The relativistic polarization propagator for the calculation of electronic excitations in heavy systems

In this work, we present a new four-component implementation of the polarization propagator for accurate calculations of excited states in heavy systems. Differences to existing nonrelativistic realizations are detailed and the energetically lowest final states of the ns²np⁶ → ns²np⁵(n + 1)s¹ and ns²np⁶ → ns²np⁵(n + 1)p¹ transitions in noble gases are calculated and compared with experimental data. Already for the light atoms Ne and Ar spin-orbit coupling leads to noticeable zero field splitting that gradually increases in the heavier homologues and eventually invalidates the LS-based description of singlet and triplet excited states. For all four noble gases Ne through Xe, we observe a very good agreement with experimental transition energies in the considered energetic range where the extended version of the propagator implementation in general yields better excitation energy differences than the strict variant. In the extended version, off-diagonal first-order contributions in the two-particle-two-hole block are included that are not present in the strict variant. In case of Kr and Xe, nonrelativistic approaches already exhibit unacceptable deviations in the reproduction of transition energies and the spectral structure. The obtained excited final states are analyzed in terms of atomic contributions to the donor and acceptor orbitals constituting the corresponding wave functions. The relativistic polarization propagator provides a consistent description of electron correlation and relativistic effects especially relevant for the heavier systems where these two contributions are no longer separable.