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

Abstract

The results produced by the cluster and the supercell approaches, when applied to the study of the vacancy and 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 containg 128±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.

Quantum‐mechanical condensed matter simulations with CRYSTAL

“…In another recent study, several features of nonperiodic clusters, of increasing size (containing up to 1,293 atoms and about 13,000 AOs), of defective diamond were investigated at the hybrid B3LYP level and compared to the outcomes of fully periodic calculations (Salustro, Ferrari, Orlando, & Dovesi, ). Two different defects were put in the center of the clusters (a vacancy and the [100] split self‐interstitial), whose structural, electronic, and spectroscopic features were recently investigated with periodic calculations (Baima, Zelferino, Olivero, Erba, & Dovesi, ; Salustro et al, ).…”

Substitutional nitrogen in diamond: A quantum mechanical investigation of the electronic and spectroscopic properties

“…Conversely, recent quantum-mechanical characterization of several point-defects in diamond [53][54][55][56][57][58][59][60][61][62] has shown a notable accuracy of hybrid functionals (which include in their formulation a certain percentage of exact exchange interaction) in predicting the electronic properties of these systems. Accordingly, the present paper reports new calculations of the charge and spin densities, band structure, IR and Raman frequencies and hyperfine coupling constant of the C centre (N S ) in diamond based on the energy-minimised atomic configuration of the defective lattice.…”

The Infrared spectrum of very large (periodic) systems: global versus fragment strategies—the case of three defects in diamond

“…In this latter case many problems (border termination, saturation, loss of the infinite nature of the system) make the model more delicate and doubtful (see for example Ref. [13]). The accuracy and efficiency of the fragment scheme is discussed by comparison with the full Hessian diagonalization (FHD) scheme with reference to three cases.…”