Multiplets of free d- and f-metal ions: A systematic DFT study

In this work we apply in a systematic way our multi-determinantal model to calculate the fine structure of the whole atomic multiplet manifold. The key feature of this approach is the explicit treatment of near-degeneracy correlation using ad hoc configuration interaction (CI) within the active space of Kohn–Sham (KS) orbitals with open d- or f-shells. The calculation of the CI-matrices is based on a central symmetry decomposition of the energies of all single determinants (micro-states) calculated according to Density Functional Theory (DFT) for frozen KS-orbitals corresponding to the averaged configuration, eventually with fractional occupations, of the d- or f-orbitals and/or the direct calculation of the electrostatic reduced matrix elements (Racah or Slater–Condon parameters) occurring in the corresponding active space. We performed DFT calculations on all divalent and trivalent d^2–d^8 metal ions, as well as the f^2–f^12 lanthanide(III) ions. We compare the results of both variants of the method with the data available in the literature. Both procedures yield multiplet energies with an accuracy of about hundred wave numbers and fine structure splitting accurate to less than a tenth of this amount.