Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

How reward modulates mimicry: EMG evidence of greater automatic facial mimicry of more rewarding faces

Spontaneous mimicry is a marker of empathy. Conditions characterized by reduced spontaneous mimicry (e.g., autism) also display deficits in sensitivity to social rewards. We tested if spontaneous mimicry of socially rewarding stimuli (happy faces) depends on the reward value of stimuli in 32 typical participants. An evaluative conditioning paradigm was used to associate different reward values with neutral target faces. Subsequently, electromyographic activity over the Zygomaticus Major was measured whilst participants watched video clips of the faces making happy expressions. Higher Zygomaticus Major activity was found in response to happy faces conditioned with high reward versus low reward. Moreover, autistic traits in the general population modulated the extent of spontaneous mimicry of happy faces. This suggests a link between reward and spontaneous mimicry and provides a possible underlying mechanism for the reduced response to social rewards seen in autism.

Synthesis and phase behaviour of a homologous series of polymethacrylate-based side-chain liquid crystal polymers

The homologous series of side chain liquid crystal polymers, the poly[x-(4-methoxyazobenzene- 40-oxy)alkyl methacrylate]s, has been prepared in which the length of the flexible alkyl spacer has been varied from 3 to 11 methylene units. All the polymers exhibit liquid crystalline behaviour. The propyl and butyl members show exclusively nematic behaviour. The pentyl, hexyl, octyl and decyl members show a nematic and a smectic A phase while the heptyl, nonyl and undecyl homologues exhibit only a smectic A phase. The smectic A phase has been studied using X-ray diffraction and assigned as a smectic A1 phase in which the side chains are fully overlapped and the backbones are confined to lie between the smectic layers. For the nonyl member an incommensurate smectic phase is observed. The dependence of the transition temperatures on the length of the flexible spacer is understood in terms of the average shapes of the side chains.

Crystal structures of Λ-[Ru(phen)2dppz]2+ with oligonucleotides containing TA/TA and AT/AT steps show two intercalation modes

The ruthenium complex [Ru(phen)2(dppz)] (where phen is a phenanthroline and dppz a dipyridyl–phenazine ligand) is known as a ‘light switch’ complex because its luminescence in solution is significantly enhanced in the presence of DNA. This property is poised to serve in diagnostic and therapeutic applications, but its binding mode with DNA needs to be elucidated further. Here, we describe the crystal structures of the L enantiomer bound to two oligonucleotide duplexes. The dppz ligand intercalates symmetrically and perpendicularly from the minor groove of the d(CCGGTACCGG)2 duplex at the central TA/TA step, but not at the central AT/AT step of d(CCGGATCCGG)2. In both structures, however, a second ruthenium complex links the duplexes through the combination of a shallower angled intercalation into the C1C2/G9G10 step at the end of the duplex, and semi-intercalation into the G3G4 step of an adjacent duplex. The TA/TA specificity of the perpendicular intercalation arises from the packing of phenanthroline ligands against the adenosine residue.

Characterizing typographic expertise: do we process typefaces like faces?

Studies of face recognition and discrimination provide a rich source of data and debate on the nature of their processing, in particular through using inverted faces. This study draws parallels between the features of typefaces and faces, as letters share a basic configuration, regardless of typeface, that could be seen as similar to faces. Typeface discrimination is compared using paragraphs of upright letters and inverted letters at three viewing durations. Based on previously reported effects of expertise, the prediction that designers would be less accurate when letters are inverted, whereas nondesigners would have similar performance in both orientations, was confirmed. A proposal is made as to which spatial relations between typeface components constitute holistic and configural processing, posited as the basis for better discrimination of the typefaces of upright letters. Such processing may characterize designers’ perceptual abilities, acquired through training.

Synthesis and crystal structure of a novel octa-aqua bridged star-shaped Ni4K complex

A penta-nuclear. star-shaped hetero-metallic compound containing a unique Ni4KO8 core has been synthesized. The X-ray single crystal structure analysis reveals that in the complex, [K(Ni(LH)(2))(4)(OH2)(8)](Br)(ClO4)(8)center dot 11H(2)O (LH=(CH3)(2)HN+(CH2)(3)N=CHC6H4O-) the eight coordinate central K+ ion is encapsulated by four terminal [Ni(LH)(2)](2+) units through the double water bridges between K+ and each Ni(II) ions.

