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 oneelectron twofixedcenter 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 ^{2}Σ ^{+} states. In this case, these solutions are the roots of a set of two coupled threeterm 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.
 Publication:

Chemical Physics
 Pub Date:
 May 2006
 DOI:
 10.1016/j.chemphys.2005.10.031
 arXiv:
 arXiv:physics/0607081
 Bibcode:
 2006CP....324..323S
 Keywords:

 31.15.p;
 31.15.Ar;
 02.70.Wz;
 31.50.Bc;
 3150.Df;
 Calculations and mathematical techniques in atomic and molecular physics;
 Ab initio calculations;
 Symbolic computation;
 Potential energy surfaces for ground electronic states;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 This is an analytical breakthrough for a special case of the quantum 3body problem. The results have been published in Chem. Phys. and an internal report at the Forschungszentrum Juelich (Germany). (see references)