Atoms in molecules as non-overlapping, bounded, space-filling open quantum systems

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates the observations of chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule.     

Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data

The concept of very weak solution introduced by Giga (Math Z 178:287–329, 1981) for the Stokes equations has hardly been studied in recent years for either the Navier–Stokes equations or the Navier–Stokes type equations. We treat the stationary Stokes, Oseen and Navier–Stokes systems in the case of a bounded open set, connected of class C^1,1{\mathcal{C}^{1,1}} of \mathbbR³{\mathbb{R}^3}. Taking up once again the duality method introduced by Lions and Magenes (Problèmes aus limites non-homogènes et applications, vols. 1 & 2, Dunod, Paris, 1968) and Giga (Math Z 178:287–329, 1981) for open sets of class C^￥{\mathcal{C}^{\infty}} [see also chapter 4 of Necas (Les méthodes directes en théorie des équations elliptiques. (French) Masson et Cie, éd., Paris; Academia, éditeurs, Prague, 1967), which considers the Hilbertian case p = 2 for general elliptic operators], we give a simpler proof of the existence of a very weak solution for stationary Oseen and Navier–Stokes equations when data are not regular enough, based on density arguments and a functional framework adequate for defining more rigourously the traces of non-regular vector fields. In the stationary Navier–Stokes case, the results will be valid for external forces not necessarily small, which lets us extend the uniqueness class of solutions for these equations. Considering more regular data, regularity results in fractional Sobolev spaces will also be discussed for the three systems. All these results can be extended to other dimensions.     

Ab initio calculation of the elastic properties and the lattice dynamics of the AlAs x Sb1−x alloy under pressure

The lattice dynamics and the elastic properties of the ternary AlAs _x Sb_1?x alloy have been studied using the density-functional perturbation theory within the local density approximation and employing the virtual-crystal approximation. We study the variation of the optical phonon frequencies (ω_TO and ω_LO), the high-frequency (?_∞) and static (?₀) dielectric coefficients, the dynamic effective charge (Z*) and the elastic constants (C ₁₁, C ₁₂, C ₄₄) as a function of the composition (x) and the pressure. We have also predicted the behavior of the optical and acoustical phonons with composition x at the X and L high symmetry points under pressure and determined the Grüneisen parameter. We have found that no mechanical instabilities are associated with the structural transition at high pressures for all compositions.     

Exterior Stokes problem in the half-space

The purpose of this work is to solve the exterior Stokes problem in the half-space . We study the existence and the uniqueness of generalized solutions in weighted L ^p theory with 1 < p < ∞. Moreover, we consider the case of strong solutions and very weak solutions. This paper extends the studies done in Alliot, Amrouche (Math. Methods Appl. 23:575–600, 2000) for an exterior Stokes problem in the whole space and in Amrouche, Bonzom (Exterior Problems in the Half-space, submitted) for the Laplace equation in the same geometry as here.      

Atomic contributions to bond dissociation energies in aliphatic hydrocarbons

This paper explores the atomic contributions to the electronic vibrationless bond dissociation enthalpy (BDE) at 0 K of the central C-C bond in straight-chain alkanes (C(n)H(2n+2)) and trans-alkenes (C(n)H(2n)) with an even number of carbon atoms, where n=2, 4, 6, 8. This is achieved using the partitioning of the total molecular energy according to the quantum theory of atoms in molecules by comparing the atomic energies in the intact molecule and its dissociation products. The study is conducted at the MP2(full)6-311++G(d,p) level of theory. It is found that the bulk of the electronic energy necessary to sever a single C-C bond is not supplied by these two carbon atoms (the alpha-carbons) but instead by the atoms directly bonded to them. Thus, the burden of the electronic part of the BDE is primarily carried by the two hydrogens attached to each of the alpha-carbons and by the beta-carbons. The effect drops off rapidly with distance along the hydrocarbon chain. The situation is more complex in the case of the double bond in alkenes, since here the burden is shared between the alpha-carbons as well as the atoms directly bonded to them, namely, again the alpha-hydrogens and the beta-carbons. These observations may lead to a better understanding of the bond dissociation process and should be taken into account when locally dense basis sets are introduced to improve the accuracy of BDE calculations.     

Structural and magnetic properties of evaporated Fe thin films on Si(1 1 1), Si(1 0 0) and glass substrates

We present experimental results on the structural and magnetic properties of series of Fe thin films evaporated onto Si(1 1 1), Si(1 0 0) and glass substrates. The Fe thickness, t, ranges from 6 to110 nm. X-ray diffraction (XRD) and atomic force microscopy (AFM) have been used to study the structure and surface morphology of these films. The magnetic properties were investigated by means of the Brillouin light scattering (BLS) and magnetic force microscopy (MFM) techniques. The Fe films grow with (1 1 0) texture; as t increases, this (1 1 0) texture becomes weaker for Fe/Si, while for Fe/glass, the texture changes from (1 1 0) to (2 1 1). Grains are larger in Fe/Si than in Fe/glass. The effective magnetization, 4πM_eff, inferred from BLS was found to be lower than the 4πM_S bulk value. Stress induced anisotropy might be in part responsible for this difference. MFM images reveal stripe domain structure for the 110 nm thick Fe/Si(1 0 0) only.     

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals

Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1-C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H-H interaction, rather than denoting the presence of "nonbonded steric repulsions", makes a stabilizing contribution of up to 10 kcal mol(-1) to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules-the physics of an open system-demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H-H interatomic surface is shown to account for the resulting stability. It is pointed out that H-H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H-H bonding is shown to be distinct from "dihydrogen bonding", a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).