High-precision minmax solution of the two-center Dirac equation

We present a high-precision solution of the Dirac equation by numerically solving the minmax two-center Dirac equation with the finite-element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or heavy atomic nuclear charge $Z$. A result is shown for the molecular ion ${\mathrm{H}}_{2}{}^{+}$ and the heavy quasimolecular ion ${\mathrm{Th}}_{2}{}^{179+}$, with estimated fractional uncertainties of approximately ${10}^{\ensuremath{-}23}$ and approximately ${10}^{\ensuremath{-}21}$, respectively. The result of the minmax FEM's high precision of the solution of the two-center Dirac equation allows solid control over the required accuracy level and is promising for the application and extension of our method.