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.

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.

The Electronic Structures and Energies of the Lowest Excited States of the Ns0, Ns+, Ns- and Ns-H Defects in Diamond.

This paper reports the energies and charge and spin distributions of the mono-substituted N defects, N0s, N+s, N-s and Ns-H in diamonds from direct Δ-SCF calculations based on Gaussian orbitals within the B3LYP function. These predict that (i) Ns0, Ns+ and Ns- all absorb in the region of the strong optical absorption at 270 nm (4.59 eV) reported by Khan et al., with the individual contributions dependent on the experimental conditions; (ii) Ns-H, or some other impurity, is responsible for the weak optical peak at 360 nm (3.44 eV); and that Ns+ is the source of the 520 nm (2.38 eV) absorption. All excitations below the absorption edge of the diamond host are predicted to be excitonic, with substantial re-distributions of charge and spin. The present calculations support the suggestion by Jones et al. that Ns+ contributes to, and in the absence of Ns0 is responsible for, the 4.59 eV optical absorption in N-doped diamonds. The semi-conductivity of the N-doped diamond is predicted to rise from a spin-flip thermal excitation of a CN hybrid orbital of the donor band resulting from multiple in-elastic phonon scattering. Calculations of the self-trapped exciton in the vicinity of Ns0 indicate that it is essentially a local defect consisting of an N and four nn C atoms, and that beyond these the host lattice is essential a pristine diamond as predicted by Ferrari et al. from the calculated EPR hyperfine constants.

The d Orbital Multi Pattern Occupancy in a Partially Filled d Shell: The KFeF3 Perovskite as a Test Case.

The occupancy of the d shell in KFeF3 is t2g4eg2, with five α and one ß electrons. The Jahn-Teller lift of degeneracy in the t2g sub-shell produces a tetragonal relaxation of the unit cell (4.09 vs. 4.22 Å, B3LYP result) not observed experimentally. In order to understand the origin of this apparent contradiction, we explored, with a 2 × 2 × 2 supercell (40 atoms per cell), all possible local structures in which contiguous Fe atoms have a different occupancy of the t2g orbitals with the minority spin electron. A total of 6561 configurations (with occupancies from (8,0,0) to (3,2,2) of the 3 t2g orbitals of the 8 Fe atoms) have been explored, with energies in many cases lower (by up to 1550 µEh per 2 Fe atoms) than the one of the fully ordered case, both for the ferromagnetic and the anti-ferromagnetic solutions. The results confirm that the orientation of the ß d electron of Fe influences the electrostatics (more efficient relative orientation of the Fe quadrupoles of the d shell) of the system, but not the magnetic interactions. Three hybrid functionals, B3LYP, PBE0, and HSE06, provide very similar results.

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.

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 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.

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.

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.

Quantum mechanical simulation of various phases of KVF3perovskite.

The relative stability ΔEof the cubicPm3¯m(C), of the two tetragonalP4mbm(T1) andI4mcm(T2), and of the orthorhombicPbnm(O) phases of KVF3has been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree-Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152µHa for B3LYP, 180µHa for HF, per 2 formula units) is due to the rotation of the VF6octahedra with respect to thecaxis, by 4.1-4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20µHa for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP)µHa per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3-0.5A˚3at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm-1.

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.

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 superexchange mechanism in crystalline compounds. The case of KMF3(M = Mn, Fe, Co, Ni) perovskites.

The ferromagnetic and antiferromagnetic wavefunctions of four KMF3(M = Mn, Fe, Co and Ni) perovskites have been obtained quantum-mechanically with the CRYSTAL code, by using the Hartree-Fock (HF) Hamiltonian and three flavours of DFT (PBE, B3LYP and PBE0) and anall-electronGaussian type basis set. In the Fe and Co cases, with d6and d7occupation, the Jahn-Teller distortion of the cubic cell is as large as 0.12 Å. Various features of the superexchange interaction energies (SIE), namely additivity, dependence on the M-M distance, on theMFM̂angle, and on the adopted functional, are explored. The contribution to SIE by the Coulomb, exchange and kinetic energy terms is analyzed. It is shown that, when using density functionals, SIE clearly correlates with the amount of exact (Hartree-Fock) exchange in the functional. The effect of SIE on the equilibrium geometry and volume of the unit cell is discussed, and it is shown that the key quantity is the spin polarization of the (closed shell) F ions along the M-F-M path. The effect of thismagneticpressureis evaluated quantitatively for the first time. The superexchange coupling constantJ, evaluated at the HF level and through the Ising model, underestimates the experimental values by about 60%-70%. The more sophisticated Yamaguchi model (that takes into account the contamination of the FM and AFM spin states) does not reduce the discrepancy. The B3LYP hybrid functional overestimates the experiments. These last are bracketed by HF and PBE0. For PBE, the overestimation is huge. Finally, Mulliken population data, charge and spin density maps and density of states are used to illustrate the electronic structure.

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.

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.

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.

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.