Localized and delocalized core holes and their interrelation

When there are several equivalent atomic sites over which a core hole may be delocalized the question arises whether the core hole should be thought of as localized or delocalized. The problem is analyzed in terms of relaxation and correlation effects using the Green's function approach. It is shown that the relaxation energy of a localized core hole is equal to the sum of the relaxation energy and the change of correlation energy due to relaxation of a delocalized core hole. When delocalized (symmetry adapted) orbitals are used, both relaxation and correlation effects are important and of the same order of magnitude. When localized (nonsymmetry adapted) orbitals are used, the correlation effects are much smaller than the relaxation effects. This explains the good results obtained with ΔSCF calculations employing localized orbitals.