Generalized Sturmian Functions in prolate spheroidal coordinates

L. U. ANCARANI; ANDRES LOPEZ; D. M. MITNIK

Varsovia

Conferencia; Warsaw Molecular Electronic Structure; 2020

University of Warsaw

The molecular ion H+ 2 , as well as the isotopic forms such as HD+ or D2 + , and other one?electrondiatomics such as HHe+2 or HLi+3, are the simplest molecular quantum three?body problem withCoulomb interactions. H+ 2 , in particular, has been largely studied since the early days of quantummechanics, and serves as benchmark to test any new molecular approach and numerical method.In the last decade, a spectral method named GSF has been developed and implemented tostudy successfully a variety of bound and scattering problems on atoms [1, 2], and to a muchlesser extent to ?one?centre? molecules [3]. However, for diatomic molecules, nothing has yet beenproposed. We have recently developed a spectral method which makes use of GSF in prolatespheroidal coordinates (ξ, η, ψ). To start with, we obtained accurate ground and excited statesof one?electron diatomic molecules [4]. This first step opens up the possibility to extend the useof GSF for diatomic molecules, and in particular to investigate their continuum states which is avery challenging task. The application to the ground and excited states of one?electron diatomics(H+ 2 , HHe +2 , HLi+3 ) puts our proposal on solid grounds and, at the same time, illustrates itscomputational efficiency and superiority with respect to other methods. The advantages of theGSF approach is based on the intrinsic good property that all GSF basis elements are constructed asto obey appropriate physical boundary conditions. An illustration is given by the Figure 1 in whichthe radial part of nine GSF basis elements are shown to exponentially decay in the same manner asa function of the coordinate ξ = (r1 +r2 )/R, where r1 and r2 stand for the electron?nuclei distancesand R the internuclear distance. The present GSF implementation in prolate spheroidal coordinatesfor bound states is a necessary benchmark step, paving the way for the study of the more difficulttask of studying continuum states involved in ionization of one or two?electron diatomic targets.