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The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5--1000 K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

In this paper we present results of ab initio calculations for the beryllium dimer with a basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled-cluster correction for inner-shell effects. We have developed STO basis sets, ranging in quality from double to sextuple $\ensuremath{\zeta}$, which are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\ensuremath{\alpha}}^{2}$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the electronic binding energy of the beryllium dimer is determined to be $929.0\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}1.9\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, in a very good agreement with the recent experimental value.