A calculation of the Coulomb correlation energy, U, for transition metals in Hubbard's model

Abstract

The intra-atomic electron-electron Coulomb correlation energy U, which appears in the Hubbard Hamiltonian (1963), is shown to be well approximated by the change in eigenvalue of a localized Hartree-Fock state that occurs when the occupation of that state is changed. A selfconsistent calculation of all the Hartree-Fock states within a neutral Wigner-Seitz cell is made for three electronic configurations of each of the transition metals. Values of U are deduced from the differences in the d electron eigenvalues of the configurations. It is found that the ratios U/W, where W is the bandwidth, show a trend across the transition metals which is in excellent agreement with the known magnetic properties of their ground states.