Practical post-Kohn-Sham methods for time-reversal symmetry breaking references

Reduced scaling algorithms based on auxiliary subspace methods for correlation energies from the random phase approximation(RPA) as well as correlation self-energies from the GW method are derived for time-reversal symmetry breaking Kohn-Sham (KS) references. This allows for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur for example in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the newly developed reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by two orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW -BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.