Multiplet structure and charge distributions in silicon and germanium dimers

Calculations of binding-energy curves and charge distributions have been carried out for low-lying states of ${\mathrm{Si}}_2$ and ${\mathrm{Ge}}_2$ using the local-density-functional formalism. Calculated spectroscopic constants are in good agreement with experiment for the states of ${\mathrm{Si}}_2$ which have been identified, so that predictions for other states should be reliable. The binding-energy curves of the two dimers are remarkably similar, as are the $s-p$ valence orbitals of silicon and germanium atoms. Charge-density differences are similar to those calculated previously for ${\mathrm{C}}_2$ and orbital densities show pronounced differences from results of a recent pseudopotential calculation, even in regions far from the cores.