Accurate local density functional calculations with relativistic two-spinor minimax and finite element method for the alkali dimers

The 2-spinor minimax method combined with the numerical finite element method has proved to be very accurate. One obtains benchmark values in relativistic density functional calculations for diatomic molecules, with the error decreasing systematically with basis set size. In particular, the relativistic contamination errors and the variational collapse, which may occur in the relativistic 4-spinor calculations, are avoided in the 2-spinor minimax formulation of the Dirac equation by exact projection against the negative continuum. In the present work, we investigate the relativistic and nonrelativistic local-density functionals on alkali dimers (Li2 through Fr2), presenting accurate results in the sense that we have an optimized error control. We show that our results have minimal solution errors and report the most accurate values obtained for the respective functional, thus exhibiting the correct behaviour of these functionals and corresponding trends with increasing the atomic charge Z. In comparison with experiment the alkali dimers exhibit different behaviour than the dimers of group 11, the noble metal group including roentgenium (Rg, Z = 111), which were investigated in our previous papers. This is a clear indication that the correlation functional is important for the proper description of alkali dimers.