Testing quantum electrodynamics in the lowest singlet states of the beryllium atom

High-precision results are reported for the energy levels of the $2{}^{1}S$ and $2{}^{1}P$ states of the beryllium atom. Calculations are performed using fully correlated Gaussian basis sets and taking into account the relativistic, quantum electrodynamics (QED), and finite nuclear mass effects. Theoretical predictions for the ionization potential of the beryllium ground state $75192.699\left(7\right){\mathrm{cm}}^{-1}$ and the $2{}^{1}P\to 2{}^{1}S$ transition energy $42565.441\left(11\right){\mathrm{cm}}^{-1}$ are compared to known but less accurate experimental values. The accuracy of the four-electron computations approaches that achieved for the three-electron atoms, which enables determination of the nuclear charge radii and precision tests of QED.