Aperiodic defects in periodic solids

To date, computational methods for modeling defects (vacancies, adsorbates, etc.) have relied on periodic supercells in which the defect is far enough from its repeated image that they can be assumed non-interacting. Yet, the relative proximity and periodic repetition of the defect's images may lead to spurious, unphysical artifacts, especially if the defect is charged and/or open-shell, causing a very slow convergence to the thermodynamic limit (TDL). In this article, we introduce a "defectless" embedding formalism such that the embedding field is computed in a pristine, primitive-unit-cell calculation. Subsequently, a single (i.e., "aperiodic") defect, which can also be charged, is introduced inside the embedded fragment. By eliminating the need for compensating background charges and periodicity of the defect, we circumvent all associated unphysicalities and numerical issues, achieving a very fast convergence to the TDL. Furthermore, using the toolbox of post-Hartree-Fock methods, this scheme can be straightforwardly applied to study strongly correlated defects, localized excited states, and other problems for which existing periodic protocols do not provide a satisfactory description.