t 2 g $$ {t}_{2g} $$ d $$ d $$ orbital ordering patterns in KBF 3 $$ {}_3 $$ (B = Sc, Ti, Fe, Co) perovskites.

The orbital ordering (OO) resulting from the partial occupancy of the t 2 g $$ {t}_{2g} $$ d $$ d $$ subshell of the transition metals in KBF 3 $$ {}_3 $$ (B = Sc, Ti, Ffe, Co) perovskites, and the many possible patterns arising from the coupling between the B sites, have been investigated at the quantum mechanical level ( all electron $$ \mathrm{all}\ \mathrm{electron} $$ Gaussian type basis set, B3LYP hybrid functional) in a 40 atoms supercell. The numerous patterns are distributed into 162 classes of equivalent configurations. For each fluoroperovskite, one representative per class has been calculated. The four compounds behave similarly: an identical dependence of the energy and volume (or cell parameters) on the OO pattern; the spanned energy interval is small (1 to 2 mE h $$ {}_h $$ per formula unit), suggesting that most of the configurations are occupied at room and even at low temperature. A linear model, taking into account the relative orbital order in contiguous sites, reproduces the energy order in the full set for each compound, suggesting that it could be used for studying OO in larger supercells.

The energies and charge and spin distributions in the low-lying levels of singlet and triplet N2V defects in diamond from direct variational calculations of the excited states.

This paper reports the energies and charge and spin distributions of the low-lying excited states in singlet and triplet N2V defects in diamond from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP, PBE0, and HSE06 functionals. They assign the observed absorption at 2.463 eV, first reported by Davies et al. [Proc. R. Soc. London 351, 245 (1976)], to the excitation of a N(sp3) lone-pair electron in the singlet and triplet states, respectively, with estimates of ∼1.1 eV for that of the unpaired electrons, C(sp3). In both cases, the excited states are predicted to be highly local and strongly excitonic with 81% of the C(sp3) and 87% of the N(sp3) excited charges localized at the three C atoms nearest neighbor (nn) to the excitation sites. Also reported are the higher excited gap states of both the N lone pair and C unpaired electron. Calculated excitation energies of the bonding sp3 hybrids of the C atoms nn to the four inner atoms are close to that of the bulk, which indicates that the N2V defect is largely a local defect. The present results are in broad agreement with those reported by Udvarhelyi et al. [Phys. Rev. B 96, 155211 (2017)] from plane wave HSE06 calculations, notably for the N lone pair excitation energy, for which both predict an energy of ∼2.7 eV but with a difference of ∼0.5 eV for the excitation of the unpaired electron.

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds.

The ferromagnetic and antiferromagnetic wave functions of the KMnF3 perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and ß electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and ß eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic-antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.

The role of the A monovalent cation in the AVF3 perovskite series. A quantum mechanical investigation.

The relative stability of various phases of five AVF3 compounds (A = Li, Na, K, Rb and Cs) is investigated starting from the cubic (C) Pm3̄m (221) prototype structure, with five atoms (one formula unit) in the primitive cell. To the authors' knowledge, only three of these compounds have been investigated experimentally (Na, K and Rb), and they are reported as being cubic. The picture emerging from the present simulation is quite different: CsVF3 and RbVF3 are dynamically stable in the cubic structure, KVF3 is tetragonal, with space group (SG) I4/mcm (no. 140) and 10 atoms in the unit cell; note, however, that an orthorhombic Pnma (62) phase (four formula units) exists, which is not a subgroup of I4/mcm (140), and is very close in energy to the tetragonal phase. Further symmetry lowering is observed in the Na and Li compounds that are orthorhombic. The energy gain and volume reduction with respect to the cubic aristotype increase along the series K, Na and Li, and is very large for the last two compounds. Both FM and AFM solutions have been explored, and they show a very similar path along the SG modifications. The present scheme for determining the lowest energy SG is general, and can be applied to any perovskite. The B3LYP full range hybrid functional and the Hartree-Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code have been used.

Geometrical Stability and Nonlinear Optical Properties of Crystallogen and Pnictogen Fullerene Analogues.

