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Classical and Semiclassical Studies of the Hydrogen Molecule

Thomas Sauvaget 1
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Abstract : The aim of this work is to account for the global shape of some Born-Oppenheimer (BO) curves of the hydrogen molecule, in particular the ground state, at the semiclassical level. In the first two chapters we review semiclassical cycle expansion techniques which proved useful in the study of the resonant spectrum of the helium atom, another few-body Coulomb system. Then we first study in detail the geometry of the classical phase space of the hydrogen molecule. This being done, we analyze the dynamics in three of its subspaces and compute various quantities related to their shortest periodic orbits. We then turn to semiclassical studies. One of these subspaces is discarded on instability grounds, while the other two are used as a basis for the construction of semiclassical approximations to the ground state BO curve. We find that each of the two subspaces allow to describe one of the two asymptotic trends of the BO curve. This allows to provide a classical underpinning to bond formation in H2.
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Thomas Sauvaget. Classical and Semiclassical Studies of the Hydrogen Molecule. Chaotic Dynamics [nlin.CD]. University of Nottingham (UK), 2006. English. ⟨tel-02371554⟩

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