First-principles density functional theory (DFT) is employed to study the electronic structure of oxygen and gallium vacancies in monoclinic bulk β-Ga₂O₃ crystals. Hybrid exchange–correlation functional B3LYP within the density functional theory and supercell approach were successfully used to simulate isolated point defects in β-Ga₂O₃. Based on the results of our calculations, we predict that an oxygen vacancy in β-Ga₂O₃ is a deep donor defect which cannot be an effective source of electrons and, thus, is not responsible for n-type conductivity in β-Ga₂O₃. On the other hand, all types of charge states of gallium vacancies are sufficiently deep acceptors with transition levels more than 1.5 eV above the valence band of the crystal. Due to high formation energy of above 10 eV, they cannot be considered as a source of p-type conductivity in β-Ga₂O₃.

The vibrational infrared (IR) and Raman spectra of seven substitutional defects in bulk silicon are computed, by using the quantum mechanical CRYSTAL code, the supercell scheme, an all electron Gaussian type basis set and the B3LYP functional. The relative stability of various spin states has been evaluated, the geometry optimized, the electronic structure analyzed. The IR and Raman intensities have been evaluated analitically. In all cases the IR spectrum is dominated by a single N peak (or by two or three peaks with very close wavenumbers), whose intensity is at least 20 times larger than the one of any other peak. These peaks fall in the 645–712 cm⁻¹ interval, and a shift of few cm⁻¹ is observed from case to case. The Raman spectrum of all defects is dominated by an extremely intense peak at about 530 cm⁻¹, resulting from the (weak) perturbation of the peak of pristine silicon.

Site symmetry analysis allows one to define four possible spatial configurations for inserting O atoms into the α-Al ₂ O ₃ crystalline lattice.

The local geometry, electronic structure, and vibrational features of three vicinal double interstitial defects in diamond, I_CI_C, I_CI_N, and I_NI_N, are investigated and compared with those of three “simple” ⟨100⟩ interstitial defects, I_CC, I_CN, and I_NN, previously reported by Salustro et al. [Phys. Chem. Chem. Phys. 20, 16615 (2018)], using a similar quantum mechanical approach based on the B3LYP functional constructed from Gaussian-type basis sets, within a supercell scheme, as implemented in the CRYSTAL code. For the first time, the Fermi contact term and hyperfine coupling tensor $\mathcal{B}$ of the four open shell structures, I_CI_C, I_CI_N, I_CC, and I_CN, are evaluated and compared with the available experimental EPR data. For the two double interstitial defects, the agreement with experiment is good, whereas that for the single interstitials is found to be very poor, for which a likely reason is the incorrect attribution of the EPR spectra to uncertain atomic details of the micro-structure of the samples. The infrared spectra of the three double interstitial defects exhibit at least two peaks that can be used for their characterization.