Towards a transferable design of solid-state embedding models on the example of a rutile TiO₂ (110) surface

In this work, we present general and robust transferable principles for the construction of quantum-mechanically treated clusters in a solid-state embedding (SSE) approach, beyond the still prevalent trial and error approach. Thereby, we probe the quality of different cluster shapes on the accuracy of chemisorption energies of small molecules and small polaron formation energies at the rutile TiO₂ (110) surface as test cases. Our analyses show that at least the binding energies and electronic structures in the form of the density of states tend to be quite robust already for small, nonoptimal cluster shapes. In contrast to that, the description of polaron formation can be dramatically influenced by the employed cluster geometry possibly leading to an erroneous energetic ordering or even to a wrong prediction of the polaronic states themselves. Our findings show that this is mainly caused by an inaccurate description of the Hartree potential at boundary and surrounding atoms, which are insufficiently compensated by the embedding environment. This stresses the importance of the cluster size and shape for the accuracy of general-purpose SSE models that do not have to be refitted for each new chemical question. Based on these observations, we derive some general design criteria for solid state embedded clusters.