Lowest excitation energy of Be9

Variational calculations employing explicitly correlated Gaussian functions and explicitly including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation] have been performed to determine the lowest singlet transition energy in the Be9 atom. The non-BO wave functions were used to calculate the α2 relativistic corrections (α=1/137.035999679). With those corrections and with the α3 and α4 QED corrections determined previously by others, we obtained 54677.35cm-1 for the 3S1→2S1 transition energy. This result falls within the error bracket for the experimental transition of 54677.26(10)cm-1. This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.