The V + I defects in diamond: An ab initio investigation of the electronic structure, of the Raman and IR spectra, and of their possible recombination.

The double defect in diamond, vacancy (V) plus 〈100〉 self-split-interstitial (V+I), is investigated at the ab initio quantum mechanical level, by considering the vicinal case VI1 (V is one of the first neighbors of one of the two C atoms constituting the I defect) and the two possible "second neighbors" cases, VI2D, VI2S, in which a carbon atom is a first neighbor of both V and I. The case in which the two defects are at a larger distance is simulated by considering the two isolated defects separately (VI∞). A 6-21G local Gaussian-type basis set and the B3LYP hybrid functional are used for most of the calculations; richer basis sets and other functionals (a global hybrid as PBE0, a range-separated hybrid as HSE06, LDA, PBE, and Hartree-Fock) have also been used for comparison. With this computational approach we evaluate the energy difference between the various spin states, the location of the corresponding bands in the energy gap of pristine diamond, as well as the defect formation energy of the four defects. The path for the recombination of V and I is explored for the vicinal case, by using the distinguished reaction coordinate strategy. A barrier as high as 0.75 eV is found with B3LYP between VI1 and the perfect diamond recombined structure; when other hybrids are used, as PBE0 or HSE06, the barrier increases up to 1.01 eV (pure density functional theory produces lower barriers: 0.62 and 0.67 for PBE and LDA, respectively). Such a barrier is lower than the one estimated in a very indirect way through experimental data, ranging from 1.3 to 1.7 eV. It confirms however the evidence of the extremely low recombination rate also at high temperature. The Raman (and IR) spectra of the various defects are generated, which permit one to unambiguously attribute to these defects (thanks also to the graphical animation of the modes) many of the peaks observed in damaged diamond above the dominant peak of perfect bulk. For the residual non-attributed peaks, more complicated aggregations of defects should be explored.