Synthesis, crystal structures, magnetic properties and catecholase activity of double phenoxido-bridged penta-coordinated dinuclear nickel(II) complexes derived from reduced Schiff-base ligands: mechanistic inference of catecholase activity

Three double phenoxido-bridged dinuclear nickel(II) complexes, namely [Ni-2(L-1)(2)(NCS)(2)] (1), [Ni-2(L-2)(2)(NCS)(2)] (2), and [Ni-2(L-3)(2)(NCS)(2)] (3) have been synthesized using the reduced tridentate Schiff-base ligands 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL1), 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL2), and 2-[1-(3-dimethylarnino-propylamino)-ethyl]-phenol (HL3), respectively. The coordination compounds have been characterized by X-ray structural analyses, magnetic-susceptibility measurements, and various spectroscopic methods. In all complexes, the nickel(II) ions are penta-coordinated in a square-pyramidal environment, which is severely distorted in the case of 1 (Addison parameter tau = 0.47) and 3 (tau = 0.29), while it is almost perfect for 2 (tau = 0.03). This arrangement leads to relatively strong antiferromagnetic interactions between the Ni(II) (S = 1) metal centers as mediated by double phenoxido bridges (with J values of -23.32 (1), -35.45 (2), and -34.02 (3) cm(3) K mol(-1), in the convention H = -2JS(1)S(2)). The catalytic activity of these Ni compounds has been investigated for the aerial oxidation of 3,5-di-tert-butylcatechol. Kinetic data analysis following Michaelis-Menten treatment reveals that the catecholase activity of the complexes is influenced by the flexibility of the ligand and also by the geometry around the metal ion. Electrospray ionization mass spectroscopy (ESI-MS) studies (in the positive mode) have been performed for all the coordination compounds in the presence of 3,5-DTBC to characterize potential complex-substrate intermediates. The mass-spectrometry data, corroborated by electron paramagnetic resonance (EPR) measurements, suggest that the metal centers are involved in the catecholase activity exhibited by the complexes.

Synthesis, crystal structure, and catecholase activity of three trinuclear heterometallic NiII2-MnII complexes derived from a salen-type Schiff base ligand

Three new trinuclear heterometallic nickel(II)manganese(II) complexes, [(NiL)2Mn(NCS)2] (1), [(NiL)2Mn(NCO)2] (2), and [{NiL(EtOH)}2Mn(NO2)2]center dot 2EtOH (3), have been synthesized by using [NiL] as the so-called ligand complex [where H2L = N,N'-bis(salicylidene)-1,3-propanediamine] and have been structurally characterized. Crystal structure analyses revealed that complexes 1 and 2 are angular trinuclear species, in which two terminal four-coordinate square planar [NiL] moieties are coordinated to a central MnII through double phenoxido bridges. The MnII is in a six-coordinate distorted octahedral environment that is bonded additionally to two mutually cis nitrogen atoms of terminal thiocyanate (in 1) and cyanate (in 2). In complex 3, in addition to the double phenoxo bridge, the two terminal NiII ions are linked to the central MnII by means of a nitrite bridge (1?N:2?O) that, together with a coordinated ethanol molecule, gives rise to an octahedral environment around the NiII ions and consequently the structure becomes linear. Catecholase activity of these three complexes was examined by using 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. All three complexes mimic catecholase activity and the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first-order kinetics with respect to the catalyst. The EPR spectra of the complexes exhibit characteristic six line spectra, which indicate the presence of high-spin octahedral MnII species in solution state. The ESI-MS positive spectrum of 1 in the presence of 3,5-DTBC has been recorded to investigate possible complexsubstrate intermediates.

Synthesis, chemical, electrochemical characterization of oxomolybdenum(V) complexes of 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole ligand: crystal structure of ligand and oxomolybdenum(VI) complex and density functional theory (DFT) calculation

This work reports the ligational behavior of the neutral bidentate chelating molecule 2-(3,5-dimethyl pyrazol-1-yl) benzothiazole towards the oxomolybdenum(V) center. Both mononuclear complexes of the type (MoOX3L)-O-V and binuclear complexes of the formula (Mo2O4X2L2)-O-V (where X = Cl, Br) are isolated in the solid state. The complexes are characterized by elemental analyses, various spectroscopic techniques (UV-Vis IR), magnetic susceptibility measurement at room temperature, and cyclic voltammetry for their redox behavior at a platinum electrode in CH3CN. The mononuclear complexes (MoOX3L)-O-V are found to be paramagnetic while the binuclear complexes Mo2O4X2L2 are diamagnetic. Crystal and molecular structure of the ligand and the dioxomolybdenum complex (MoO2Br2L)-O-VI (obtained from the complex MoOBr3L during crystallization) have been solved by single crystal X-ray diffraction technique. Relevant DFT calculations of the ligand and the complex (MoO2Br2L)-O-VI are also carried out.

