Parameter-free one-center model potential for an effective one-electron description of molecular hydrogen

Abstract

For the description of an ${\mathrm{H}}_{2}$ molecule, an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the ${\mathrm{H}}_{2}$ molecule. In order to test the model potential and examine its properties, it is employed to determine excitation energies, transition moments, and oscillator strengths in a range of internuclear distances, $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}<R<2.5\phantom{\rule{0.3em}{0ex}}\mathrm{a.u}$. In addition, it is used as a description of an ${\mathrm{H}}_{2}$ target in calculations of the cross sections for photoionization and for partial excitation in collisions with singly charged ions. The comparison of the results obtained with the model potential with literature data for ${\mathrm{H}}_{2}$ molecules yields a good agreement and encourages therefore an extended use of the potential in various other applications or in order to consider the importance of two-electron and anisotropy effects.