Phases of a polar spin-1 Bose gas in a magnetic field

The two Bose–Einstein condensed phases of a polar spin-1 gas at nonzero magnetizations and temperatures are investigated. The Hugenholtz–Pines theorem is generalized to this system. Crossover to a quantum phase transition is also studied. Results are discussed in a mean field approximation.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Rate constant for the reaction of OH radicals with CH3C(O)Cl determined by direct kinetic method

Summary The fast flow technique with OH resonance fluorescence detection has been applied at T = 298 ± 2 K to study the kinetics of the overall reaction: H + CH₃C(O)Cl → products (1) A rate constant value of k₁ = (1.02 ± 0.12) x 10¹⁰ cm³ mol^-1 s^-1 has been determined which is the first direct kinetic parameter reported for reaction (1) in the literature (the error given refers to 2σ accuracy).     

Probing small molecule binding to amyloid fibrils

Much effort has focussed in recent years on probing the interactions of small molecules with amyloid fibrils and other protein aggregates. Understanding and control of such interactions are important for the development of diagnostic and therapeutic strategies in situations where protein aggregation is associated with disease. In this perspective article we give an overview over the toolbox of biophysical methods for the study of such amyloid-small molecule interactions. We discuss in detail two recently developed techniques within this framework: linear dichroism, a promising extension of the more traditional spectroscopic techniques, and biosensing methods, where surface-bound amyloid fibrils are exposed to solutions of small molecules. Both techniques rely on the measurement of physical properties that are very directly linked to the binding of small molecules to amyloid aggregates and therefore provide an attractive route to probe these important interactions.     

A diagonal measure and a local distance matrix to display relations between objects and variables

Proper permutation of data matrix rows and columns may result in plots showing striking information on the objects and variables under investigation. To control the permutation first, a diagonal matrix measure D was defined expressing the size relations of the matrix elements. D is essentially the absolute norm of a matrix where the matrix elements are weighted by their distance to the matrix diagonal. Changing the order of rows and columns increases or decreases D. Monte Carlo technique was used to achieve maximum D in the case of the object distance matrix or even minimal D in the case of the variable correlation matrix to get similar objects or variables close together. Secondly, a local distance matrix was defined, where an element reflects the distances of neighboring objects in a limited subspace of the variables. Due to the maximization of D in the local distance matrix by row and column changes of the original data matrix, the similar objects were arranged close to each other and simultaneously the variables responsible for their similarity were collected close to the diagonal part defined by these objects. This combination of the diagonal measure and the local distance matrix seems to be an efficient tool in the exploration of hidden similarities of a data matrix. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical study of the mechanism of valence tautomerism in cobalt complexes

Valence tautomerism is studied in the [Co(II-HS)(sq)(2)(bpy)]/[Co(III-LS)(sq)(cat)(bpy)] mononuclear cobalt complex by using DFT methods (HS, high spin; LS, low spin; cat, catecholate; sq, semiquinone; bpy, 2,2'-bipyridine). Calculations at the B3LYP* level of theory reproduce well the energy gap between the Co(II-HS) and Co(III-LS) forms giving an energy gap of 4.4 kcal/mol, which is comparable to the experimental value of 8.9 kcal/mol. Potential energy surfaces and crossing seams of the electronic states of the doublet, quartet, and sextet spin states are calculated along minimum energy paths connecting the energy minima corresponding to the different spin states. The calculated minimum energy crossing points (MECPs) are located at 8.8 kcal/mol in the doublet/sextet surfaces, at 10.2 kcal/mol in the doublet/quartet surfaces, and at 8.4 kcal/mol in the quartet/sextet surfaces relative to the doublet ground state. Considering the energy of the three spin states and the crossing points, the one-step relaxation mechanism between the Co(II-HS) and Co(III-LS) forms is the most probable. This research shows that mapping MECPs can be a useful strategy to analyze the potential energy surfaces of systems with complex deformation modes.     

Popular distances in 3-space

Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn^1/3 log log n m(n) n^3/5 β(n), where c> 0 is a constant and β(n) is an extremely slowly growing function, related to the inverse of the Ackermann function.