Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

Abstract

During the last decades outstanding results on the precision description of light diatomic molecular compounds have been achieved. The most advanced calculations of electron binding energies have been realized mainly in the framework of the nonrelativistic approach with a consistent account of relativistic and radiative QED corrections. Recently, it has been shown that methods based on the Dirac equation are also suitable for obtaining highly accurate results in simple light molecules. In this paper, we present a completely relativistic method and discuss its application to the description of diatomic systems. In particular, the electronic spectra of the light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^{2+}$ and He$^+$-H$^+$ are analyzed. For this purpose, the two-center Dirac equation is solved by a dual-kinetic balanced finite-basis-set method for axially symmetric systems, called A-DKB. This method allows for a complete relativistic consideration of the electron at fixed inter-nuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. Without pursuing the goal of high accuracy calculations, the advantages and disadvantages of the approach, as well as possible applications of the method, are discussed in detail.