An Unrestricted Hartree-Fock Self-consistent Huckel-like Procedure. Application to the Magnetic Properties of Radicals and Metallic Clusters

The Huckel method, which can be considered an SCF method on the orthogonalized Lowdin basis, is extended to the UHF model. Some applications to :re-radicals and to metallic clusters are given. A strong magnetization can appear, even in small size clusters. Correlation with the Hund rule is discussed. A calculation carried out on a tetrahedral cluster explains the origin of the strong magnetization in elements located in the middle of the transition elements period. Examples of antiferro- and ferrimagnetic clusters are given

The Geometry of the Osculating Nilpotent Group Structures of the Heisenberg Calculus

We explore the geometry that underlies the osculating nilpotent group structures of the Heisenberg calculus. For a smooth manifold $M$ with a distribution $H\subseteq TM$ analysts use explicit (and rather complicated) coordinate formulas to define the nilpotent groups that are central to the calculus. Our aim in this paper is to provide insight in the intrinsic geometry that underlies these coordinate formulas. First, we introduce `parabolic arrows' as a generalization of tangent vectors. The definition of parabolic arrows involves a mix of first and second order derivatives. Parabolic arrows can be composed, and the group of parabolic arrows can be identified with the nilpotent groups of the (generalized) Heisenberg calculus. Secondly, we formulate a notion of exponential map for the fiber bundle of parabolic arrows, and show how it explains the coordinate formulas of osculating structures found in the literature on the Heisenberg calculus. The result is a conceptual simplification and unification of the treatment of the Heisenberg calculus.Comment: Some parts rewritten; section 3 added. 33 page

A Poisson transform adapted to the Rumin complex

Let $G$ be a semisimple Lie group with finite center, $K\subset G$ a maximal compact subgroup, and $P\subset G$ a parabolic subgroup. Following ideas of P.Y.\ Gaillard, one may use $G$-invariant differential forms on $G/K\times G/P$ to construct $G$-equivariant Poisson transforms mapping differential forms on $G/P$ to differential forms on $G/K$. Such invariant forms can be constructed using finite dimensional representation theory. In this general setting, we first prove that the transforms that always produce harmonic forms are exactly those that descend from the de Rham complex on $G/P$ to the associated Bernstein-Gelfand-Gelfand (or BGG) complex in a well defined sense. The main part of the article is devoted to an explicit construction of such transforms with additional favorable properties in the case that $G=SU(n+1,1)$. Thus $G/P$ is $S^{2n+1}$ with its natural CR structure and the relevant BGG complex is the Rumin complex, while $G/K$ is complex hyperbolic space of complex dimension $n+1$. The construction is carried out both for complex and for real differential forms and the compatibility of the transforms with the natural operators that are available on their sources and targets are analyzed in detail.Comment: 36 pages, comments are welcome, v2: final version, to appear in J. Topol. Ana

Theoretical Study of Adsorption of Carbonyl Compounds on Ionic Crystals: I. Formaldehyde, Glyoxal, o- and p-Benzoquinone on the (100) Face of Sodium Chloride

We have stmdied the adsorption of molecules such as formaldehyde, glyoxal, o- and p-benzoquinone on the (100) face of sodium chloride. The electronic adso["\u27Jltion energy is evaluated by means of an »ab~ini.tio« SCF method and the dispersion enexgy by means of a semi-empirical Lennard-Jones pair potential. The total adsorption energies are equal to 2.3 kcal/mole for the formaldehyde along the { 0, 1, 0} ddrection abo;ve 01-, and to 4.6, 7.3 and 7.6 kcal/mole respectively for .the glyoxal and the p- and o-benzoquinone along the {O, 1, 1} direction above ain anion alignment. We also show the effect of the superficial defects as steps and kinks, in the adsorption phenomena. Vaxious applications are envisaged

Finite group extensions and the Baum-Connes conjecture

In this note, we exhibit a method to prove the Baum-Connes conjecture (with coefficients) for extensions with finite quotients of certain groups which already satisfy the Baum-Connes conjecture. Interesting examples to which this method applies are torsion-free finite extensions of the pure braid groups, e.g. the full braid groups, or certain fundamental groups of complements of links in S^3.Comment: AMS-Latex, logical structure clarified, final version, to appear in Geometry and Topolog