  The system of an iron phthalocyanine molecule on the Au(111) surface, has
been studied recently due to its peculiar properties. In particular, several
surprising results of scanning tunneling spectroscopy changing the position of
the molecule and applying magnetic field can be explained by the {\it
non-Landau} Fermi liquid state of a 2-channel spin-1 Kondo model with
anisotropy. The localized orbitals near the Fermi level are three, one of
symmetry $z^2$ and two (nearly) degenerate $\pi$ orbitals of symmetry $xz$ and
$yz$. Previous studies using the numerical renormalization group neglected one
of these orbitals to render the problem tractable. Here we investigate, using a
slave-boson mean-field approximation, if the splitting $S$ between $\pi$
orbitals caused by spin-orbit coupling (SOC) justifies this approximation. We
obtain an abrupt transition from a 3-band regime to a 2-band one at a value of
$S$ which is about 1/3 of the atomic SOC for Fe, justifying the 2-band model
for the system.
