We report high-precision calculations of the $1s^{2}2s2p\left(2{}^{3}P^o\right)$, $1s^{2}2s3s\left(3{}^{3}S^e\right)$, and $1s^{2}2s4s\left(4{}^{3}S^e\right)$ states of the ${}^9\mathrm{Be}$ isotope and beryllium with infinite nuclear mass $\left({}^{\infty }\mathrm{Be}\right)$. For each state, the nonrelativistic wave function is obtained in an independent variational calculation by expanding it in a large basis of all-electron explicitly correlated Gaussian (ECG) functions, with up to 15 000 ECGs employed. In our calculations, the electrons and the nucleus are treated on an equal footing, which allows the direct inclusion of all relevant nuclear recoil effects. Leading relativistic and quantum electrodynamics corrections to the energy levels are subsequently evaluated within perturbation theory, using the variational nonrelativistic wave functions as zeroth-order states. These highly accurate nonrelativistic wave functions are also used to compute the fine-structure splittings for ${}^9\mathrm{Be}$ and ${}^{\infty }\mathrm{Be}$. The employed approach accounts for the leading-order spin–orbit and electron spin–spin interactions $(\propto {\alpha }^2)$, contribution from the electron anomalous magnetic moment $(\propto {\alpha }^3)$, and the most significant couplings between the target states and nearby electronic states $(\propto {\alpha }^4)$. Our results show a notable improvement in accuracy compared with previous theoretical calculations and are in good agreement with the best available experimental data.

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• Atomic spectra
• Electronic structure of atoms & molecules
• Fine & hyperfine structure
• Atoms
• First-principles calculations
• Perturbative methods
• Schroedinger equation