Local decomposition of hybridization functions: Chemical insight into correlated molecular adsorbates

Hybridization functions are an established tool for investigating the coupling between a correlated subsystem (often a single transition metal atom) and its uncorrelated environment (the substrate and any ligands present). The hybridization function can provide valuable insight into why and how strong correlation features such as the Kondo effect can be chemically controlled in certain molecular adsorbates. To deepen this insight, we introduce a local decomposition of the hybridization function, based on a truncated cluster approach, enabling us to study individual effects on this function coming from specific parts of the systems (e.g., the surface, ligands, or parts of larger ligands). It is shown that a truncated-cluster approach can reproduce the Co 3d and Mn 3d hybridization functions from periodic boundary conditions in Co(CO)₄/Cu(001) and MnPc/Ag(001) qualitatively well. By locally decomposing the hybridization functions, it is demonstrated at which energies the transition metal atoms are mainly hybridized with the substrate or with the ligand. For the Kondo-active $3dx2−y2$ orbital in Co(CO)₄/Cu(001), the hybridization function at the Fermi energy is substrate-dominated, so we can assign its enhancement compared with ligand-free Co to an indirect effect of ligand–substrate interactions. In MnPc/Ag(001), the same is true for the Kondo-active orbital, but for two other orbitals, there are both direct and indirect effects of the ligand, together resulting in such strong screening that their potential Kondo activity is suppressed. A local decomposition of hybridization functions could also be useful in other areas, such as analyzing the electrode self-energies in molecular junctions.