The linear and nonlinear optical (NLO) properties of fullerene and fullerene-like structures, including crystallogen and pnictogen elements, are computed quantum mechanically. The tensors of optical polarizability, α, and second hyperpolarizability, γ, for a series of buckyball fullerene analogues, namely, Si60, Ge60, Sn60, Pb60, P60, As60, Sb60, and Bi60, are reported and analyzed. The eight considered nanocages are here classified into four categories: nanocages stabilized in the X60 form, including C60, As60, Sb60, and Bi60; nanocages that are not stabilized in the X60 form but are found to be stable in a distorted buckled b-X60 form, with X = Si and Ge; nanocages stabilized only in an exohedral decorated X60-Y60 form, X = Sn, Y = H or F; and finally nanocages that are not stable in either distorted or decorated form; however, their corresponding tabular nanotubes are found to be stable; such group includes P and Pb elements. A suggested nomenclature for the above-mentioned fullerenes is given for the first time, where many geometrical, energetic, and optical parameters are discussed extensively. These systems are energetically stable. The cohesive energies of Bi60 and Sn60-F60 range from -1.2 to -4.8 eV/atom and can be compared to -2.4 and -3.3 eV/atom from the corresponding 2D bismuthene and stanene monolayers, respectively. While bismuthellene, Bi60, shows vigorous optical responses compared to standard fullerene, the (9, 0) phosphorus nanotube gives not only enhanced polarizability and second hyperpolarizability but also an inducing first hyperpolarizability, ß, which was null by symmetry in the case of spherical fullerenes. The proposed models are expected to be promising materials for optoelectronic and NLO applications.

Strategies for the optimization of the structure of crystalline compounds.

When different proposals exist (or can reasonably be formulated) for the size of the unit cell (in terms of number of atoms) and space group of crystalline compounds, a strategy for exploring with simulation methods the various cases and for investigating their relative stability must be defined. The optimization schemes of periodic quantum mechanical codes work in fact at fixed space group and number of atoms per unit cell, so that only the fractional coordinates of the atoms and the lattice parameters are optimized. A strategy is here presented, based on four standard tools, used synergistically and in sequence: (1) the optimization of inner coordinates and unit cell parameters; (2) the calculation of the vibrational frequencies not only at Γ , but also at a set of k → points (in the example presented here they are eight, generated by a shrinking factor 2), looking for possible negative wavenumbers. The latter correspond to maxima, rather than minima, along the coordinate described by the corresponding normal mode; (3) the exploration of the total energy along the mode with negative wavenumber, looking for the minimum of the curve; (4) the identification of the new space group corresponding to the reduced symmetry resulting from the previous step. The strategy is illustrated with reference to the KMnF3 perovskite compound, for which many space groups are proposed in the literature, ranging from cubic Pm 3 ¯ m to tetragonal P 4 m bm or I 4 m cm and orthorhombic (Pnma and Cmcm) down to monoclinic (P21 /m). The corresponding primitive cells contain 5, 10, and 20 atoms in the various cases, and the point symmetry reduces from 48 to 4 operators. In nature, the KMnF3 phase transitions also include the magnetic phases. For simplicity, here we limit the analysis to the ones that take place between ferromagnetic phases, as they are sufficiently rich for illustrating the proposed strategy. As the total energy differences involved can be as small as, say, 10-50 µHartree, a high numerical accuracy at each one of the steps mentioned above is required. The present calculations, performed with the CRYSTAL code, by using an all electron basis set and the Hartree-Fock and B3LYP functionals, document such an accuracy. The energy difference between the tetragonal I 4 m cm and cubic Pm 3 ¯ m phases is 225 µHartree, with a volume reduction of 0.58 Å3 ; the differences between the orthorhombic and tetragonal phases are an order of magnitude smaller, being 23 µHartree and 0.06 Å3 for total energy and cell volume, respectively.

The effect of composition on phonon softening in ABO3-type perovskites: DFT modelling.

