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

TL;DR

This paper analyzes the electronic spectra of light one-electron quasi-molecular ions using a relativistic two-center Dirac equation approach with a finite-basis-set method, providing a comprehensive relativistic treatment and comparison with existing results.

Contribution

It introduces the A-DKB method for solving the two-center Dirac equation, enabling complete relativistic analysis of light quasi-molecular ions at fixed internuclear distances.

Findings

Relativistic effects are significant for the studied ions.

The A-DKB method provides accurate results compared to nonrelativistic calculations.

Advantages and disadvantages of the approach are thoroughly discussed.

Abstract

The electronic spectra of light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the two-center Dirac equation is solved by the dual-kinetically balanced finite-basis-set method for axially symmetric systems termed as A-DKB. This method allows a complete relativistic consideration of these systems at fixed internuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. The advantages and disadvantages of the approach are discussed in details.