What is it about?
Herein, we present analytical solutions for the electronic energy eigenvalues of the hydrogen molecular ion H_2^+ , 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, i.e., for 2Σ+ states. 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.
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Why is it important?
Although H2^+ was known to be separable, we could never mathematically solve or categorize the solutions for the energies. We finally know what they are: a generalization of the Lambert W function.
Perspectives
The Hydrogen molecular ion in the fixed nuclei approximation (Born-Oppenheimer) is now reduced to a pedagogical problem that can be done entirely within a computer algebra system.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: New approach for the electronic energies of the hydrogen molecular ion, Chemical Physics, May 2006, Elsevier,
DOI: 10.1016/j.chemphys.2005.10.031.
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