Ground and excited S 1 states of the beryllium atom

Benchmark calculations of the total and transition energies of the four lowest S1 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 0.02-0.09cm^-1 are well within the estimated error limits for the experimental values.