The 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 (ES). 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 ES. For an isoceles trimer with distances a, l, l between the atoms, the Kondo temperature is negligigle 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). [T. Jamneala et al., Phys. Rev. Lett. 87, 256804 (2001)].