Perceptual and physiological responses to the visual complexity of fractal patterns

Fractals have experienced considerable success in quantifying the complex structure exhibited by many natural patterns and have captured the imagination of scientists and artists alike. With ever widening appeal, they have been referred to both as "fingerprints of nature" and "the new aesthetics." Our research has shown that the drip patterns of the American abstract painter Jackson Pollock are fractal. In this paper, we consider the implications of this discovery. We first present an overview of our research from the past five years to establish a context for our current investigations of human response to fractals. We discuss results showing that fractal images generated by mathematical, natural and human processes possess a shared aesthetic quality based on visual complexity. In particular, participants in visual perception tests display a preference for fractals with mid-range fractal dimensions. We also present recent preliminary work based on skin conductance measurements that indicate that these mid-range fractals also affect the observer's physiological condition and discuss future directions based on these results.     

Theoretical study of a 1 : 1 complex between quinone and hydroquinone

The Variable Electronegativity Pariser–Parr–Pople method has been successfully applied to calculate the potential energy curve for the formation of a 1: 1 complex between quinone and hydroquinone. A consistent evaluation of core and electronic repulsion integrals is important to obtain a meaningful curve. A computationally simple procedure has been suggested for separating interactions due to electron exchange between the components from other intermolecular interactions. In agreement with experimental deductions the preferred configuration for the quinone-hydroquinone complex is found to be one in which the molecules are in parallel planes with their C—O bonds parallel. The equilibrium separation between the molecular planes is found to be 2.3 Å and the stabilization energy in this position is 1.2 eV. In this equilibrium position forces due to electron exchange constitute the major contributing factor to the stability of the complex.     

Organotin biocides. X. Synthesis,structure and biocidal activity of organotin derivatives of 2-mercaptobenzothiazole, 2-mercaptobenzoxazole and 2-mercaptobenzimidazole

Ten organotin derivatives of 2-mercaptobenzothiazole (Hmbt), 2-mercaptobenzoxazole (Hmbo) and 2-mercaptobenzimidazole (Hmbi) have been synthesised and thier structures characterised by spectroscopic methods. Triorganotin derivatives are all S-bonded to the ligand and four-coordinate at tin except Bu₃Sn(mbo) which is five-coordinate trans-ONSnR₃ polymer at 78K. The crystal structure of Cy₃Sn(mbt) has been determined and confirms the tetrahedral geometry at tin. Bu₂Sn(mbt)₂ is weakly six-coordinate by N,S chelating ligands. Biocidal activity patterns are presented for Cy₃Sn(mbt), Ph₃Sn(mbt) and Ph₃Sn(mbo).     

Molecular-orbital calculations on some mesoionic compounds

Molecular-orbital calculations have been performed on sydnone, sydnone imine, ψ-oxatriazole, and isosydnone rings and their positive ionized forms by the Pariser–Parr–Pople–Brown–Heffernan method. The importance of elaborate open-shell calculations and the effect of introducing nonneighbor core resonance integrals in this order of approximation are investigated. The available experimental data on closely related compounds are qualitatively in agreement with the calculated values. The computed charges and bond orders demonstrate that certain structural features are common to all five-membered mesoionic ring systems and in agreement with recent experimental findings.     

Kinetic study of reaction of [ReN(H2O)(CN)4]2− with quinoline-2-carboxylate and pyridine-2,3-dicarboxylate anions

The kinetics of the reaction between [ReN(H₂O)-(CN)₄]²⁻ with different κ² N,O-donor ligands (quin⁻ and 2,3-dipic⁻, respectively) have been studied in the pH 4–12 range in aqueous solution. Two consecutive reaction steps with the formation of the [ReN(η¹-quin)(CN)₄]³⁻ and [ReN(μ²-quin) (CN)₃]²⁻ complexes, respectively, were spectrophotometrically observed and kinetically investigated. The same reaction mechanism is proposed for these two ligands. The first fast reaction (for quin⁻) is attributed to the aqua substitution of [ReN(H₂O)(CN)₄]²⁻ with forward and reverse rate constants of 1.96(5) × 10⁻¹ M⁻¹ s⁻¹ and 5.6(3) × 10⁻² s⁻¹, while a rate of 2.64(3) M⁻¹ s⁻¹ was observed for the reaction between the conjugate base [ReN(OH)(CN)₄]³⁻ and quin⁻ at 40.2 °C. Due to small absorbance changes, it was difficult to obtain any good quality data for the fast reactions for 2,3-dipic⁻. The second, slower reaction is attributed to cyano substitution with rate constants (k ₃ K ₁) of 4.17(4) × 10⁻³ for quin⁻ and 4.68(7) × 10⁻³ M⁻¹ s⁻¹ for 2,3-dipic⁻, at 80.02 °C, respectively. The acid dissociation constant for the aqua complex was spectrophotometrically determined as 11.58(3) and 11.54(2) and kinetically as 11.51(8) and 11.41(1), at 80.4 °C, respectively. Negative values of −83.5(2) and −144.1(2) J K⁻¹ mol⁻¹ as well as the of 71.4(3) and 47.3(3) kJ mol⁻¹, for the slow quin⁻ and 2,3-dipic⁻ reactions, respectively, point to an ordered transition state where bond formation is responsible for the major driving force of the reaction. The and for the fast forward reaction of quin⁻ is indicative of expected associative activation in the transition state. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Can <Emphasis Type="Italic">α</Emphasis>- and <Emphasis Type="Italic">β</Emphasis>-alanine containing peptides Be distinguished based on the CID spectra of their protonated ions?

