For instance, for a f 7 → d 1 transition in a lanthanide compound (here europium), the GGA Kohn-Sham MO occupations corresponding to the 4f 6 d 1 configuration is 6/7e for the (7) MOs strongly localized on the Eu/4f orbital, and 1/5e for the (5) MOs mostly localized on the Eu/5d orbital. See, for example, the case of the Eu(η 9 -C 9 H 9 ) 2 complex, for which the 30030 multiplet energy levels have been calculated. 413 (3.6.11) Krylov : To properly deal with symmetry breaking, we need to look at properties that are rigorously defined -for example, it is difficult to discuss what spin symmetry means within DFT because S 2 is a two-electron operator. So spin-contaminated (as traditionally computed) KS DFT or TDDFT solutions might, in fact represent the correct spin densities of the spin-pure correlated many body wave functions -for example, an open shell doublet radical (such as CH 3 ) in which the unpaired electron has alpha spin, is known to have areas with the excess beta-spin density. This cannot be reproduced by a spin-adapted (ROHF) KS determinant (which only allows for the excess alpha density), hence suggesting that a spin-polarized KS determinant provides a more appropriate description.