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A technique based on summation of dominating classes of correlation diagramsto all orders in Coulomb interaction is used to calculate the energies of thelowest $s,p$ and $d$ states of Ba II, Ra II, Fr I, E119 I and E120 II. Breitand quantum electrodynamic corrections are also included. Comparison withexperiment for Ba II, Ra II and Fr I demonstrates that the accuracy of thecalculations is on the level of 0.1%. The technique has been applied to predictthe spectra of superheavy elements E119 and E120$^+$. The role of the {\emladder diagrams} (V. A. Dzuba, Phys. Rev. A {\bf 78}, 042502 (2008)) which isthe most recent addition to the method has been emphasised. Their inclusionsignificantly improves the accuracy of the calculations and expands theapplicability of the method.

All-order calculations of the spectra of Ba II, Ra II, Fr I and superheavy elements E119 I and E120 II