dorsal/arxiv
View SchemaNew Approach for the Electronic Energies of the Hydrogen Molecular Ion
| Authors | Tony C. Scott, Monique Aubert-Frecon, Johannes Grotendorst |
|---|---|
| Categories | |
| ArXiv ID | physics/0607081 |
| URL | https://arxiv.org/abs/physics/0607081 |
| DOI | 10.1016/j.chemphys.2005.10.031 |
| Journal | Chemical Physics, vol. 324, pp. 323-338 (2006) |
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.
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"abstract": "Herein, we present analytical solutions for the electronic energy eigenvalues\nof the hydrogen molecular ion H2+, namely the one-electron two-fixed-center\nproblem. These are given for the homonuclear case for the countable infinity of\ndiscrete states when the magnetic quantum number m is zero. In this case, these\nsolutions are the roots of a set of two coupled three-term recurrence\nrelations. The eigensolutions are obtained from an application of EXPERIMENTAL\nMATHEMATICS using Computer Algebra as its principal tool and are vindicated by\nnumerical and algebraic demonstrations. Finally, the mathematical nature of the\neigenenergies is identified. The eigenenergies are related to a generalization\nof the Lambert W function.",
"arxiv_id": "physics/0607081",
"authors": [
"Tony C. Scott",
"Monique Aubert-Frecon",
"Johannes Grotendorst"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1016/j.chemphys.2005.10.031",
"journal_ref": "Chemical Physics, vol. 324, pp. 323-338 (2006)",
"title": "New Approach for the Electronic Energies of the Hydrogen Molecular Ion",
"url": "https://arxiv.org/abs/physics/0607081"
},
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