Calculation of Coulomb interaction strengths for 3d transition metals and actinides

Abstract

Coulomb interaction strengths (U_dd and U_ff) have been calculated from Hartree-Fock-Slater atomic calculations for 3d transition and 5f actinide elements, respectively. By decomposing the different contributions to the response (screening) to the 3d charge fluctuation, we show that a substantial reduction in U_dd arises due to the relaxation of the 3d charge distribution itself. This, combined with the screening due to the response of the 4s charge density, is shown to provide a very compact screening charge comparable to the metallic case, explaining the success of the atomic calculations for estimating U even in the metals. A pronounced dependence of U_dd (or U_ff) on the number of electrons n_d (n_f) or the electronic configuration is also shown here.