Search results for " Geometry"

Syntheses, crystal structures and magnetic properties of di- and trinuclear croconato-bridged copper(ii) complexes

2002

The new croconato-bridged copper(II) compounds [Cu2(terpy)2(H2O)2(C5O5)](NO3)2·H2O (1) and [Cu3(phen)5(C5O5)2](CF3SO3)2 (2) (C5O52− = croconate, dianion of 4,5-dihydroxycyclopent-4-ene-1,2,3-trione; terpy = 2,2′:6′,2″-terpyridine; phen = 1,10-phenanthroline) have been prepared, and their crystal structures and variable temperature magnetic susceptibilities determined. The structure of complex 1 consists of croconato-bridged dinuclear [Cu2(terpy)2(H2O)2(C5O5)]2+ complex ions, nitrate counter ions and water of hydration. The croconato ligand exhibits an asymmetrical bis-bidentate coordination mode through four of its five oxygen atoms. The two crystallographically independent copper atoms hav…

[MoO2(SCPh2CO2)2]2− and [MoO(SCPh2CO2)2]− anion complexes. A theoretical structure characterization

1995

Abstract Geometry optimization of [MoO 2 (SCH 2 CO 2 ) 2 ] 2− and [MoO(SCH 2 CO 2 ) 2 ] − systems as models of [MoO 2 (SCPh 2 CO 2 ) 2 ] 2− and [MoO(SCPh 2 CO 2 ) 2 ] − anion complexes have been carried out at STO-3G, 3-21G, LANL1MB and LANL2DZ basis set levels. A comparison of the theoretical results and X-ray experimental data has been performed. STO-3G minimal basis set produces the best geometrical agreement, in particular the distances and orientations of the different ligands linked to molybdenum transition metal. A large structural overlap with STO-3G optimized geometry and X-ray data has been found for the [MoO 2 (SCPh 2 CO 2 ) 2 ] 2− and [MoO(SCPh 2 CO 2 ) 2 ] − anion complexes.

Syntheses, crystal structures and magnetic properties of dinuclear copper(II) complexes with pyrazino[2,3-f  ][4,7]phenanthroline (pap) as bridging l…

2000

Three dinuclear copper(II) complexes with pyrazino[2,3-f][4,7]phenanthroline (pap) as bridging ligand have been prepared; [Cu2(pap)(C2O4)2]·5H2O 1, [Cu2(pap)(H2O)7(SO4)]SO4·3H2O 2 and [Cu2(pap)(H2O)3(NO3)3]NO33. These are the first metal complexes of pap which have been characterized by X-ray crystallography and magnetic susceptibility measurements. In 1 the dinuclear complex is intercepted by a mirror plane; the bridging pap and the terminal oxalate ligands are bidentate in the equatorial plane of copper. In addition copper has weak axial interactions to oxygen atoms of oxalate in two neighbouring molecules. In 2 the two crystallograpically independent copper atoms are both six-co-ordinate…

A trigonal-bipyramidal cyanide cluster with single-molecule-magnet behavior: synthesis, structure, and magnetic properties of ([MnII(tmphen)2]3[MnIII…

2003

Usage des points massiques et des courbes de Bézier pour la modélisation des cubiques

2017

International audience; Cet article étend l'étude des points singuliers et des points d'inflexion des courbes rationnelles cubiques en s'ins-pirant de la méthode proposée par M. Sakai dans le cadre des points massiques. L'intérêt des points massiques est de généraliser le tracé des courbes admettant des points doubles et de contrôler sans calcul supplémentaire l'en-semble des fonctions algébriques cubiques. Un exemple d'application est la réalisation de lettre à l'anglaise ou lettre manuscrite. Les courbes de Bézier permettent d'approcher des profils complexes, le travail présenté permet d'aborder de la même manière l'ensemble des courbes, ce que ne permet pas les splines cubiques d'Hermite.

Points massiques, cubiques Bézier rationnelles et leur points singuliers

2018

National audience; Cet articleétend l'étude des points singuliers des courbes rationnelles cubiques. Ellle porte sur les points d'inflexion, les points doubles et points de rebroussement. Les courbes cubiques rationnelleś etudiées sont décrites au moyen de la technique des points massiques. Un point massique est soit un point pondéré soit un vecteur pur. Il prend le statut de point de contrôle pour une représentation pa-ramétrique exploitable sur ordinateur dans le domaine de la géométrie de la Conception Assistée par Ordinateur. L'intérêt des points massiques est de pouvoir généraliser le tracé des courbes admettant des points doubles et de contrôler sans calcul supplémentaire l'ensemble d…

Minimal unit vector fields

2002

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

The exterior derivative as a Killing vector field

1996

Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.

Differential geometric LARS via cyclic coordinate descent method

2012

We address the problem of how to compute the coefficient path implicitly defined by the differential geometric LARS (dgLARS) method in a high-dimensional setting. Although the geometrical theory developed to define the dgLARS method does not need of the definition of a penalty function, we show that it is possible to develop a cyclic coordinate descent algorithm to compute the solution curve in a high-dimensional setting. Simulation studies show that the proposed algorithm is significantly faster than the prediction-corrector algorithm originally developed to compute the dgLARS solution curve.

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives.

2012

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and …