Généralisation des orbitales moléculaires alternantes

¹ Laboratoire d’Electromagnétisme. Université Biaise Pascal (Clermont II), U.F.R. Sciences, B.P. 45, 63170 Aubière, France.
² Laboratoire d’Electronique. Université Biaise Pascal (Clermont II), U.F.R. Sciences, B.P. 45, 63170 Aubière, France.

Résumé

La généralisation du formalisme A.M.O. à des systèmes dont la bande de valence est remplie de façon quelconque pose un certain nombre de problèmes quant au choix des fonctions de départ et à leur mélange. Nous discutons plusieurs solutions possibles dans le cas d’une bande au quart remplie. Si l’application aux polymères électroactifs semble possible, l’intérêt principal nous semble cependant résider dans la méthodologie : construction d’une nouvelle classe de fonctions d’onde.

Abstract

This paper reports an attempt to generalize the alternant molecular orbital (AMO) scheme to systems with any filling of the valence band. The accuracy of AMO’s for alternant organic compounds with an important electronic correlation has been proven, chiefly about quasi one — dimensional organic conductors and/or polymeric chains. All these systems do have an half-filled energy band. Going to an arbitrary filling several questions arise : how to select mono-electronic orbitals to set up the total determinantal wave function ? how to mix these orbitals ? in order to reach which kind of pairing ? We propose and discuss three different approaches for the cas of a quarter — filled energy band. Our results are essentially qualitative, nevertheless a possible application to some electroactive polymers could be regarded on a phenomenological point of view. The main interest of the generalization, however, lies in the methodology itself. A new class of wave functions is encountered in these systems with a number of electron per core not equal to one. It has been theoretically forecasted by Fukutome but could not appear for simple test-examples such as the electron gas. This has to be contrasted with the situation occurring within the conventional scheme (e.g. that discussed by Calais).