The Kernel energy method: Application to graphene and extended aromatics

The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of π‐electrons, Clar sextets, and the approximate overall aromaticity. Sivaramakrishnan et al. [J Phys Chem A, 2005, 109, 1621] define similar “ring conserved isodesmic reactions (RCIR).” The principal innovation of this article is the suggestion that kernels may be mathematically extracted from an extended aromatic molecule such as graphene by a fissioning of aromatic bonds. Hartree Fock (HF) and Møller‐Plesset (MP2) chemical models using a Gaussian basis of 3‐21G orbitals are used to calculate the total energy of a graphene flake. This demonstration calculation is performed on a graphene flake in which dangling bonds are saturated with hydrogens (C₇₈H₂₆) composed of a total of 104 atoms arranged in 27 benzenoid rings. The KEM with both types of chemical model are shown to be accurate to nearly 1 kcal/mol, of a total energy, which is nearly 3000 atomic units, that is, with an absolute error within “chemical accuracy” and a relative error of the order of 5 × 10⁵% of the total energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Mixed exterior Laplace's problem

In [C. Amrouche, V. Girault, J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator. An approach in weighted Sobolev spaces, J. Math. Pures Appl. 76 (1997) 55-81], authors study Dirichlet and Neumann problems for the Laplace operator in exterior domains of Rn. This paper extends this study to the resolution of a mixed exterior Laplace's problem. Here, we give existence, unicity and regularity results in Lp's theory with 1<p<∞, in weighted Sobolev spaces.     

On the Two and Three Dimensional Oseen Potentials

We prove continuity properties for the Oseen potential. As a consequence, we show some new properties on solutions of the Oseen equations. The study relies on weighted Sobolev spaces in order to control the behavior of functions at infinity.     

Diffraction of fast metastable atoms by micrometric reflection gratings

Diffraction of thermal velocity metastable atoms by non-magnetic and magnetic reflection gratings of micrometric period has been observed. This observation is made possible by the use of an ultra narrow beam generated by metastability exchange. Grazing incidence angles are exploited to minimise the quenching of metastable atoms on the grating surface. Potential applications are beam splitting, atom holography and probing of micro-sized solid surfaces.     

Fluorine-fluorine spin-spin coupling constants in aromatic compounds: correlations with the delocalization index and with the internuclear separation

This paper describes a new empirical approach for the evaluation of fluorine-fluorine spin-spin coupling constants (J(FF)) in aromatic compounds. The correlations between J(FF) and the delocalization index calculated within the framework of the theory of atoms in molecules (AIM) and with the fluorine-fluorine internuclear separation are investigated. Both the internuclear separation and the delocalization index are found to be highly correlated with J(FF). A regression model in which the experimental J(FF) coupling constant is fitted exponentially to the internuclear separation and linearly to the delocalization index yields a squared correlation coefficient as high as 0.96 for a data set consisting of 33 coupling constants spread over a range of 85 Hz.     

Application of the quantum theory of atoms in molecules to selected physico-chemical and biophysical problems: focus on correlation with experiment

This article reviews how the quantum theory of atoms in molecules (QTAIM) can be used to predict experimental physico-chemical properties of molecules of biologic interest: the amino acids, the polycyclic aromatic hydrocarbons (PAH), and the opiates, for example, morphine and PEO. The predicted experimental properties are as diverse as the partial molar volumes, the free energies of hydration, the second code-letter in the genetic code, the resonance energies, and the proton spin-spin coupling constants. Recent examples of the utilization of QTAIM to construct excellent statistical models (with squared correlation coefficients (r(2)) > 0.9) correlating properties of the electron density and of the pair density to experiment are reviewed. Some new results on the solvent effects on electron delocalization are also presented.     

The Neumann problem in the half-spaceLe problème de Neumannn dans le demi-espace

We study here the nonhomogeneous Neumann problem in the half-space $\text{R}{}^{\mathrm{N}}{}_{\mathrm{+}}$ with N?2. We give in L^p theory, with 1<p<∞, a basic existence and regularity results in weighted Sobolev spaces. To cite this article: C. Amrouche, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 151–156.     

Spontaneous Reduction of a Hydroborane To Generate a B−B Single Bond by the Use of a Lewis Pair

The ansa‐aminohydroborane 1‐NMe₂‐2‐(BH₂)C₆H₄ crystallizes in an unprecedented type of dimer containing a B?H bond activated by one FLP moiety. Upon mild heating and without the use of any catalyst, this molecule liberates one equivalent of hydrogen to generate a diborane molecule. The synthesis and structural characterization of these new compounds, as well as the kinetic monitoring of the reaction and the DFT investigation of its mechanism, are reported.