Comparison between cluster and supercell approaches: the case of defects in diamond

The results produced by the cluster and the supercell approaches, when applied to the study of the vacancy and ⟨100⟩⟨100⟩ split self-interstitial defects in diamond, are critically compared. The same computer code, Crystal, basis set and DFT functional (the hybrid B3LYP) are used. Clusters of increasing size (from 35 to 969 C atoms) are considered, and the results compared to those from a supercell containing 128±1128±1 atoms, for which the interaction between defects in different cells can be considered negligible. It is shown that geometry and energy data (atomic relaxation, defect formation energy, relative energy between different spin states) show a very local nature and then converge rapidly with the cluster size. Other properties, frequently used for the characterization of the defects using relatively small clusters (band gaps, impurity energy levels in the gap, Raman spectra), converge slowly and, also at the limit of the very large clusters here considered, still differ from the periodic counterpart.