Transition energies of Rn- and Fr-like actinide ions by relativistic intermediate Hamiltonian Fock-space coupled-cluster methods

Graphical abstract: Mean absolute error of 14 calculated La3+ excitation energies relative to experiment (103 cm−1). The four columns show, from left to right, results for first-order, second-order, intermediate Hamiltonian (XIH) with a large basis and with an even larger basis. Highlights: ► Excitations of Rn- and Fr-like ions of the four lightest actinides are studied. ► Relativity and correlation are treated at high level. ► Large, converged basis sets and model spaces are used. ► Agreement with experimentally known energies is 0.1 eV or better. ► Predictions for unknown transitions are expected to have similar accuracy. - Abstract: The extrapolated intermediate Hamiltonian (XIH) Fock-space coupled cluster method in the 1-hole 1-particle sector is applied to calculate excitation energies of Xe-like La3+ and the Rn-like actinides Ac3+, Th4+, Pa5+ and U6+. Large basis sets and model spaces are used, the latter made possible by the XIH scheme. Comparison with experiment for the La ion shows very good agreement, with a mean absolute error of 0.11 eV for 14 excitations in the largest basis (37s33p25d23f14g12h11i6k), lending credence to predicted energies for the actinide ions. Significant Breit term contributions appear, and the DCB Hamiltonian is therefore used. Excellent results are obtained in the one-particle sector, where more experimental values are available. The MAE for 17 transition energies of La2+ is below 0.01 eV, and 18 levels of the Fr-like actinide ions Ac2+, Th3+ and U5+ give a MAE of 0.06 eV. Second-order perturbation theory values differ considerably from all-order and experimental energies.