Self-interstitial aggregation in diamond

First-principles methods are used to investigate the self-interstitial and its aggregates in diamond. The experimental assignment of the spin-1 $R2\mathrm{}$ EPR center to the single interstitial has been questioned because of the small fine-structure term observed. We calculate the spin-spin interaction tensor for the three interstitial defects $I_1^{〈001〉},$ $I_2^{\mathrm{NN}},$ and $I_3$ and compare with the experimental D tensors. The results give support for the assignments of the single and di-interstitials to microscopic models and allow us to conclusively identify a recently observed EPR center, $O3,$ with $I_3.$ This identification, in turn, suggests a low-energy structure for $I_4$ and a generic model for an extended defect called the platelet. We also determine the optical properties of $I_1^{〈001〉}$ as well as its piezospectroscopic or stress tensor and find these to be in agreement with experiment. Several multi-interstitial defects are found to possess different structural forms which may coexist. We propose that a different form of the charged $I_2$ defect gives rise to the $3H$ optical peak. Several structures of the platelet are considered, and we find that the lowest-energy model is consistent with microscopic and infrared studies.