4-Component relativistic calculations of L3 ionization and excitations for the isoelectronic species UO22+, OUN+ and UN2

Abstract

We present a 4-component relativistic study of uranium 2p_3/2 ionization and excitation in the isoelectronic series UO₂²⁺, OUN⁺ and UN₂. We calculate ionization energies by ΔSCF at the Hartree–Fock (HF) and Kohn–Sham (KS) level of theory. At the ΔHF level we observe a perfectly linear chemical shift of ionization energies with respect to uranium atomic charges obtained from projection analysis. We have also developed a non-canonical 2nd-order Møller–Plesset code for wave function based correlation studies. We observe the well-known failure of Koopmans' theorem for core ionization due to the dominance of orbital relaxation over electron correlation effects. More unexpectedly, we find that the correlation contribution has the same sign as the relaxation contribution and show that this is due to a strong coupling of relaxation and correlation. We simulate uranium L₃ XANES spectra, dominated by 2p_3/2 → U6d transitions, by restricted excitation window time-dependent density functional theory (REW-TDDFT) and the complex polarization propagator (CPP) approach and demonstrate that they give identical spectra when the same Lorentz broadening is chosen. We also simulate XANES spectra by the Hartree–Fock based static exchange (STEX) method and show how STEX excitation energies can be reproduced by time-dependent Hartree–Fock calculations within the Tamm–Dancoff approximation. We furthermore show that Koopmans' theorem provide a correct approximation of ionization energies in the linear response regime and use this observation to align REW-TDDFT and CPP spectra with STEX ones. We point out that the STEX method affords the most detailed assignment of spectra since it employs virtual orbitals optimized for the selected core ionization. The calculated XANES spectra reflect the loss of bound virtual orbitals as the molecular charge is reduced along the isoelectronic series.