Accurate calculations for the Dirac electron in the field of two-center Coulomb field: Application to heavy ions

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

“…Without pursuing the goal of the highest numerical accuracy, we show that the A-DKB approach can be effectively used to calculate the bound-electron energies in light diatomic compounds by solving the two-center Dirac equation. The accuracy of our calculations is comparable to [12], i.e. it is at the 10 −8 level, which represents an alternative to ultraaccurate calculations, see, e.g.…”

“…We estimated the accuracy of our values at 10 −8 by comparing them with numerical results performed within the framework of the nonrelativistic approach [37,38]. Although the A-DKB method was initially adapted to study quasi-molecules with heavy nuclei [28][29][30], the results obtained for light systems show sufficient accuracy with the data presented in the literature and are comparable to those for heavy compounds [12]. While this question is not crucial for this work, the A-DKB approach is capable of high-precision calculations using the methods described in [18,19].…”

“…Among the goals of such calculations is a precise determination of the ground state energy of the bound electron, allowing a comprehensive comparison with experimental data. For example, based on analytical evaluations in heavy ions, a calculation accuracy of 10 −8 has recently been achieved in [12]. Advanced numerical calculations aimed at the accurate determination of the electron binding energy have yielded outstanding results, reaching an accuracy of 10 −14 -10 −13 relative magnitude for the low-lying states of the molecular ion H 2 + [13][14][15][16][17].…”