Stochastic search of the quantum conformational space of small lithium and bimetallic lithium-sodium clusters

In this paper we report the results obtained by an implementation and application of the simulated annealing optimization procedure to the exploration of the conformational space of small neutral and charged lithium clusters (Li(n)(q), n = 5, 6, 7; q = 0, +/-1) and of the bimetallic lithium/sodium clusters (Li5Na) in their lowest spin states. Our methodology eliminates the structure guessing procedure in the process of generating cluster configurations. We evaluate the quantum energy, typically with the Hartree-Fock Hamiltonian, of randomly generated points in the conformational space and use a modified Metropolis test in the annealing algorithm to generate candidate structures for atomic clusters. The structures are further optimized by analytical methods (gradient following) at the M?ller-Plesset second order perturbation theory level (MP2), in conjunction with basis sets including polarization functions with and without diffuse functions. High accuracy ab initio energies at the coupled clusters level, with single, double, and triple substitutions from the Hartree-Fock determinant (CCSD(T)), on the MP2 geometries were calculated and used to establish the relative stability of the isomers within each potential energy surface. Various cluster properties were computed and compared to existing values in order to validate our methods. Our results show excellent agreement with previous experimental and theoretical reports. Even at these small sizes, evidence for 10 new structures never reported before for the lithium clusters and four new structures for the bimetallic clusters is presented.     

Thick clusters for the radially symmetric nonlinear Schrödinger equation

This article is devoted to the study of radially symmetric solutions to the nonlinear Schrödinger equation

$\varepsilon^2 \Delta u - V(r)u + |u|^{p-1}u = 0\, {\rm in} B,\quad \frac{\partial u}{\partial n} = 0\, {\rm on}\,{\partial}B,$

where B is a ball in \({\mathbb{R}}^N\) , 1 <  p <  (N +  2)/(N ? 2), N ≥ 3 and the potential V is radially symmetric. We construct positive clustering solutions in an annulus having O(1/?) critical points, as well as sign changing solutions with O(1/?) zeroes concentrating near zero.

     

A simple analysis of the influence of the solvent-induced electronic polarization on the <Superscript>15</Superscript>N magnetic shielding of pyridine in water

Electronic polarization induced by the interaction of a reference molecule with a liquid environment is expected to affect the magnetic shielding constants. Understanding this effect using realistic theoretical models is important for proper use of nuclear magnetic resonance in molecular characterization. In this work, we consider the pyridine molecule in water as a model system to briefly investigate this aspect. Thus, Monte Carlo simulations and quantum mechanics calculations based on the B3LYP/6-311++G (d,p) are used to analyze different aspects of the solvent effects on the ¹⁵N magnetic shielding constant of pyridine in water. This includes in special the geometry relaxation and the electronic polarization of the solute by the solvent. The polarization effect is found to be very important, but, as expected for pyridine, the geometry relaxation contribution is essentially negligible. Using an average electrostatic model of the solvent, the magnetic shielding constant is calculated as −58.7 ppm, in good agreement with the experimental value of −56.3 ppm. The explicit inclusion of hydrogen-bonded water molecules embedded in the electrostatic field of the remaining solvent molecules gives the value of −61.8 ppm.     

Diffusion coefficients of first-generation polyamidoamine dendrimer and its β-cyclodextrin conjugate in aqueous solution by means of molecular dynamics simulations

Abstract  

The structure and diffusion behavior of the neutral and charged first-generation polyamidoamine (PAMAM-G1) dendrimer and its β-cyclodextrin (β-CD) conjugate in aqueous solutions were studied by molecular dynamics (MD) simulations. Diffusion coefficients were obtained from mean square displacement data, considering 500-ps intervals of normal diffusive regime within three simulation runs. Calculated diffusion coefficients were compared with experimental values obtained from diffusion ordered spectroscopy (DOSY) experiments for both neutral and charged dendrimer and conjugate structures. Our results show good agreement between calculated and experimental results, accounting for the reliability of our MD simulations.     

Students’ Conceptions of Congruency Through the Use of Dynamic Geometry Software

This paper describes students’ interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK￠ model of conceptions, suggests that incorporating technology in mathematics classrooms enabled a measure-preserving conception of congruency with which students’ could shift focus from shapes to properties. Students also interacted with dynamic diagrams in a novel way, which we call the functional mode of interaction with diagrams, relating outputs and inputs that result when dragging a figure. Students’ participation in classroom interactions through discourse and through actions on diagrams provided evidence of learning using tools within dynamic geometry software.     

Rational inversion of the Laplace transform

This paper studies new inversion methods for the Laplace transform of vector-valued functions arising from a combination of A-stable rational approximation schemes to the exponential and the shift operator semigroup. Each inversion method is provided in the form of a (finite) linear combination of the Laplace transform of the function and a finite amount of its derivatives. Seven explicit methods arising from A-stable schemes are provided, such as the Backward Euler, RadauIIA, Crank-Nicolson, and Calahan scheme. The main result shows that, if a function has an analytic extension to a sector containing the nonnegative real line, then the error estimate for each method is uniform in time.     

Free‐decomposability in varieties of semi‐Heyting algebras

In this paper we prove that the free algebras in a subvariety $\mathcal V$ of the variety $\mathcal {SH}$ of semi‐Heyting algebras are directly decomposable if and only if $\mathcal V$ satisfies the Stone identity.     

N-Arylation of 3-Formylquinolin-2(1H)-ones Using Copper(II)-Catalyzed Chan–Lam Coupling

3-formyl-2-quinolones have attracted the scientific community’s attention because they are used as versatile building blocks in the synthesis of more complex compounds showing different and attractive biological activities. Using copper-catalyzed Chan–Lam coupling, we synthesized 32 new N-aryl-3-formyl-2-quinolone derivatives at 80 °C, in air and using inexpensive phenylboronic acids as arylating agents. 3-formyl-2-quinolones and substituted 3-formyl-2-quinolones can act as substrates, and among the products, the p-methyl derivative 9a was used as a substrate to obtain different derivatives such as alcohol, amine, nitrile, and chalcone.