The evolution of ferroelectric instability in ABO3 perovskites is systematically investigated for tantalates, niobates and titanates at the hybrid density-functional theory level. The influence of the A cation is analysed in terms of the frequency of the lowest F1u IR-active phonon mode at different volumes for (Cs, Rb, K, Na)TaO3, (Ba, Pb, Sn, Ge)TiO3 and (Rb, K, Na, Li)NbO3 and correlated with the ionic radius as well as the degree of hybridization in the bonds. The atomic displacement corresponding to each mode is described as a function of volume, and the static permittivity is calculated for the stable Pm3̄m phases. It is shown that the amplitude of the atomic displacements associated with the soft mode linked to the ferroelectric instability increases at a given volume when the ionic radius of the cation A decreases and when the hybridization of the B-O bond increases. This provides criteria for optimizing the dielectric properties of materials and for suggesting effective solid solutions. Tantalum perovskites presenting para-ferroelectric phase transitions, some of which are close to ambient conditions, are interesting materials for high-permittivity dielectrics in view of lead-free compounds with a high static dielectric response.

The role of spin density for understanding the superexchange mechanism in transition metal ionic compounds. The case of KMF3 (M = Mn, Fe, Co, Ni, Cu) perovskites.

In many recent papers devoted to first row transition metal fluorides and oxides, not much attention is devoted to the spin density, a crucial quantity for the determination of the superexchange mechanism, and then for the ferro-antiferromagnetic energy difference. Usually, only the eigenvalues of the system are represented, in the form of band structures or, more frequently, of density of states (DOS). When discussing the orbital ordering and the Jahn-Teller effect, simple schemes with cubes and lobes are used to illustrate the shape of the d occupancy. But the eigenvectors, and the resulting spin density function, as obtained from the calculations, are rarely shown. When represented, only a fuzzy shape that recalls the d orbital shape can be observed. On the basis of these considerations, spin density maps for 5 compounds of the KMF3 (M from Mn to Cu) family have been produced, which clearly illustrate which d orbital is singly or doubly occupied. At variance with respect to the near totality of the papers devoted to these systems, we use an all electron scheme, a Gaussian type basis set, and the Hartree-Fock Hamiltonian or the B3LYP hybrid functional (the resulting maps turn out to be very similar, in the scale used for our figures). The spin density in the five cases can easily be interpreted in terms of the shape of the d orbitals as appearing in textbooks.

The calculated energies and charge and spin distributions of the excited GR1 state in diamond.

This paper reports the energies and charge and spin distributions of both the vertically excited and fully relaxed GR1 states of the neutral singlet vacancy in diamond obtained from direct Δ-SCF calculations used previously to describe the low-lying excited states in AFII NiO and α-Al2O3. The calculations are based on the B3LYP functional in its standard form, with a C basis set that is identical to that which was used previously in numerous calculations of the ground state properties of defective diamond. Both the vertically excited and thermally relaxed GR1 states are predicted to be excitonic and insulating, with extensive re-distribution of charge and spin density and back-donation to the donor site. The present calculations suggest that the triplet state makes no contribution to the GR1 excitation. The predicted energy of the zero phonon line (1.57 eV) compares with the observed value of 1.67 eV, which also suggests that the GR1 state is neutral. The bandgaps lead to an estimate of the next higher (GR2) excited state energy, which is close to that found in the observed spectra. Similar calculations are used to predict the energies of the higher gap states at (5.0-5.5) eV, including the bulk value of 7.3 eV, which compares with the experimental value of (7.3-7.4) eV. An explanation is suggested as to why only the GR1 luminescence is observed. This paper also suggests an alternative channel for the recovery of the ground state in photoluminescence studies.

Self-trapped excitons in diamond: A Δ-SCF approach.

