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

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 La ³⁺ and the Rn-like actinides Ac ³⁺, Th ⁴⁺, Pa ⁵⁺ and U ⁶⁺. 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 La ²⁺ is below 0.01 eV, and 18 levels of the Fr-like actinide ions Ac ²⁺, Th ³⁺ and U ⁵⁺ give a MAE of 0.06 eV. Second-order perturbation theory values differ considerably from all-order and experimental energies.