A multi-orbital Hund's rules-based ionic Hamiltonian for transition metal atoms: high-order equation of motion method approach and Kondo resonances

A multi-orbital ionic Hamiltonian is presented to analyze the many-body properties of the d-transition metal atoms. This Hamiltonian considers all the atomic states obeying the first Hund's rule and also includes all orbital degeneracy, as well as the interaction of the atom with a metal. We analyze the solution of this ionic Hamiltonian by means of the equation of Motion method up to the fourth order, V4, in the atom-metal interaction. Equations for the appropriate Green-functions for analyzing the chemical and transport properties of the system are given for different atom occupancies. In particular, we introduce a full analysis of the multi-orbital Hamiltonian including atomic configurations with N, N + 1 and N - 1 electrons, and discuss its Kondo properties. The shells d1, d2 and d3 are analyzed in detail and Kondo energies are deduced in all these cases showing good agreement with the conventional known results.