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,, 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+ 1 and- 1 electrons, and discuss its Kondo properties. The shells,andare analyzed in detail and Kondo energies are deduced in all these cases showing good agreement with the conventional known results.