Intra-atomic correlation energies in cubic metals with canonicaldbands

A calculation of the intra-atomic $d$-band correlation energies on the basis of a Hubbard interaction between $d$ electrons is presented. The calculations are performed for canonical $d$ bands in the face-centered and body-centered cubic structures. It is shown that using a single-particle approximation of the ground state, the correlation energy can be represented as a function of the occupation numbers of the five canonical subbands. The correlation energies are calculated as a function of the average number of $d$ electrons. It is shown that the results are very different from Friedel's simple model of correlation energies which neglects band-structure effects.