Ground and excited S1 states of the beryllium atom

Benchmark calculations of the total and transition energies of the four lowest $^{1}S$ states of the beryllium atom are performed. The computational approach is based on variational calculations with finite mass of the nucleus. All-particle explicitly correlated Gaussian (ECG) functions are used to expand the total non-Born-Oppenheimer nonrelativistic wave functions and the ECG exponential parameters are optimized using the standard variational method. The leading relativistic and quantum electrodynamics energy corrections are calculated using the first-order perturbation theory. A comparison of the experimental transition frequencies with the ones calculated in this work shows excellent agreement. The deviations of $0.02--0.09\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ are well within the estimated error limits for the experimental values.