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The Rayleigh‐Schrödinger perturbation series of quasi‐degenerate systems |
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| Authors: | Christian Brouder Gérard H.E. Duchamp Frédéric Patras Gábor Z. Tóth |
| Affiliation: | 1. Institut de Minéralogie et de Physique des Milieux Condensés, Université Pierre et Marie Curie‐Paris 6, CNRS UMR7590, Bo?te courrier 115, 4 place Jussieu, 75252 Paris cedex 05, France;2. Laboratoire d'Informatique de Paris‐Nord, CNRS UMR 7030, Institut Galilée, Université Paris‐Nord, 99 avenue Jean‐Baptiste Clément, 93430 Villetaneuse, France;3. Laboratoire J.‐A. Dieudonné, CNRS UMR 6621, Université de Nice, Parc Valrose, 06108 Nice Cedex 02, France;4. Theoretical Department, Research Institute for Particle and Nuclear Physics, P.O. box 49, Budapest, 1525, Hungary |
| Abstract: | We describe the first representation of the general term of the Rayleigh‐Schrödinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. A relation with several combinatorial objects used for special cases (degenerate or non‐degenerate systems) is established. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 |
| Keywords: | Perturbation theory Rayleigh‐Schrö dinger trees quasidegenerate systems multireference systems |