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 3<em>d</em> and Mn 3<em>d</em> hybridization functions from periodic boundary conditions in Co(CO)<sub>4</sub>/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 the 3d<sub>x2−y2</sub> orbital in Co(CO)<sub>4</sub>/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.
Theoretical Screening of Single Transition Metal Atoms Embedded in MXene Defects as Superior Electrocatalyst of Nitrogen Reduction Reaction
