New Approach for the Electronic Energies of the Hydrogen Molecular Ion

Abstract

Herein, we present analytical solutions for the electronic energy eigenvalues of the hydrogen molecular ion H2+, namely the one-electron two-fixed-center problem. These are given for the homonuclear case for the countable infinity of discrete states when the magnetic quantum number m is zero. In this case, these solutions are the roots of a set of two coupled three-term recurrence relations. The eigensolutions are obtained from an application of EXPERIMENTAL MATHEMATICS using Computer Algebra as its principal tool and are vindicated by numerical and algebraic demonstrations. Finally, the mathematical nature of the eigenenergies is identified. The eigenenergies are related to a generalization of the Lambert W function.

This is an analytical breakthrough for a special case of the quantum 3-body problem. The results have been published in Chem. Phys. and an internal report at the Forschungszentrum Juelich (Germany). (see references)

References in corpus (1)

• General Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function

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• Efimovian states of three charged particles
• Theoretical investigation of the Freeman resonance in the dissociative ionization of $H_2+$
• Solving One-Electron Systems in a Novel Gaussian-Sinc Mixed Basis Set
• Generalized spheroidal wave equation for real and complex valued parameters. An algorithm based on the analytic derivatives for the eigenvalues