The Kondo effect observed in recent STM experiments on transport through CoPc and TBrPP-Co molecules adsorbed on Au(111) and Cu(111) surfaces, respectively, is discussed within the framework of a simple model (Phys. Rev. Lett. 97, 076806 (2006)). It is shown that, in the Kondo regime and by varying the adequate model parameters, it is possible to produce a crossover from a conductance Kondo peak (CoPc) to a conductance Fano dip (TBrPP-Co). In the case of TBrPP-Co/Cu (111) we show that the model reproduces the changes in the shape of the Fano dip, the raising of the Kondo temperature and shifting to higher energies of the dip minimum when the number of nearest neighbors molecules is lowered. These features are in line with experimental observations indicating that our simple model contains the essential physics underlying the transport properties of such complex molecules. [2,3] in transport through a Co atom adsorbed on an Au(111) surface, a great deal of attention has been devoted to investigate, both theoretical and experimentally, such effect in either isolated Co atoms [4,5] or in Co-containing molecules [6,7,8,9] adsorbed on metal surfaces. The possibility of tuning the Kondo temperature [6,9] has been recently demonstrated, increasing considerably the interest of these systems. In particular it has been shown that, the characteristics, and even the existence, of the Kondo resonance can be controlled by distorting a CoPc molecule adsorbed on a Au(111) surface [6]. More recently [9] the Kondo temperature in a TBrPP-Co molecule adsorbed on a Cu(111) surface has been increased by decreasing the number of nearestneighbor TBrPP-Co molecules. The authors of [9] argued that this is due to a reduction of surfaces states when the number of nearest neighbors molecules around a given one is increased.One of the most interesting aspects of those two works is that while in the case of CoPc/Au(111) a Kondo peak was observed, in the experiments on TBrPP-Co/Cu(111) the conductance showed a Fano dip, as in isolated Co atoms adsorbed on metal surfaces [1,4,5]. Those two molecules, although largely different, have two outstanding similarities: i) both have the Co atom in the their geometric centers, and, ii) their STM images show four clearly defined lobes [6]. The enormous complexity of the electronic structure of these molecules and the manybody physics involved hinder a detailed account of these systems. One of the main goals of the present work is to show, using a simple model that catches the most prominent features of both molecules, under which circumstances dips or peaks appear in the transmission.A model Hamiltonian was taken assuming the following small atomic arrangement [8]: a central site with a single atomic orbital, a strong Coulomb repulsion at the Co atom and four lobes of the molecule described by four atomic orbitals placed on a square, which center is the Co atom (see Fig. 1 of Ref.[8]). Two additional orbitals located above and below the Co atom are included to represent the apex of the STM tip and an at...