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ25' → Γ15) in the unrelaxed (optical) and structurally relaxed (thermal) configurations, from direct Δ-self-consistent-field (SCF) calculations based on B3LYP, PBE0, HSE06, and GGA functionals. For the B3LYP functional, which has the best overall performance, the energy of the optical state, 7.27 eV, is within the observed range of (7.2-7.4) eV and is predicted to be insulating, with indirect bandgaps of (5.6-5.8) eV. Mulliken analyses of the excited state wavefunction indicate extensive redistributions of charge and spin resulting in a strongly excitonic state with a central charge of -0.8ǀeǀ surrounded by charges of +0.12ǀeǀ at the four nearest neighbor sites. The thermally relaxed state is predicted to be similarly excitonic, with comparable bandgaps and atomic charges. Calculations of the ground and excited state relaxations lead to a Stokes shift of 0.47 eV and predicted Γ-point luminescence energy of 6.89 eV. Assuming a similar shift at the band edge (X1), an estimate of 5.29 eV is predicted for the luminescence energy, which compares with the observed value of 5.27 eV. Excited state vibrational spectra show marked differences from the ground state, with the introduction of an infrared peak at 1150 cm-1 and a modest shift of 2 cm-1 in the TO(X) Raman mode at 1340 cm-1. Similar calculations of the lowest energy bi- and triexcitons predict these to be bound states in both optical and thermal configurations and plausible precursors to exciton condensation. Estimates of bi- and triexciton luminescence energies predict red shifts with respect to the single exciton line, which are compared to the recently reported values.

Interstitial carbon defects in silicon. A quantum mechanical characterization through the infrared and Raman spectra.

The Infrared (IR) and Raman spectra of various interstitial carbon defects in silicon are computed at the quantum mechanical level by using an all electron Gaussian type basis set, the hybrid B3LYP functional and the supercell approach, as implemented in the CRYSTAL code (Dovesi et al. J. Chem. Phys. 2020, 152, 204111). The list includes two 〈100〉 split interstitial IXY defects, namely ICC and ICSi , a couple of related defects that we indicate as IX IY , the so called C i C s 0 in its A and B form, as well as SiCi Si and Cs Ci Cs , in which the interstitial carbon atom is twofold coordinated. The second undergoes a large relaxation, and the final configuration is close to ICC Cs . Geometries, relative stabilities, electronic, and vibrational properties are analysed. All these defects show characteristic features in their IR spectrum (above 730 cm- 1 ), whereas the Raman spectrum is dominated, in most of the cases, by the pristine silicon peak at 530 cm-1 , that hides the defect peaks.

The ferromagnetic and anti-ferromagnetic phases (cubic, tetragonal, orthorhombic) of KMnF3. A quantum mechanical investigation.

Many space groups are proposed in the literature for the KMnF3 perovskite (see, for example, Knight et al., J. Alloys Compd., 2020, 842, 155935), ranging from cubic (C) (Pm3̄m) to tetragonal (T) ( or I4/m) down to orthorhombic (O) (Pbnm). The relative stability ΔE of these phases, both ferromagnetic (FM) and antiferromagnetic (AFM), has been investigated quantum mechanically by using both the B3LYP hybrid functional and the Hartree-Fock Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The O phase is slightly more stable than the T phase which in turn is more stable than the C phase, in agreement with experimental evidence. The C to T to O transition is accompanied by a volume reduction. The mechanism of stabilization of the AFM solution with respect to the FM one is discussed. Spin density maps and profiles, Mulliken charges, magnetic moments and bond population data are used for supporting the proposed mechanism. The IR and Raman spectra of the FM and AFM C, T and O cells are discussed; the only noticeable difference between the C, T and O spectra appears at wavenumbers lower than 150 cm-1. The effect of pressure is also explored in the 0-20 GPa interval. The stability order (O > T > C) at 0 GPa persists also at high pressure, and the differences between the phases increase.

The NV-N+ charged pair in diamond: a quantum-mechanical investigation.

The NV-N+ charged pair in diamond has been investigated by using a Gaussian-type basis set, the B3LYP functional, the supercell scheme and the CRYSTAL code. It turns out that: (i) when the distance between the two defects is larger than 6-7 Å, the properties of the double defect are the superposition of the properties of the individual defects. (ii) The energy required for the reaction NV0 + Ns→ NV- + N+ is roughly -1.3 eV at about 12 Å, irrespective of the basis set and functional adopted, and remains negative at any larger distance. (iii) These results support the observation of a charge transfer mechanism through a Ns→ NV0 donation occurring in the ground state, through a tunnelling process, without irradiation. (iv) The IR spectrum of the two subunits is characterized by specific peaks, that might be used as fingerprints. (v) Calculation of electrostatic interaction permitted an estimate of the effective charge of the defects.