The fragmentation reactions of isomeric dipeptides containing α- and β-alanine residues (αAla-αAla, αAla-βAla, βAla-αAla, and βAla-βAla) were studied using a combination of low-energy and energy resolved collision induced dissociation (CID). Each dipeptide gave a series of different fragment ions, allowing for differentiation. For example, peptides containing an N-terminal β-Ala residue yield a diagnostic imine loss, while lactam ions at m/z 72 are unique to peptides containing β-Ala residues. In addition, MS³ experiments were performed. Structure-specific fragmentation reactions were observed for y₁ ions, which help identify the C-terminal residue. The MS³ spectra of the b₂ ions are different suggesting they are unique for each peptide. Density functional theory (DFT) calculations predict that b₂ ions formed via a neighboring group attack by the amide are thermodynamically favored over those formed via neighboring group attack by the N-terminal amine. Finally, to gain further insight into the unique fragmentation chemistry of the peptides containing an N-terminal β-alanine residue, the fragmentation reactions of protonated β-Ala-NHMe were examined using a combination of experiment and DFT calculations. The relative transition-state energies involved in the four competing losses (NH₃, H₂O, CH₃NH₂, and CH₂=NH) closely follow the relative abundances of these as determined via CID experiments.     

Probing the origin of the compromised catalysis of E. coli alkaline phosphatase in its promiscuous sulfatase reaction

The catalytic promiscuity of E. coli alkaline phosphatase (AP) and many other enzymes provides a unique opportunity to dissect the origin of enzymatic rate enhancements via a comparative approach. Here, we use kinetic isotope effects (KIEs) to explore the origin of the 109-fold greater catalytic proficiency by AP for phosphate monoester hydrolysis relative to sulfate monoester hydrolysis. The primary 18O KIEs for the leaving group oxygen atoms in the AP-catalyzed hydrolysis of p-nitrophenyl phosphate (pNPP) and p-nitrophenylsulfate (pNPS) decrease relative to the values observed for nonenzymatic hydrolysis reactions. Prior linear free energy relationship results suggest that the transition states for AP-catalyzed reactions of phosphate and sulfate esters are "loose" and indistinguishable from that in solution, suggesting that the decreased primary KIEs do not reflect a change in the nature of the transition state but rather a strong interaction of the leaving group oxygen atom with an active site Zn2+ ion. Furthermore, the primary KIEs for the two reactions are identical within error, suggesting that the differential catalysis of these reactions cannot be attributed to differential stabilization of the leaving group. In contrast, AP perturbs the KIE for the nonbridging oxygen atoms in the reaction of pNPP but not pNPS, suggesting a differential interaction with the transferred group in the transition state. These and prior results are consistent with a strong electrostatic interaction between the active site bimetallo Zn2+ cluster and one of the nonbridging oxygen atoms on the transferred group. We suggest that the lower charge density of this oxygen atom on a transferred sulfuryl group accounts for a large fraction of the decreased stabilization of the transition state for its reaction relative to phosphoryl transfer.     

Speciation of nitrogen containing aromatics by atmospheric pressure photoionization or electrospray ionization fourier transform ion cyclotron resonance mass spectrometry

We determine the elemental compositions of aromatic nitrogen model compounds as well as a petroleum sample by atmospheric pressure photoionization (APPI) and electrospray Ionization (ESI) with a 9.4 Tesla Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. From the double-bond equivalents calculated for the nitrogen-containing ions from a petroleum sample, we can infer the aromatic core structure (pyridinic versus pyrrolic nitrogen heterocycle) based on the presence of M(+.) (odd-electron) versus [M+H](+) (even-electron) ions. Specifically, nitrogen speciation can be determined from either a single positive-ion APPI spectrum or two ESI (positive- and negative-ion) spectra. APPI operates at comparatively higher temperature than ESI and also produces radical cations that may fragment before detection. However, APPI fragmentation of aromatics can be eliminated by judicious choice of instrumental parameters.     

Characterization and oxidative addition reactions for iridium cod complexes

Three different [Ir(LL′)(cod)] complexes (LL′ = N-aryl-N-nitrosohydroxylaminato) (cupf), trifluoroacetylacetonato (tfaa), and (methyl 2-(methylamino)-1-cyclopentene-1-dithiocarboxylato-κN,κS) (macsm)) were synthesized, characterized, and their rates of oxidative addition with methyl iodide were determined. Formation of an isosbestic point during the oxidative addition of methyl iodide with the complexes containing tfaa and cupf as bidentate ligands indicated formation of only one product, while an increase in absorbance maximum observed for macsm confirms that the same reaction between the complex and methyl iodide occurs. Kinetic results for all complexes, except [Ir(tfaa)(cod)], showed simple second-order kinetics with a zero intercept (within experimental error). Rates of oxidative addition for bidentate ligands in acetonitrile showed an increase of an order of magnitude with a change in the type of bidentate ligands. Computational chemistry using density functional theory calculations showed that the oxidative addition reaction proceeds through a “linear” transition state with the methyl iodide unit tilted towards the LL′-bidentate ligand.