Ground bound state in the fully adiabatic∞H2+ion

Abstract

The fully adiabatic ${}^{\ensuremath{\infty}}{\mathrm{H}}_{2}^{+}$ ion is considered by using the improved version of our multibox variational procedure [A.M. Frolov, Phys. Rev. E 64, 036704 (2001)]. This procedure has been developed and successfully tested in highly accurate computations of bound-state spectra of various three-body systems. Note that our method is not based on the Born-Oppenheimer approximation, i.e., it is a nonadiabatic approach. In this study, we determine the ground-state energies of the adiabatic ${\mathrm{HD}}^{+},$ ${\mathrm{HT}}^{+},$ and ${\mathrm{T}}_{2}^{+}$ ions with finite nuclear masses. The computed variational energies for the ${\mathrm{HD}}^{+},$ ${\mathrm{HT}}^{+},$ and ${\mathrm{T}}_{2}^{+}$ ions are $\ensuremath{-}0.597897968645036508\mathrm{a}.\mathrm{u}.,$ $\ensuremath{-}0.598176134669766232\mathrm{a}.\mathrm{u}.,$ and $\ensuremath{-}0.59950691011154145113\mathrm{a}.\mathrm{u}.,$ respectively. The ground-state energy and bound-state properties of ${}^{\ensuremath{\infty}}{\mathrm{H}}_{2}^{+}$ ion are also presented. In general, the observed agreement between our variational energies and analogous energies determined with the use of pure adiabatic methods can be considered as very good.