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The generalized dual-kinetic-balance approach for axially symmetric systemsis employed to solve the two-center Dirac problem. The spectra of one-electronhomonuclear quasimolecules are calculated and compared with the previouscalculations. The analysis of the monopole approximation with two differentchoices of the origin is performed. Special attention is paid to the lead andxenon dimers, Pb$^{82+}$-Pb$^{82+}$-e$^{-}$ and Xe$^{54+}$-Xe$^{54+}$-e$^{-}$,where the energies of the ground and several excited $\sigma$-states arepresented in the wide range of internuclear distances. The developed methodprovides the quasicomplete finite basis set and allows for construction of theperturbation theory, including within the bound-state QED.

One-electron energy spectra of heavy highly charged quasimolecules