Oxygen and vacancy defects in silicon. A quantum mechanical characterization through the IR and Raman spectra.

The Infrared (IR) and Raman spectra of various defects in silicon, containing both oxygen atoms (in the interstitial position, Oi) and a vacancy, are computed at the quantum mechanical level by using a periodic supercell approach based on a hybrid functional (B3LYP), an all-electron Gaussian-type basis set, and the Crystal code. The first of these defects is VO: the oxygen atom, twofold coordinated, saturates the unpaired electrons of two of the four carbon atoms on first neighbors of the vacancy. The two remaining unpaired electrons on the first neighbors of the vacancy can combine to give a triplet (Sz = 1) or a singlet (Sz = 0) state; both states are investigated for the neutral form of the defect, together with the doublet solution, the ground state of the negatively charged defect. Defects containing two, three, and four oxygen atoms, in conjunction with the vacancy V, are also investigated as reported in many experimental papers: VO2 and VOOi (two oxygen atoms inside the vacancy, or one in the vacancy and one in interstitial position between two Si atoms) and VO2Oi and VO22Oi (containing three and four oxygen atoms). This study integrates and complements a recent investigation referring to Oi defects [Gentile et al., J. Chem. Phys. 152, 054502 (2020)]. A general good agreement is observed between the simulated IR spectra and experimental observations referring to VOx (x = 1-4) defects.

Substitutional carbon defects in silicon: A quantum mechanical characterization through the infrared and Raman spectra.

The infrared (IR) and Raman spectra of eight substitutional carbon defects in silicon are computed at the quantum mechanical level by using a periodic supercell approach based on hybrid functionals, an all electron Gaussian type basis set and the CRYSTAL code. The single substitutional C s case and its combination with a vacancy (C s V and C s SiV) are considered first. The progressive saturation of the four bonds of a Si atom with C is then examined. The last set of defects consists of a chain of adjacent carbon atoms C s i , with i = 1-3. The simple substitutional case, C s , is the common first member of the three sets. All these defects show important, very characteristic features in their IR spectrum. One or two C related peaks dominate the spectra: at 596 cm-1 for C s (and C s SiV, the second neighbor vacancy is not shifting the C s peak), at 705 and 716 cm-1 for C s V, at 537 cm-1 for C s 2 and C s 3 (with additional peaks at 522, 655 and 689 for the latter only), at 607 and 624 cm-1 , 601 and 643 cm-1 , and 629 cm-1 for SiC s 2 , SiC s 3 , and SiC s 4 , respectively. Comparison with experiment allows to attribute many observed peaks to one of the C substitutional defects. Observed peaks above 720 cm-1 must be attributed to interstitial C or more complicated defects.

Predicted strong spin-phonon interactions in Li-doped diamond.

DFT calculations of the Li substitutional defect in diamond based on the B3LYP functional and a 64-atom supercell indicate that (i) the quartet (Sz = 3/2) state is lower in energy than the doublet (Sz = 1/2) state by 0.07 eV (810 K) for fully relaxed static structures and by 0.09 eV (1045 K) with the inclusion of zero-point vibrations, (ii) the effective charges at the Li and four neighbouring C sites are similar in the two spin states, but there are substantial differences in the corresponding spin distributions, and (iii) there are unprecedented differences in the Raman spectra of the two spin states, in terms of both frequency distributions and intensities, that can most reasonably be attributed to strong spin-phonon coupling, in view of the very similar charge distributions in the two states. These differences are an order of magnitude greater than those reported previously for any bulk transition metal or rare-earth compound. The basis sets and functional used in these calculations predict many of the relevant constants (a0, c11, c44) of diamond mostly to within 1% of the experimental values, most notably the TO(X) Raman frequency and the phonon density of states. Comparisons with the calculated Raman spectra of the quintet (Sz = 2) and singlet (Sz = 0) spin states of the neutral vacancy defect, which have similar spin distributions at the four neighbouring C atoms (Cn) to the vacancy site as those at the corresponding Cn sites in the quartet and singlet states of the Li defect, show that the differences in the two Raman spectra of the latter defect are closely related to those in the former.

