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High-precision calculations of the energy levels of the superheavy elementsE119 and E120+ are presented. Dominating correlation corrections beyondrelativistic Hartree-Fock are included to all orders in the Coulomb interactionusing the Feynman diagram technique and the correlation potential method. TheBreit interaction and quantum electrodynamics radiative corrections areconsidered. Also, the volume isotope shift is determined. A similar treatmentfor Cs, Fr, Ba+ and Ra+ is used to gauge the accuracy of the calculations andto refine the ab initio results.

Calculations of the spectra of superheavy elements E119 and E120+