Prediction of ¹P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians

Benchmark variational calculations are performed for the seven lowest 1s²2s np (¹P), n 28, states of the beryllium atom. The calculations explicitly include the effect of finite mass of ⁹Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s²2s np (¹P) →1s²2s² (¹S) transition is about 12 cm^-1. The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm^-1.