Superintegrability in Two Dimensions and the Racah–Wilson Algebra

The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the \({\mathfrak{su}(1,1)}\) algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively. The construction makes explicit the isomorphism between the Racah–Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for \({\mathfrak{su}(1, 1)}\) , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah–Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

The raspberry model for protein-like particles: Ellipsoids and confinement in cylindrical pores

The study of protein mass transport via atomistic simulation requires time and length scales beyond the computational capabilities of modern computer systems. The raspberry model for colloidal particles in combination with the mesoscopic hydrodynamic method of lattice Boltzmann facilitates coarse-grained simulations that are on the order of microseconds and hundreds of nanometers for the study of diffusive transport of protein-like colloid particles. The raspberry model reproduces linearity in resistance to motion versus particle size and correct enhanced drag within cylindrical pores at off-center coordinates for spherical particles. Owing to the high aspect ratio of many proteins, ellipsoidal raspberry colloid particles were constructed and reproduced the geometric resistance factors of Perrin and of Happel and Brenner in the laboratory-frame and in the moving body-frame. Accurate body-frame rotations during diffusive motion have been captured for the first time using projections of displacements. The spatial discretization of the fluid leads to a renormalization of the hydrodynamic radius, however, the data describes a self-consistent hydrodynamic frame within this renormalized system.     

Reaction of quinine, 9-epiquinine and their acetates in superacid in the presence of hydrogen peroxide: an access to new fluorhydrins and/or ketones

In HF-SbF₅, in the presence of H₂O₂ (source of OH⁺ equivalent) quinine 1a yields 10-keto derivatives 4a and 5a and cyclic ether 3 as the major product. In the same conditions 1b, 2a, and 2b give the 10-keto and 10-fluoro-3-hydroxy analogs.     

Cross-docking of inhibitors into CDK2 structures. 1

Predicting protein/ligand binding affinity is one of the most challenging computational chemistry tasks. Numerous methods have been developed to address this challenge, but they all have limitations. Failure to account for protein flexibility has been a shortcoming of many methods. In this cross-docking study the data set comprised 150 inhibitor complexes of the protein kinase CDK2. Gold and Glide performed well in terms of docking accuracy. The chance of cross-docking a ligand within a 2 A RMSD of its experimental pose was found to be 50%. Relative binding potency was not properly predicted from scoring functions, even though cross-docking of each inhibitor into each protein structure was performed and only scores of correctly docked ligands were considered. An accompanying paper (Voigt, J. H.; Elkin, C.; Madison, V. S. Duca, J. S. J. Chem. Inf. Model. 2008, 48, 669-678) covers cross-docking and docking accuracy from the perspective of using multiple protein structures.     

The protective role of melanin against UV damage in human skin

Human skin is repeatedly exposed to UVR that influences the function and survival of many cell types and is regarded as the main causative factor in the induction of skin cancer. It has been traditionally believed that skin pigmentation is the most important photoprotective factor, as melanin, besides functioning as a broadband UV absorbent, has antioxidant and radical scavenging properties. Besides, many epidemiological studies have shown a lower incidence for skin cancer in individuals with darker skin compared to those with fair skin. Skin pigmentation is of great cultural and cosmetic importance, yet the role of melanin in photoprotection is still controversial. This article outlines the major acute and chronic effects of UVR on human skin, the properties of melanin, the regulation of pigmentation and its effect on skin cancer prevention.     

Adsorption of L-lysine on Cu(110): a RAIRS study from UHV to the liquid phase

The adsorption of L-lysine on a Cu(110) surface has been investigated under UHV conditions from the sublimation of a crystalline phase. The adsorption was characterized by Fourier transform reflection absorption infrared spectroscopy (FT-RAIRS) during exposure and Auger electron spectroscopy (AES). At room temperature, the lysine molecules' adsorption geometry varies as a function of the exposure. At low coverage, the molecules are adsorbed via the oxygen atoms of the deprotonated carboxylate group and the nitrogen atom of the amino group. At high coverage, close to the monolayer, the molecules reorient to be anchored to the surface via one oxygen of a sideways-tilted carboxylate moiety. This first step is followed by the growth of multilayers of nonoriented molecules. In contrast, adsorption on an oxygen-modified copper surface leads to a rather disordered layer. The results are compared with the adsorption carried out on a polycrystalline copper surface after immersion in solutions of lysine at various pH values. The adsorption was monitored by polarization modulation infrared spectroscopy (PM-IRRAS). The chemistry of the adsorbed molecules is function of the starting chemical form of the lysine molecules imposed by the pH of the solution. The combination of the two techniques and various sets of adsorption conditions will give important insight into the adsorption of biomolecules on metal surfaces and the influence of water and surface oxygen.     

Swelling and deswelling of adsorbed microgel monolayers triggered by changes in temperature, pH, and electrolyte concentration

The formation and characterization of close-packed monolayers of negative, poly(N-isopropylacrylamide)-based microgel particles onto positively charged silicon wafers is described. The silicon wafers were rendered positive by first oxidizing their surface to silica and then adsorbing a layer of poly(ethyleneimine). The thickness of the deposited microgel monolayers (under aqueous conditions) has been determined by spectroscopic ellipsometry as a function of temperature (20-60 degrees C), pH (3-8), and added NaCl concentration (0-1 M). No actual desorption of the microgel particles was evident on changing the conditions, but a swelling/deswelling transition was observed around 32 degrees C. The thickness of the monolayer has been compared with the hydrodynamic diameter of the free microgel particles, dispersed in aqueous solution. For the poly(N-isopropylacrylamide) microgel particles, without any bulk ionisable comonomer groups present, the temperature dependence of the ellipsometric thickness of the monolayer mirrors closely that of the hydrodynamic diameter of the free particles. When ionizable (-COOH) groups are introduced into the microgel particles, however, this correspondence is largely lost because the microgel particles forming the deposited monolayer now contract strongly onto the oppositely charged substrate surface.     

Coexistence of Two Thermally Induced Intramolecular Electron Transfer Processes in a Series of Metal Complexes [M(Cat‐N‐BQ)(Cat‐N‐SQ)]/[M(Cat‐N‐BQ)2] (M=Co,Fe, and Ni) bearing Non‐Innocent Catechol‐Based Ligands: A Combined Experimental and Theoretical Study

The different thermally induced intermolecular electron transfer (IET) processes that can take place in the series of complexes [M(Cat‐N‐BQ)(Cat‐N‐SQ)]/[M(Cat‐N‐BQ)₂], for which M=Co ( 2 ), Fe ( 3 ) and Ni( 4 ), and Cat‐N‐BQ and Cat‐N‐SQ denote the mononegative (Cat‐N‐BQ^?) or dinegative (Cat‐N‐SQ^2?) radical forms of the tridentate Schiff‐base ligand 3,5‐di‐tert‐butyl‐1,2‐quinone‐1‐(2‐hydroxy‐3,5‐di‐tert‐butylphenyl)imine, have been studied by variable‐temperature UV/Vis and NMR spectroscopies. Depending on the metal ion, rather different behaviors are observed. Complex 2 has been found to be one of the few examples so far reported to exhibit the coexistence of two thermally induced electron transfer processes, ligand‐to‐metal (IET^LM) and ligand‐to‐ligand (IET^LL). IET^LL was only found to take place in complex 3 , and no IET was observed for complex 4 . Such experimental studies have been combined with ab initio wavefunction‐based CASSCF/CASPT2 calculations. Such a strategy allows one to solicit selectively the speculated orbitals and to access the ground states and excited‐spin states, as well as charge‐transfer states giving additional information on the different IET processes.