We investigate equilibrium and transport properties of a copper phthalocyanine (CuPc) molecule adsorbed on Au(111) and Ag(111) surfaces. The CuPc molecule has essentially three localized orbitals close to the Fermi energy resulting in strong local Coulomb repulsion not accounted for properly in density functional calculations. Hence, they require a proper many-body treatment within, e.g., the Anderson impurity model (AIM). The occupancy of these orbitals varies with the substrate on which CuPc is adsorbed. Starting from density functional theory calculations, we determine the parameters for the AIM embedded in a noninteracting environment that describes the residual orbitals of the entire system. While correlation effects in CuPc on Au(111) are already properly described by a single orbital AIM, for CuPc on Ag(111) the three orbital AIM problem can be simplified into a two orbital problem coupled to the localized spin of the third orbital. This results in a Kondo effect with a mixed character, displaying a symmetry between SU(2) and SU(4). The computed Kondo temperature is in good agreement with experimental values. To solve the impurity problem we use the recently developed fork tensor product state solver. To obtain transport properties, a scanning tunneling microscope (STM) tip is added to the CuPc molecule absorbed on the surface. We find that the transmission depends on the detailed position of the STM tip above the CuPc molecule in good agreement with differential conductance measurements.
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