Structural reinvestigation of ammonium hypophosphite: was dihydrogen bonding observed long ago?

The past decade has seen the explosive emergence of "dihydrogen bonds", interactions between the electrons of M-H sigma-bonds, where M is less electronegative than H (M = Al, B, Ga, Ir, Mo, Mn, Os, Re, Ru, W) and traditional proton donors. But 70 years ago, such an interaction was proposed by Zachariasen and Mooney [J. Chem. Phys. 1934, 2, 34-37] on the basis of their single-crystal X-ray diffraction structure (heavy atoms positions only) of ammonium hypophosphite (NH(4)H(2)PO(2)). We redetermined this structure at high resolution with a focus on the hydrogen atoms, using a modern diffractometer equipped with a CCD detector. Molecular orbital calculations were performed to investigate the charge density and the bond polarity of the P-H bonds and to assess their potential for participation in dihydrogen bonds. Neither the theory nor the X-ray structure supports the original claim of H...H interactions in this salt.     

Multistep reaction analysis. A numerical approach based on relaxation theory

A general numerical method and program for simulation of the kinetics of multistep reactions is described, with details for collation of data, construction of a mechanistic model, and simulation of reciprocal relaxation times and calculation of individual rate constants. The working scheme of the program includes an initial approximate simulation by adjustment of the rate constants followed by their optimization with a Powell minimization subroutine. The procedure is applied to aromatic nucleophilic addition.     

Structure of sodium glycodeoxycholate micellar aggregates from small-angle X-ray scattering and light-scattering techniques

Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements were accomplished on sodium glycodeoxycholate (NaGDC) aqueous electrolyte solutions as a function of NaGDC and NaCl concentrations with the aim to determine with satisfactory approximation the NaGDC micellar aggregate structure at a gross molecular level, assuming monodispersity. Different conditions of interparticle interactions by varying ionic strength (NaCl concentration from 0 to 0.70 M) and NaGDC concentration (from 0.02 to 0.10 M) were studied. Smeared scattering intensities and electron pair distance distribution functions, radii of gyration, and aggregate heights are in satisfactory agreement with the corresponding functions calculated using a 2(1) helix as model. It is formed by trimers, each one composed by three NaGDC and nine H2O molecules related by a 3-fold rotation axis, and can be described by a hollow cylinder, probably filled by water molecules, characterized by a conventional radius of 23.7 A and a trimer repeat along the helical axis of 3.6 A. The helix is considerably inhomogeneous since the volume of the cylinder occupied by NaGDC molecules is less than one-third of the total. On the other hand, calculations performed with the average radial electronic density of the helix without water molecules or totally filled by water molecules (a NaGDC/H2O molecular ratio of about 1/50) or by using a three-shell average radial electronic density, independently evaluated on absolute scale, do not show significant differences, thus supporting the helical model. The aggregate size increases for all the samples by increasing either the NaCl or NaGDC concentration. The NaGDC low concentration (0.02 M) samples with NaCl within the range 0.30-0.70 M are characterized by short cylindrical aggregates that do not give rise to sensible interference effects. This assertion is supported by the satisfactory fit between the observed apparent mean hydrodynamic radii and the calculated ones by means of the method of Ortega and Garcia de la Torre (J. Chem. Phys. 2003, 119, 9914), valid for rods with a length-to-diameter ratio > or = 0.1 in dilute solution (noninteracting rods). The NaGDC moderate concentration (0.10 M) samples with NaCl within the range 0.20-0.60 M are characterized by cylindrical aggregates that, in the presence of repulsive Coulombic interactions progressively more and more screened, produce interference effects, due to the hard-body repulsion and attractive forces, but the agreement between observed and calculated SAXS data is satisfactory. The results of the low and moderate NaGDC concentration samples seem to indicate that the aggregation number increase, produced by adding 0.10 M NaCl, is constant within an ionic strength range and occurs by the addition of oligomers formed by trimers. The samples with a variable NaGDC concentration (0.02-0.10 M) at a fixed and high NaCl concentration (0.6 M) contain cylindrical aggregates that give rise to an attractive term effect prevailing on the hard-body repulsive one. The same situation seems to occur in the NaGDC moderate concentration samples.     

Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods. The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P_t. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure ν. Moreover, we solve the Kolmogorov equation and prove the so-called "identite du carre du champs". This will be used to study the Sobolev space W^1,2(H,ν) and to obtain information on the domain of the infinitesimal generator of P_t.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

A new algorithm that generates the image of the attractor of a generalized iterated function system

Numerical Algorithms - We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space...     

A Bound of the Finslerian Ricci Scalar

In the Riemannian as well as in the Finslerian geometry, certain conditions on the Ricci scalar or the Ricci tensor provide obstructions on the topology of the base manifold and so on the configuration of cut points by limitations of the injectivity radius, see the Bonnet–Myers theorem and its variants and generalizations. In this paper, we show that conversely, prescribing the injectivity radius of a Finsler manifold, some limitations of the Ricci scalar are obtained. Some consequences of the condition that the Ricci tensor is h-parallel with respect to the Chern–Rund connection are found. In addition, some classes of examples are provided.