Oxidoalkoxidovanadium(V) complexes: synthesis, characterization and comparison of X-ray crystal structures

The reaction of VO(acac)(2) with the ONO-chelator obtained by the condensation of salicylaldehyde with 2-hydroxybenzoylhydrazine (H2L) in a monohydric alcohol. (ROH) medium produces VO(OR)L]-type oxidoalkoxido complexes (1-7) where R = Me, Pr-n, Pr-i, Bu-n, Bu-i, Bu-t and (n)Pen. All the complexes show the metal atom to have a five-coordinate square pyramidal environment, although in some complexes there is an additional weak V center dot center dot center dot O interaction in the sixth axial position. In acetonitrile medium and in the presence of a cis-diol (ethylene glycol), H2L reacts with VO(acac)(2) to form a six-coordinate complex, [VO(OCH2CH2OH)L] (8). When the reaction is carried out in acetonitrile medium in the presence of 2-amino ethanol, a completely different type of product containing the square pyramidal complex anion [VO2L](-) associated with the cation [NH3CH2CH2OH](+) is obtained. It was noted previously that on being reacted with monodentate nitrogen donor bases B (which are stronger than pyridine), the [VO(OR)L] complexes react to form the same complex anion [VO2L](-) associated with the corresponding cation [BH](+). The coordination environment around the V(V) acceptor center of the water soluble [BH](+)[VO2L](-)satisfies one of the several requirements for an efficient antidiabetic vanadium species such as water solubility, nature of donor atoms of the ligand and their disposition around the VO2+ acceptor center.

Effect of a methyl group on the spontaneous resolution of a square-pyramidal coordination compound: crystal packing and conglomerate formation

Reaction of [Cu(pic)2]·2H2O (where pic stands for 2-picolinato) with 2-({[2-(dimethylamino)ethyl]amino}methyl)phenol (HL1) produces the square-pyramidal complex [CuL1(pic)] (1), which crystallizes as a conglomerate (namely a mixture of optically pure crystals) in the Sohncke space group P212121. The use of the methylated ligand at the benzylic position, i.e. (±)-2-(1-{[2-(dimethylamino)ethyl]amino}ethyl)phenol (HL2), yields the analogous five-coordinate complex [CuL2(pic)] (2) that crystallizes as a true racemate (namely the crystals contain both enantiomers) in the centrosymmetric space group P21/c. Density functional theory (DFT) calculations indicate that the presence of the methyl group indeed leads to a distinct crystallization behaviour, not only by intramolecular steric effects, but also because its involvement in non-covalent C–H···π and hydrophobic intermolecular contacts appears to be an important factor contributing to the crystal-lattice (stabilizing) energy of 2

Synthesis, characterization, crystal structure, and DNA-binding of ruthenium(II) complexes of heterocyclic nitrogen ligands resulting from a benzimidazole-based quinazoline derivative

The reaction of cis-[RuCl2(dmso)(4)] with [6-(2-pyridinyl)-5,6-dihydrobenzimidazo[1,2-c] quinazoline] (L) afforded in pure form a blue ruthenium(II) complex, [Ru(L-1)(2)] (1), where the original L changed to [2-(1H-benzoimidazol-2-yl)-phenyl]-pyridin-2-ylmethylene-amine (HL1). Treatment of RuCl3 center dot 3H(2)O with L in dry tetrahydrofuran in inert atmosphere led to a green ruthenium(II) complex, trans-[RuCl2(L-2)(2)] (2), where L was oxidized in situ to the neutral species 6-pyridin-yl-benzo[4,5]imidazo[1,2-c] quinazoline (L-2). Complex 2 was also obtained from the reaction of RuCl3 center dot 3H(2)O with L-2 in dry ethanol. Complexes 1 and 2 have been characterized by physico-chemical and spectroscopic tools, and 1 has been structurally characterized by single-crystal X-ray crystallography. The electrochemical behavior of the complexes shows the Ru(III)/Ru(II) couple at different potentials with quasi-reversible voltammograms. The interaction of these complexes with calf thymus DNA by using absorption and emission spectral studies allowed determination of the binding constant K-b and the linear Stern-Volmer quenching constant K-SV

