This work concerns ab initio calculations of the complete potential energy curve and spectroscopic constants for the ground state X 1 Σ + g of the beryllium dimer, Be 2 .High accuracy and reliability of the results is one of the primary goals of the paper. To this end we apply large basis sets of Slater-type orbitals combined with highlevel electronic structure methods including triple and quadruple excitations. The effects of the relativity are also fully accounted for in the theoretical description. For the first time the leading-order quantum electrodynamics effects are fully incorporated for a many-electron molecule. Influence of the finite nuclear mass corrections (post-Born-Oppenheimer effects) turns out to be completely negligible for this system. The predicted well-depth (D e = 934.5 ± 2.5 cm −1 ) and the dissociation energy (D 0 = 808.0 cm −1 ) are in a very good agreement with the most recent experimental data. We confirm the existence of the weakly bound twelfth vibrational level [Patkowski et al., Science 326, 1382(2009] and predict that it lies just about 0.5 cm −1 below the onset of the continuum.

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.