Microscopic Characterization of Oxygen Defects in Diamond as Models for N3 and OK1 Defects: A Comparison of Calculated and Experimental Electron Paramagnetic Resonance Data.

The local structure and composition of the diamond paramagnetic defects labelled N3 and OK1 in which two heteroatoms (one of them is nitrogen) occupy vicinal substitutional positions are still a matter of debate. The electron paramagnetic resonance (EPR) is the technique adopted experimentally to characterize these defects, whose ground state is a doublet. In the present study, two models suggested in literature that contain N and O impurities are investigated at the quantum mechanical level by using the supercell model, a local Gaussian-type basis set, and the hybrid B3LYP functional as implemented in the CRYSTAL code. The computed EPR results (the Fermi contact and the available elements of the hyperfine coupling and electric field gradient tensors) are in good agreement (much better than in all previous, in some cases recently, studies) with an experiment. The two defects are further characterized in terms of local geometry, charge and spin density distributions, and IR and Raman spectra.

First principles calculations of the vibrational properties of single and dimer F-type centers in corundum crystals.

The present paper investigates the F-type centers in α-Al2O3 through their electronic and vibrational properties from first principle calculations using a periodic supercell approach, a hybrid functional, and all-electron Gaussian basis sets as implemented in the CRYSTAL17 code. Single F-type and dimer F2-type centers related to oxygen vacancies in various charge states were considered. The defect-induced vibrational modes were identified and found to appear mainly in the low (up to 300 cm-1) and high (above 700 cm-1) frequency regions, depending on the defect charge. The perturbation introduced by the defects to the thermal nuclear motion in the crystal lattice is discussed in terms of atomic anisotropic displacement parameters. The calculated Raman spectra are discussed for the first time for such defects in α-Al2O3, suggesting important information for future experimental and theoretical studies and revealing deeper insight into their behavior.

Interstitial defects in diamond: A quantum mechanical simulation of their EPR constants and vibrational spectra.

The local geometry, electronic structure, and vibrational features of three vicinal double interstitial defects in diamond, ICIC, ICIN, and ININ, are investigated and compared with those of three "simple" ⟨100⟩ interstitial defects, ICC, ICN, and INN, 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 B of the four open shell structures, ICIC, ICIN, ICC, and ICN, 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.

The spectroscopic characterization of interstitial oxygen in bulk silicon: A quantum mechanical simulation.

The vibrational Infrared and Raman spectra of six interstitial oxygen defects in silicon containing a Si-O-Si bridge between adjacent Si atoms are obtained from all-electron B3LYP calculations within a supercell scheme, as embodied in the CRYSTAL code. Two series of defects have been considered, starting from the single interstitial defect, O1. The first consists of four defects, O1,n, in which two O1 defects are separated by (n - 1) Si atoms, up to n = 4. The second consists of four defects, On, in which nO1 defects surround a single Si atom, with n = 1-4, where O4 has the same local nearest neighbor structure as α-quartz. For both series of defects, the equilibrium geometries, charge distributions, and band structures are reported and analyzed. The addition of 1-4 oxygen atoms to the perfect lattice generates 3-12 new vibrational modes, which, as a result of the lighter atomic mass of O with respect to Si, are expected to occur at wavenumbers higher than 521 cm-1, the highest frequency of pristine silicon, thereby generating a unique new Raman spectrum. However, only a small subset of these new modes is found in the spectrum. They appear at 1153 cm-1 (O1), at 1049 cm-1 and 1100 cm-1 (O1,2), at 1108 cm-1 (O1,3), at 1130 cm-1 and 1138 cm-1 (O1,4), and 773 cm-1, 1057 cm-1, and 1086 cm-1 (O4), and can be considered "fingerprints" of the respective defects, as they are sufficiently well separated from each other. Graphical animations indicate the nature and intensity of each of the observed modes which are not overtones or combinations.