Experimental data on the spectroscopic properties of SHEs and their ions are extremely limited due to their short half-lives and low production rates, which make direct measurements challenging. Consequently, theoretical calculations are currently the primary tool for investigating their electronic structure. Accurate calculations involving SHEs are computationally demanding because they require methods capable of capturing strong electron correlation and relativistic effects in a self-consistent way.

To achieve a balance between accuracy and computational efficiency, we employ a hybrid framework combining the linearised coupled cluster method with the configuration interaction method and perturbation theory. This approach is used to calculate the energy levels, ionisation potentials, electron affinities, field isotope shifts, and static dipole polarisabilities of the SHEs livermorium (Lv) and tennessine (Ts). The accuracy of this method is benchmarked against the lighter homologues tellurium, iodine, polonium, and astatine, for which reliable experimental data are available.

Our calculations provide predictions for Lv and Ts, with energy levels, ionisation potentials, and electron affinities estimated to be accurate within a few percent, and polarisabilities accurate to approximately ten percent. Several strong electric-dipole transitions in Lv and Ts are predicted to be in the optical range, suggesting potential experimental accessibility. For the ions of Lv and Ts, our results provide the first theoretical predictions of their electronic structure.

These results help fill critical gaps in the spectroscopic data for SHEs and their ions, and provide reliable theoretical benchmarks for future spectroscopic experiments.