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 ${}^9\mathrm{Be}$ atom. The non-BO wave functions were used to calculate the ${\alpha }^2$ relativistic corrections ($\alpha =1/137.035999679$). With those corrections and with the ${\alpha }^3$ and ${\alpha }^4$ QED corrections determined previously by others, we obtained $54677.35{\mathrm{cm}}^{-1}$ for the $3{}^{1}S\to 2{}^{1}S$ transition energy. This result falls within the error bracket for the experimental transition of $54677.26(10){\mathrm{cm}}^{-1}$. This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.

• Received 23 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.043001