Ab-initio Wannier Functions, Coulomb Matrix Elements Hartree (-Fock) and LSDA Calculations for the 3d Transition Metals Fe, Co, Ni and Cu

Abstract

We show that ab-initio band structure methods, namely the linearizedmuffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA), can be used for a first-principles calculation of well localized Wannier functions. This is achieved by using a method proposed by Marzari and Vanderbilt. The resulting maximally localized Wannier functions for the 3d transition metals Fe, Co, Ni and Cu have at least 87% of their charge density within the home muffin-tin sphere. These Wannier functions serve as a minimal basis, i.e. a one-particle basis containing only 4s, 4p and 3d-orbitals, in which the many-particle Hamiltonian is expanded. We propose two independent methods to evaluate Coulomb matrix elements from Wannier functions. The tight-binding (hopping) matrix elements are obtained from completely non-interacting valence electrons moving in the effective frozen-core potential. Hence, in contrast to other approaches which use the local density approximation (LDA) as the starting point, we start from a well defined situation where the problem of double counting interactions (already included in the effective LDA band structure) is avoided. The result is an electronic multi-band Hamiltonian in second quantization with first-principles one- and two-particle matrix elements which is studied within the Hartree-Fock approximation. For the 3d ferromagnets, the resulting magnetic moments of this treatment are found to be about 20 to 30% larger than within the local spin-density approximation (LSDA) and experimental results. The band structure shows the 3d-bands below the 4s and 4p-bands. Responsible for this behavior is the Fock self-energy term which subtracts the self-interactions included in the Hartree self-energy term.