23 resultados para Rhombohedral symmetry


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Axis of quinary symmetry occur in molecular symmetry, as in the case of fullerenes, and in crystalline symmetry, in the quasicrystals. Minerals with pentagonal faces do not have this element of symmetry, as the pyrite (FeS2) which shows a ridge that is different from the other ones, in any face of the crystal. The purpose of this paper is to demonstrate conceptual differences between pyritohedron and regular pentagonal dodecahedron symmetries, discussing students' difficulties to identify them. Also is proposed a didactic experiment with spatial models of the above-mentioned forms and the demonstration of its symmetries in clinographic projections.

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A simple, four-step method for better introducing undergraduate students to the fundamentals of molecular orbital (MO) theory of the polyatomic molecules H2O, NH3, BH3 and SiH4 using group theory is reported. These molecules serve to illustrate the concept of ligand group orbitals (LGOs) and subsequent construction of MO energy diagrams on the basis of molecular symmetry requirements.

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It is through the application of an electronic partition approach called Symmetry-Adapted Perturbation Theory (SAPT) that the nature of hydrogen bonds and van der Waals interactions can be unveiled according to the contribution of electrostatic, charge transfer, exchange repulsion, polarization, and dispersion terms. Among these, electrostatic partition governs the formation of the hydrogen bonds, whose energies are arguably high. However, the weakness of the interaction strength is caused by dispersion forces, whose contribution decisively lead to the stabilization of complexes formed via van der Waals interactions.

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Along the historical background of science, the hydrogen bond became widely known as the universal interaction, thus playing a key role in many molecular processes. Through the available theoretical approaches, many of these processes can be unveiled on the basis of the molecular parameters of the subject intermolecular system, such as the variation of bond length and mainly the frequency shift observed in the proton donor. Supported by the natural bond analysis (NBO) with the quantification of the hybridization contributions, the structural deformations and vibrational effects cited above are also attributed to the outcome of the intermolecular interaction strength, which consequently can be estimated by means of the quantum theory of atoms in molecules (QTAIM) as well as evaluated by the symmetry-adapted perturbation theory (SAPT). Moreover, to identify the preferential interaction sites for proton donors and acceptors, the molecular electrostatic potential (MEP) is useful in this regard.

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The crystal and molecular structures of [bis(5-chloro-2-methoxybenzoate)tetraaquamanganese(II)], [pentaaqua(5-chloro-2-methoxybenzoato)cobalt(II)] (5-chloro-2-methoxybenzoate), [pentaaqua(5-chloro-2-methoxybenzoato)nickel(II)] (5-chloro-2-methoxybenzoate) and [aquabis(5-chloro-2-methoxybenzoate)zinc(II)] monohydrate were determined by a single-crystal X-ray analysis. Mn(H2O)4L2 (where L = C8H6ClO3) crystallizes in the monoclinic system, space group P21/c. [Co(H2O)5L]L and [Ni(H2O)5L]L both are isostructural, space group P212121. The crystals of [Zn(H2O)L2] H2O are monoclinic, space group Pc. Mn(II) ion is positioned at the crystallographic symmetry center. Mn(II) and Co(II) ions adopt the distorted octahedral coordination but Zn(II) tetrahedral one.The carboxylate groups in the complexes with M(II) cations function as monodentate, bidentate and/or free COO-groups. The ligands exist in the crystals as aquaanions. The complexes of 5-chloro-2-methoxybenzoates with Mn(II), Co(II) and Zn(II) form bilayer structure.

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The complexes of silver(I) with 2,3-, 2,4-, 2,6-, 3,4-, 3,5-dimethoxy-, and 2,3,4- and 3,4,5-trimethoxybenzoic acid anions have been synthesized and characterized by elemental analysis, IR spectroscopy, thermogravimetric and X-ray studies. Their solubility in water has been also determined at 293K. All analysed complexes were found to be crystalline, anhydrous compounds with low symmetry. The carboxylate groups act as bidentate or monodentate ligands. The thermal stability of compounds has been examined in air in temperature range of 293-1173K. The analysed complexes were found to be stable at room temperature and their solubilities in water at 293K to be in the order of 10-4 mol.dm-3.

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Karyotypes of 14 populations including eight species of the genus Lobelia were studied using root tip mitotic metaphases. All populations were tetraploid with 2n = 28 chromosomes. The chromosome base number x = 7 was confirmed for the genus. Karyotype analysis showed that chromosome size varied from 1.05 µm to 2.02 µm with predominance of M and SM chromosome types. The karyotypes were similar among themselves with small intra- and interspecific variations on the size of haploid sets, symmetry indexes and centromere position of some chromosome pairs. These results showed that karyotypes of Brazilian lobelias of the subgenus Tupa were probably due to polyploidy associated with chromosomal rearrangements probably in small chromatin segments.

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Lecythidaceae is the family of the Brazil nut, and comprises about 300 species belonging to 17 genera with pantropical distributions. One hundred and twenty-two species belonging to nine genera are distributed throughout Brazil, demonstrating its greatest diversity in the Amazon rainforest where Lecythidaceae is also one of the most abundant families. It is usually difficult to collect fertile material from these trees because of their canopy heights, and species determinations using sterile material can be complex because of their morphological similarities. There have been relatively few studies of this family even though it is one of the most important groups in the Amazon region, and a detailed taxonomic treatment of the species of Lecythidaceae in the Tupé Sustainable Development Reserve was therefore the goal of the present work. Ten species were found, Allantoma lineata (Mart. ex O.Berg) Miers, Bertholletia excelsa Bonpl., Couratari tenuicarpa A.C.Sm., Lecythis poiteaui O. Berg; and six species of Eschweilera, the richest genus. The descriptions and identification keys of the species used 56 characters. The main reproductive characters useful for distinguishing the species were the pubescence of the inflorescence rachis, pedicel length and trichomes presence, floral symmetry, hood type, filament shape, stigma shape, fruit shape and size, and aril type. The most diagnostic vegetative characters were the type and color of the outer bark, inner bark color, midrib prominence, and petiole shape and pubescence.