  The mechanism of Kondo screening in strongly correlated molecules with
several unpaired electrons on a metal surface is still under debate. Here, we
provide a theoretical framework that rationalizes the emergence of Kondo
screening involving several extended molecular orbitals with unpaired
electrons. We introduce a perturbative model, which provides simple rules to
identify the presence of antiferromagnetic spin-flip channels involving charged
molecular multiplets responsible for Kondo screening. The Kondo regime is
confirmed by numerical renormalization group calculations. In addition, we
introduce the concept of Kondo orbitals as molecular orbitals associated with
the Kondo screening process, which provide a direct interpretation of
experimental $dI/dV$ maps of Kondo resonances. We demonstrate that this
theoretical framework can be applied to different strongly correlated
open-shell molecules on metal surfaces, obtaining good agreement with
previously published experimental data.
