Search results for "planarity"
showing 10 items of 59 documents
Dicopper(II) pyrazolenophanes: Ligand effects on their structures and magnetic properties
2016
Abstract The use of simple pyrazolate anions and related polychelating acyclic or macrocyclic pyrazolate derivatives as bridging ligands, and occasionally additional blocking ligands, has led to the stereospecific Cu II -mediated self-assembly of both homo- and heteroleptic di-μ-pyrazolatodicopper(II) complexes of the metallacyclophane type, so-called dicopper(II) pyrazolenophanes. Besides their unique molecular conformation features and binding abilities toward both neutral molecules and charged anionic species, which have illustrated the putative role of weak intramolecular π–π stacking, hydrogen bonding, and coordinative interactions in the self-assembling process, dicopper(II) pyrazolen…
"Table 23" of "Energy dependence of event shapes and of alpha(s) at LEP-2."
1999
Distributions of Planarity at cm energies 133, 161 and 172 GeV.
"Table 24" of "Energy dependence of event shapes and of alpha(s) at LEP-2."
1999
Distribution of Planarity at cm energy 183 GeV.
2,2-Difluoro-3-(4-fluorophenyl)-2H-benzo[e][1,3,2]oxazaborinin-3-ium-2-uide
2017
There is one independent molecule in the asymmetric unit of the title compound, C13H9BF3NO, which crystallizes in the non-centrosymmetric space groupCc. In the molecular structure, the BF2-carrying ring is distorted from planarity and its mean plane makes a dihedral angle of 42.3 (1)° with the 4-fluorophenyl ring. F atoms are involved in all of the short intermolecular contacts of the crystal structure, which link molecules to form chains along [001] and [010].
Ab initio study of rotational isomerism and electronic structure of isomeric bipyrroles
1985
Abstract Ab initio calculations using STO-3G and 4-31G basis sets have been performed on the internal rotation barriers and conformational stabilities for 2,3′- and 3,3′-bipyrrole. The twofold rotation potential predicted for both isomers at minimal basis level becomes a more involved fourfold potential when the split-valence basis set is employed, because it takes into account more properly the nonbonded interannular interactions. A transoid-gauche minimum is predicted to have the minimal absolute conformational energy in both isomers. The electronic structure of the highest occupied MOs of 2,2′-, 2,3′- and 3,3′-bipyrrole are analyzed in terms of the single pyrrole MO pattern and a similar…
Structure, magnetizability, and nuclear magnetic shielding tensors of bis-heteropentalenes. IV. Dihydrophospholophosphole isomers
2005
The geometry of the heteropentalenes formed by two phosphole units has been determined at the DFT level. The magnetic susceptibility and the nuclear magnetic shielding at the nuclei of these systems have also been calculated using gauge-including atomic orbitals and a large Gaussian basis set to achieve near Hartree-Fock estimates. A comparative study of the various isomers, of their flattened analogs, and of the parent phosphole molecule, shows that the [3,4-c] isomer is the most aromatic system in the set considered, assuming diatropicity and degree of planarity as indicators, even if it is the less stable in terms of total molecular energy. Plots of magnetic field-induced current densiti…
3-Formyl-2-furanboronic acid: X-ray and DFT studies
2004
The molecule of the title compound, C5H5BO4, is almost planar with the boronic acid group inclined to the furan ring by 3.7 (1)°. DFT (density functional theory) calculations at the B3LYP/6-311+G** level of theory (with no imaginary frequencies) were used to approximate the influence of hydrogen bonding on the molecular geometry and have confirmed the planarity of the molecule. No significant differences in geometrical parameters in the solid state and in the gas phase are associated with the presence of the O—H⋯O intermolecular hydrogen-bonding network. The crystal packing is characterized by O—H⋯O hydrogen-bonded dimers, which are additionally linked by O—H⋯O, as well as C—H⋯O interactio…
Quantum Query Complexity of Boolean Functions with Small On-Sets
2008
The main objective of this paper is to show that the quantum query complexity Q(f) of an N-bit Boolean function f is bounded by a function of a simple and natural parameter, i.e., M = |{x|f(x) = 1}| or the size of f's on-set. We prove that: (i) For $poly(N)\le M\le 2^{N^d}$ for some constant 0 < d < 1, the upper bound of Q(f) is $O(\sqrt{N\log M / \log N})$. This bound is tight, namely there is a Boolean function f such that $Q(f) = \Omega(\sqrt{N\log M / \log N})$. (ii) For the same range of M, the (also tight) lower bound of Q(f) is $\Omega(\sqrt{N})$. (iii) The average value of Q(f) is bounded from above and below by $Q(f) = O(\log M +\sqrt{N})$ and $Q(f) = \Omega (\log M/\log N+ \sqrt{N…
New Geometric Constraint Solving Formulation: Application to the 3D Pentahedron
2014
Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be …
The energy dependence of Zweig-rule-violating couplings. A dynamical calculation of ϕ → ρπ
1978
It has been argued that the violation of the Zweig rule is strongly dependent on the kinematical region, especially that it should decrease for large timeliket (asymptotic planarity). We have calculated thet-dependence of the vertex ϕρπ with two different methods, the first one using partial-wave dispersion relations and unitarity and the second one based on FESR and duality. The decrease in the timelike region is confirmed by both calculations. In the spacelike region the energy dependence of the Zweig-rule-violating coupling depends on the method of continuation to off-shell values. We only find an energy dependence if the full amplitude πρ → K $$\bar K$$ is taken into account.