Singlet-triplet energy splitting between ¹D and ³D (1s² 2s nd), n = 3, 4, 5, and 6, Rydberg states of the beryllium atom (⁹Be) calculated with all-electron explicitly correlated Gaussian functions

Accurate variational nonrelativistic quantum-mechanical calculations are performed for the five lowest ¹D and four lowest ³D states of the ⁹Be isotope of the beryllium atom. All-electron explicitly correlated Gaussian (ECG) functions are used in the calculations and their nonlinear parameters are optimized with the aid of the analytical energy gradient determined with respect to these parameters. The effect of the finite nuclear mass is directly included in the Hamiltonian used in the calculations. The singlet-triplet energy gaps between the corresponding ¹D and ³D states, are reported.