The electronic spectra of acenaphthylene and fluoranthene

Acenaphthylene (I) and fluoranthene (II) in their electronic ground state are often regarded as consisting of two weakly interacting subsystems (naphthylene/ethylene or naphthalene/ benzene), which conserve much of their individuality. This seems to suggest that the lower electronically excited states of I and II can also be linked in a simple fashion to the low energy L _b , L _a , B _b , and B _a states of naphthalene and of benzene in II and of naphthalene in I, according to either Simpson's Independent System Approach or the Molecules in Molecules scheme proposed by Longuet-Higgins and Murrell. Contrary to expectation this approach fails even for the lowest excited states of I and II, because of the extensive mixing of high energy locally excited and charge transfer configurations. These involve molecular orbitals of the subsystems naphthalene/ethylene or naphthalene/benzene, which do not contribute to their low energy L _b , L _a , B _b or B _a states.

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Zusammenfassung Es wird oft angenommen, daß sich Acenaphthylen (I) und Fluoranthen (II) in ihrem elektronischen Grundzustand in guter Näherung so verhalten, wie wenn sie sich aus zwei nur locker miteinander gekoppelten Teilsystemen (Naphthalin/Aethylen, bzw. Naphthalin/ Benzol) zusammensetzen würden. Dies legt zunächst die Vermutung nahe, daß auch die niedrigst liegenden elektronisch angeregten Zustände von I und II in einfacher Weise mit den L _b , L _a , B _b und B _a Zuständen des Naphthalins und des Benzols in Beziehung setzen lassen, indem man sich des von Simpson vorgeschlagenen Independent System Approach oder des Molecules in Molecules Verfahrens von Longuet-Higgins und Murrell bedient. Es zeigt sich aber, daß dies nicht der Fall ist.Der Grund für das Versagen der genannten Betrachtungsweise ist darin zu suchen, daß sowohl in I als auch in II bereits in den elektronisch angeregten Zuständen niedrigster Energie lokal angeregte Konfigurationen der Teilsysteme eine Rolle spielen, die nicht zu deren L _b , L _a , B _b und B _a Zuständen beitragen, sondern zu Zuständen höherer Energie.

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Résumé On suppose souvent que dans leurs états électroniques fondamentaux, l'acénaphtylène (I) et le fluoranthène (II) se comportent pratiquement comme s'ils étaient composés de deux systèmes partiels faiblement couplés (naphtalène/éthylène, respectivement naphtalène/benzène).On peut alors croire que les premiers états électroniques excités de I et de II peuvent être simplement mis en rapport avec les états L _b , L _a , B _b et B _a du naphthalène et du benzène, par exemple en se servant de la méthode «Independent System Approach » proposée par Simpson ou de la méthode «Molecules in Molecules» proposée par Longuet-Higgins et Murrell.Contrairement à cette attente, l'approximation mentionnée n'est plus valable, même pour les états excités de plus basse énergie. Ceci est dû au fait que des configurations d'excitation locale et de transfert de charge qui contribuent à ces états, et qui ont une énergie élevée, sont basées sur des orbitales moléculaires des systèmes partiels — naphtalène/éthylène ou naphtalène/benzène — qui ne contribuent pas aux états d'excitation locale de basse énergie, L _b , L _a , B _b ou B _a , de chacun de ces systèmes.

     

An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods

In this paper, we present a discontinuous Galerkin formulation of the shallow‐water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge–Kutta scheme is used for time discretization. Some results of second‐order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps. Copyright © 2006 John Wiley & Sons, Ltd.     

The traveling salesman problem in graphs with some excluded minors

Given a graph and a length function defined on its edge-set, the Traveling Salesman Problem can be described as the problem of finding a family of edges (an edge may be chosen several times) which forms a spanning Eulerian subgraph of minimum length. In this paper we characterize those graphs for which the convex hull of all solutions is given by the nonnegativity constraints and the classical cut constraints. This characterization is given in terms of excluded minors. A constructive characterization is also given which uses a small number of basic graphs.     

Analytic symmetrizations of 3 × 3 systems of first order partial differential equations with reduced dimension 4

Let L(y, D) be a first order 3 × 3 system with reduced dimension 4 depending on a real vector parameter y. Assume that, at every frozen y, L(y, D) is symmetrizable. We state geometrical conditions in order that L(y, D) is smoothly (or analytically) symmetrizable. To the memory of Jean Leray     

Rare-gas oxide excimers in matrices

A model of interaction between low-lying electronic states of oxygen atoms and a host crystal has been designed to account for luminescence and chemiluminescence processes observed during far UV photolysis of oxygenated precursors in rare-gas matrices. A mechanism that involves different trapping sites (substitution in neon, insertion in argon, krypton and xenon) explains the observed features.     

Phosphoranes par fermeture trans-annulaire: III—Conformation—configuration—labilité

The analysis of the n.m.r. spectra of the two isomers of 1,6,6-trimethyl-3-phenyl-2,8-dioxa-5-aza-1-phospha ^vbicyclo[3.3.0]octane allows us to propose a conformation for each 5-membered ring and for the configuration of the phosphorus atom. The lability of the H? P proton, revealed by high temperature experiments and by P? H ? P? D exchange, is significantly different in the two isomers.