Effective kondo model for a trimer on a metallic surface

I consider a Hubbard-Anderson model which describes localized orbitals in three different atoms hybridized both among themselves and with a continuum of extended states. Using a generalized Schrieffer-Wolf transformation, I derive an effective Kondo model for the interaction between the doublet ground state of the isolated trimer and the extended states. For an isoceles trimer with distances a, l, l between the atoms, the Kondo temperature is very small for l < a and has a maximum for finite l > a when a is small. The results agree with experiments for a Cr trimer on Au(111).