Synthesis, crystal structures and magnetic properties of two bis(μ-phenoxido)dicopper(II) complexes derived from reduced Schiff base ligands

Two phenoxido bridged dinuclear Cu(II) complexes, [Cu-2(L-1)(2)(NCNCN)(2)] (1) and [Cu-2(L-2)(2)(NCNCN)(2)]center dot 2H(2)O (2) have been synthesized using the tridentate reduced Schiff-base ligands 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL1) and 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL2), respectively. The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. Both the complexes present a diphenoxido bridging Cu2O2 core. The geometries around metal atoms are intermediate between trigonal bipyramid and square pyramid with the Addison parameters (tau) = 0.57 and 0.49 for 1 and 2, respectively. Within the core the Cu-O-Cu angles are 99.15 degrees and 103.51 degrees and average Cu-O bond distances are 2.036 and 1.978 angstrom for compounds 1 and 2, respectively. These differences have marked effect on the magnetic properties of two compounds. Although both are antiferromagnetically coupled, the coupling constants (J = -184.3 and -478.4 cm (1) for 1 and 2, respectively) differ appreciably.

Synthesis, crystal structure, and magnetic properties of a very rare double μ-1,1-azido- and a μ-1,1-(OMe)-bridged FeIII dimer containing a N,N,O-donor tridentate Schiff base ligand

Two new Fe-III complexes, [Fe2L2(mu-OMe)(2)(NCS)(2)] (1) and [Fe2L2(mu-N-3)(2)(N-3)(2)] (2), have been synthesized using a N,N,O-donor tridentate Schiff base ligand HL {2-[(2-dimethylaminoethylimino)methyl]phenol}, the condensation product of salicylaldehyde and N,N-dimethyl-1,2-diaminoethane. The complexes were characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. Both crystal structures are centrosymmetric dimers containing two Fe-III atoms, which are bridged in compound 1 by two methoxy anions and in compound 2 by two mu-1,1-azides. The chelating tridentate Schiff base and a terminal thiocyanato (for 1) or azido (for 2) group complete the hexacoordination of the distorted octahedral environment of each iron center. The magnetic properties of compound 1 show the presence of antiferromagnetic exchange interactions mediated by double methoxy bridges (J = -29.45 cm(-1)). Compound 2 shows the presence of very weak ferromagnetic exchange interactions mediated by double mu-1,1-N-3 bridges (J = 1.08 cm(-1)).

Peroxidative bromination and oxygenation of organic compounds: synthesis, X-ray crystal structure and catalytic implications of mononuclear and binuclear oxovanadium(V) complexes containing Schiffbase ligands

Treatment of of (R,R)-N,N-salicylidene cyclohexane 1,2-diamine(H(2)L(1)) in methanol with aqueous NH(4)VO(3) solution in perchloric acid medium affords the mononuclear oxovanadium(V) complex [VOL(1)(MeOH)]-ClO(4) (1) as deep blue solid while the treatment of same solution of (R,R)-N,N-salicylidene cyclohexane 1,2-diamine(H(2)L(1)) with aqueous solution of VOSO(4) leads to the formation of di-(mu-oxo) bridged vanadium(V) complex [VO(2)L(2)](2) (2) as green solid where HL(2) = (R,R)-N-salicylidene cyclohexane 1,2-diamine. The ligand HL(2) is generated in situ by the hydrolysis of one of the imine bonds of HL(1) ligand during the course of formation of complex [VO(2)L(2)](2) (2). Both the compounds have been characterized by single crystal X-ray diffraction as well as spectroscopic methods. Compounds 1 and 2 are to act as catalyst for the catalytic bromide oxidation and C-H bond oxidation in presence of hydrogen peroxide. The representative substrates 2,4-dimethoxy benzoic acid and para-hydroxy benzoic acids are brominated in presence of H(2)O(2) and KBr in acid medium using the above compounds as catalyst. The complexes are also used as catalyst for C-H bond activation of the representative hydrocarbons toluene, ethylbenzene and cyclohexane where hydrogen peroxide acts as terminal oxidant. The yield percentage and turnover number are also quite good for the above catalytic reaction. The oxidized products of hydrocarbons have been characterized by GC Analysis while the brominated products have been characterized by (1)H NMR spectroscopic studies.