Search results for "Point group"
showing 10 items of 18 documents
IRREDUCIBLE COXETER GROUPS
2004
We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group. Write W = WX1 × ⋯ × WXb × WZ3, where WX1, … , WXb are non-spherical irreducible Coxeter groups and WZ3 is a finite one. By a classical result, known as the Krull–Remak–Schmidt theorem, the group WZ3 has a decomposition WZ3 = H1 × ⋯ × Hq as a direct product of indecomposable groups, which is unique up to a central automorphism and a permutation of the factors. Now, W = WX1 × ⋯ × WXb × H1 × ⋯ × Hq is a decomposition of W as a dir…
Does Ligand Symmetry Play a Role in the Stabilization of DNA G-Quadruplex Host-Guest Complexes?
2014
In efforts to find agents with improved biological activity against cancer cells, recent years have seen an increased interest in the study of small molecules able to bind the deoxyribonucleic acid (DNA) when it assumes secondary structures known as G-quadruplexes (G4s) preferring them over the B form. Currently, several compounds reported in literature have already shown to be good candidates as G4s DNA stabilizers. Even though some specific features for the G4s affinity are known, such as a π-delocalized system able to stack at the top/end of a G-tetrad and positively charged substituents able to interact with the grooves, it is not clear yet what kind of structural features affect more t…
Commensurability classification of a family of right-angled Coxeter groups
2008
We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.
Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups
2004
International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…
Spin-order dependent anomalous Hall effect and magneto-optical effect in the noncollinear antiferromagnets Mn3XN with X=Ga , Zn, Ag, or Ni
2019
The anomalous Hall effect (AHE) and the magneto-optical effect (MOE) are two prominent manifestations of time-reversal symmetry breaking in magnetic materials. Noncollinear antiferromagnets (AFMs) have recently attracted a lot of attention owing to the potential emergence of exotic spin orders on geometrically frustrated lattices, which can be characterized by corresponding spin chiralities. By performing first-principles density functional calculations together with group-theory analysis and tight-binding modeling, here we systematically study the spin-order dependent AHE and MOE in representative noncollinear AFMs ${\mathrm{Mn}}_{3}X\mathrm{N}\phantom{\rule{4pt}{0ex}}(X=\mathrm{Ga}$, Zn, …
Extension of the MIRS computer package for the modeling of molecular spectra : from effective to full ab initio ro-vibrational hamiltonians in irredu…
2012
The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version (Nikitin, et al. JQSRT, 2003, pp. 239--249) was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possib…
Temperature-dependent polymorphism of N-(4-fluorophenyl)-1,5-dimethyl-1H-imidazole-4-carboxamide 3-oxide: experimental and theoretical studies on int…
2014
X-ray analysis of N-(4-fluorophenyl)-1,5-dimethyl-1H-imidazole-4-carboxamide 3-oxide reveals the temperature-dependent polymorphism associated with the crystallographic symmetry conversion. The observed crystal structure transformation corresponds to a symmetry reduction from I41 /a (I) to P43 (II) space groups. The phase transition mainly concerns the subtle but clearly noticeable reorganization of molecules in the crystal space, with the structure of individual molecules left almost unchanged. The Hirshfeld surface analysis shows that various intermolecular contacts play an important role in the crystal packing, revealing graphically the differences in spatial arrangements of the molecule…
Chemistry of density : extension and structural origin of Carnelley's rule in chloroethanes
2012
Low-density liquids and solids, with all intermolecular contacts longer than the sum of van der Waals radii, are formed by all ethanes chlorinated at one locant: CH2ClCH3, CHCl2CH3 and CCl3CH3. The concepts of molecular symmetry described by Carnelley and that of point groups have been compared. Carnelley's rule, when applied to liquid and solid chloroethanes clearly reveals the density dependence on the presence of intermolecular Cl⋯Cl and H⋯Cl short contacts, or their absence due to steric hindrances of overcrowded substituents. At 2.62 GPa, CH2ClCH3 freezes directly into phase II, with molecules arranged into layers with short Cl⋯Cl, H⋯Cl and H⋯H contacts. Only for CH2ClCH3, both the low…
Symmetry and Stability of the Rutile-Based TiO2 Nanowires: Models and Comparative LCAO-Plane Wave DFT Calculations
2012
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like titania nanowires (NWs) cut from a rutile-based 3D crystal along the direction of a chosen crystallographic symmetry axis (in this study we consider only Ti atom-centered axes). The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only, while the nanowires with quasi-square sections across the [110] axis are formed by the alternating {110} and {001} facets. For simulations on rutile-based nanowires possessing four different diameters for each NW type, we have performed comparative large-scale ab …
Morphotropic ceramic solid solutions of the Pb(B3+½Nb½)O3- PbTiO3binary system
2000
Abstract The structure, dielectric, ferroelectric and electromechanical properties of lead lutecium niobate-titanate (PLuNT) and lead erbium niobate-titanate (PErNT) binary systems are reported. The data of phase diagram, crystallographic symmetry and morphotropic phase boundaries (MPB) are provided. High values of the electromechanical coupling coefficients kp = 0.66, kt = 0.48, k31 = 0.36 of (1−x)PLuN − xPT ceramics are attained in compositions near the MPB at x≈0.41.