast and reliable method to measure the rotational temperature of the radical C2*. The results showed that the temperature of the plasma, which in turn can be taken as the rotational temperature of the system, is proportional to the pressure. The temperature values ranged from ca. 2300 ~ 2500 K at a pressure of 19 mmHg to 3100 ~ 3500 K for the pressure of 46 mmHg. The temperature values are somewhat smaller when we consider the theoretical spectrum as a Lorentzian curve. The overlap of the spectra was better when using the profile curve, but still were not exactly superimposed. The solution to improve the overlap of the theoretical with the experimental spectra is the use of a curve that has the convolution of two profiles analyzed: Lorentzian and Gaussian. This curve is called the Voigt profile, which will also be implemented by programmers and studied in a next work

Weakly anomalous diffusion with non-Gaussian propagators

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H approximate to 1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H = 1/2 but with a non-Gaussian propagator.

Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Gaussian deconvolution: a useful method for a form-free modeling of scattering data from mono- and multilayered planar systems

A new method for analysis of scattering data from lamellar bilayer systems is presented. The method employs a form-free description of the cross-section structure of the bilayer and the fit is performed directly to the scattering data, introducing also a structure factor when required. The cross-section structure (electron density profile in the case of X-ray scattering) is described by a set of Gaussian functions and the technique is termed Gaussian deconvolution. The coefficients of the Gaussians are optimized using a constrained least-squares routine that induces smoothness of the electron density profile. The optimization is coupled with the point-of-inflection method for determining the optimal weight of the smoothness. With the new approach, it is possible to optimize simultaneously the form factor, structure factor and several other parameters in the model. The applicability of this method is demonstrated by using it in a study of a multilamellar system composed of lecithin bilayers, where the form factor and structure factor are obtained simultaneously, and the obtained results provided new insight into this very well known system.