Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations

Abstract

Ab initio calculations of the Raman spectrum of the neutral vacancy in diamond reproduce observed spectral features of irradiated diamond up to the first-order peak.

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

“…Pure diamond is characterized by a single Raman peak at 1332 cm −1 ; the same peak, computed within the periodic approach is at 1318 cm −1 , see Refs. [39][40][41] for a detailed discussion. However, when a cluster approach is adopted, spurious peaks due to border effects are expected.…”

“…Cluster SCF equations have been solved at the Γ point of the reciprocal lattice while 4 k-points in the irreducible part of the Brillouin zone (corresponding to a "shrinking factor" of 4) had been selected for the reference S 128 supercell calculations, see Refs. [39][40][41] for details. In geometry optimization two different procedure have been followed: in the former only the H atoms have been kept fixed at their initial positions and all C atoms have been fully relaxed (we refer to these clusters as FULL); in the latter approach only C atoms in the internal shells of the clusters have been relaxed, that means all C atoms not linked to H but also not at the border of the cluster (we refer to these clusters as FRAGMENT).…”

“…The corresponding cluster has been denominated specifying that one C atom is missing or has been added: then, for instance, C 35−1 H 36 and C 35+1 H 36 indicate, respectively, a cluster with a vacancy or an interstitial defect. Cluster properties have been compared with those of supercells (S 128 ) containing, before the defect creation, 128 carbon atoms [39][40][41].…”

“…This combination has shown to provide accurate description of the properties of both regular and defective diamond. [39][40][41] In the cluster calculations, terminal hydrogen atoms have been described at the STO-3G [48] level. To increase the variational freedom in the vacancy region, the same C basis set has been placed at the vacancy site (see the GHOSTS option in the CRYSTAL manual [44] Fig.…”

“…Defect formation energies, atomic relaxations, band structure of the defect, relative energies of different spin states and Raman spectra are investigated as a function of the cluster size, and are compared directly with the results of wellconverged supercells calculations. [39][40][41]. This latter method involves a periodic array of unit cells of the host crystal containing the defect at the centre.…”