Índice de aromaticidade baseado na deslocalização, degenerescência e densidade (D3BIA) para acenos e moléculas homoaromáticas

The aromaticity index is an important tool for the investigation of aromatic molecules. This work consists on new applications of the aromaticity index developed by teacher Caio Lima Firme, so-called D3BIA (density, delocalization, degeneracy-based index of aromaticity). It was investigated its correlation with other well-known aromaticity indexes, such as HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shielding), PDI (para-delocalization index), magnetic susceptibility (), and energetic factor in the study of aromaticity of acenes and homoaromatic species based on bisnoradamantanyl cage. The density functional theory (DFT) was used for optimization calculations and for obtaining energetic factors associated with aromaticity and indexes HOMA and NICS. From quantum theory of atoms in molecules (QTAIM) it was obtained the indexes D3BIA, PDI and . For acenes, when the over-mentioned indexes were applied it was observed no correlation except for D3BIA and HOMA (R2=0.752). For bisnoradamantenyl dication and its derivatives, it was obtained a good correlation between D3BIA and NICS. Moreover, it was evaluated solely one of the factors used on D3BIA calculation, the delocalization index uniformity (DIU), so as to investigate its possible influence on stability of chemical species. Then, the DIU was compared with the formation Gibbs free energy of some pairs of carbocations, isomers or not, which each pair had small difference in point group symmetry and no difference among other well-known stability factors. The obtained results indicate that DIU is a new stability factor related to carbocations, that is, the more uniform the electron density delocalization, the more stable the is carbocation. The results of this work validate D3BIA and show its importance on the concept of aromaticity, indicating that it can be understood from degeneracy of atoms belonging the aromatic site, the electronic density in the aromatic site and the degree of uniformity of electron delocalization

Efeitos não-gaussianos em astrofísica e cosmologia

The recent astronomical observations indicate that the universe has null spatial curvature, is accelerating and its matter-energy content is composed by circa 30% of matter (baryons + dark matter) and 70% of dark energy, a relativistic component with negative pressure. However, in order to built more realistic models it is necessary to consider the evolution of small density perturbations for explaining the richness of observed structures in the scale of galaxies and clusters of galaxies. The structure formation process was pioneering described by Press and Schechter (PS) in 1974, by means of the galaxy cluster mass function. The PS formalism establishes a Gaussian distribution for the primordial density perturbation field. Besides a serious normalization problem, such an approach does not explain the recent cluster X-ray data, and it is also in disagreement with the most up-to-date computational simulations. In this thesis, we discuss several applications of the nonextensive q-statistics (non-Gaussian), proposed in 1988 by C. Tsallis, with special emphasis in the cosmological process of the large structure formation. Initially, we investigate the statistics of the primordial fluctuation field of the density contrast, since the most recent data from the Wilkinson Microwave Anisotropy Probe (WMAP) indicates a deviation from gaussianity. We assume that such deviations may be described by the nonextensive statistics, because it reduces to the Gaussian distribution in the limit of the free parameter q = 1, thereby allowing a direct comparison with the standard theory. We study its application for a galaxy cluster catalog based on the ROSAT All-Sky Survey (hereafter HIFLUGCS). We conclude that the standard Gaussian model applied to HIFLUGCS does not agree with the most recent data independently obtained by WMAP. Using the nonextensive statistics, we obtain values much more aligned with WMAP results. We also demonstrate that the Burr distribution corrects the normalization problem. The cluster mass function formalism was also investigated in the presence of the dark energy. In this case, constraints over several cosmic parameters was also obtained. The nonextensive statistics was implemented yet in 2 distinct problems: (i) the plasma probe and (ii) in the Bremsstrahlung radiation description (the primary radiation from X-ray clusters); a problem of considerable interest in astrophysics. In another line of development, by using supernova data and the gas mass fraction from galaxy clusters, we discuss a redshift variation of the equation of state parameter, by considering two distinct expansions. An interesting aspect of this work is that the results do not need a prior in the mass parameter, as usually occurs in analyzes involving only supernovae data.Finally, we obtain a new estimate of the Hubble parameter, through a joint analysis involving the Sunyaev-Zeldovich effect (SZE), the X-ray data from galaxy clusters and the baryon acoustic oscillations. We show that the degeneracy of the observational data with respect to the mass parameter is broken when the signature of the baryon acoustic oscillations as given by the Sloan Digital Sky Survey (SDSS) catalog is considered. Our analysis, based on the SZE/X-ray data for a sample of 25 galaxy clusters with triaxial morphology, yields a Hubble parameter in good agreement with the independent studies, provided by the Hubble Space Telescope project and the recent estimates of the WMAP