We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(111), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one hole at the $3d_{z^2}$ orbital of iron and two degenerate doublets corresponding to one hole either in the $3d_{xz}$ or in the $3d_{yz}$ orbital (called $pi$ orbitals) with two degenerate Hund-rule triplets with one hole in the $3d_{z}$ orbital and another one in a $pi$ orbital. We solve the model using a slave-boson mean-field approximation (SBMFA). For reasonable parameters we can describe very well the observed STS spectrum between sample bias -60 mV to 20 mV. For these parameters the Kondo stage takes place in two stages, with different energy scales $T_K^z > T_K^pi$ corresponding to the Kondo temperatures related with the hopping of the $z^2$ and $pi$ orbitals respectively. There is a strong interference between the different channels and the Kondo temperatures, particularly the lowest one is strongly reduced compared with the value in the absence of the competing channel.
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