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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.

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, Si

The spin density maps of the KMF3 (M from Mn to Cu) family have been produced illustrating which d-orbital is singly or doubly occupied from their shape.We use an all electron Gaussian type basis set, and the Hartree-Fock or hybrid functional.

The influence of the A cation on the ferroelectric instability in ABO3 perovskites, and its associated F1u IR-active phonon mode, is systematically investigated for tantalates, niobates and titanates at the hybrid density-functional theory level.

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 occupancy of the d shell in KFeF3 is t2g4eg2, with five α and one β 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 β 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.

The ferromagnetic and antiferromagnetic wave functions of the KMnF

Many space groups are proposed in the literature (see for example Knight et al., J. of Alloys and Compounds, 2020) for the KMnF3 perovskite, ranging from cubic (C) (Pm-3m) to tetragonal (T) (P4/mbm 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 that 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 the 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 appear 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 VN 2 − defect in diamond consists of a vacancy surrounded by two substitutional nitrogen atoms, which lower the local symmetry from Td to C2v. Calculations of the doublet ground state geometry, electronic structure, EPR parameters, and IR spectra of this defect are reported along with a preliminary investigation of the observed optical transition. For the most part our results were obtained using a uniform charge compensated supercell approach together with the B3LYP functional and all-electron Gaussian basis sets designed for the properties studied. In particular, the computed hyperfine and quadrupolar EPR parameters for the carbon and nitrogen atoms adjacent to the vacancy agree very well with the experiments (Fermi contact values are 245 MHz vs 241 for 13C, and 4.1 vs 4.0 for 15N). The accompanying spin distribution may be described as a damped spherical spin wave with little spin density on the nitrogen atoms. IR spectra show some interesting features in the range of approximately 360–1310 cm−1, which are absent in the pristine diamond. Functionals without exact exchange, such as PBE, better reproduce the observed zero phonon line.

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 AF

The relative stability Δ

The NV

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.

EPR data of the positively charged N2 defect (N+2) are reported from all-electron calculations based on the B3LYP hybrid functional using a local (Gaussian type) basis set, within a supercell scheme, as implemented in the CRYSTAL code. The Fermi contact Aiso term, the components of the hyperfine coupling tensor, , and the electric field gradient (only P‖ is available) are all in excellent agreement with two independent sets of experimental data, with errors of less than 4%. The equilibrium geometry, electronic structure, and IR and Raman spectra are also computed, where the two spectra are compared with those of the neutral N2 and double positive N++2, both of which have closed shell ground states. In particular the IR and Raman spectra of the three species exhibit important differences. Information on the charge, spin and geometry of defective species derived from experimental EPR data are based mostly on relatively simple models; here they are obtained directly from rigorous quantum mechanical simulations. It is shown that the extrapolation from the experimental EPR data can lead to relatively serious errors.

The ferromagnetic and antiferromagnetic wavefunctions of four KMF

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.

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 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.

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 Pm3¯m to tetragonal P4mbmorI4mcm 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 I4mcm and cubic Pm3¯m phases is 225 μHartree, with a volume reduction of 0.58 A3 ; the differences between the orthorhombic and tetragonal phases are an order of magnitude smaller, being 23 μHartree and 0.06 A3 for total energy and cell volume, respectively.

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 an all-electron Gaussian type basis set. In the Fe and Co cases, with d6 and d7 occupation, 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 the M F M ̂ angle, 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 this magneticpressure is evaluated quantitatively for the first time. The superexchange coupling constant J, 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 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 A, 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 A, 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.

The electronic structure and the equilibrium geometry of the VN3 defect in diamond are computed by using a quantum mechanical approach, the main ingredients being an all electron gaussian type basis set, a global hybrid functional, the supercell scheme (216 atoms) and the CRYSTAL code. For the first time the Fermi contact and the hyperfine coupling tensor B of the open shell structure (Sz = 1/2) are evaluated and compared with available experimental EPR (electron paramagnetic resonance) data. The agreement is excellent. The infrared (IR) spectrum is also computed. It results to be very close to the one of the so called B defect (VN4), and with similarities to the one of the other members of the VNx (x = 0, 1, 2) family, so that the attribution of specific experimental peaks to one of the five mentioned compounds is difficult and questionable. The peaks measured by Sutherland (Nature, 174, 901, 1954) and attributed to the B center might, at least in part, come from both VN3 and VN4. Being the ground state of the latter a closed shell, and then EPR inactive, a combined use of the two spectroscopies (IR and EPR) is mandatory for the identification of the relative weight of the two defects.

International audience; The elastic behavior of low albite is investigated ab initio under hydrostatic pressure up to 16 GPa. Our calculations complement and extend previous studies confirming a highly anisotropic character of the feldspar cell compression and, more importantly, revealing a clear change of all structure deformation trends around 8–9 GPa pressure. We correlate this change to the trend of the bulk modulus of low albite as a function of pressure, which we compute in different and independent ways using (1) the Birch–Murnaghan equation of state, (2) the analytical Voigt–Reuss–Hill averaging scheme of calculated elastic constants, and (3) a pressure–volume numerical differentiation procedure. The latter, in particular, uncovers a singularity in the bulk modulus between 8 and 9 GPa pressure which is evocative of a λ-type critical point. We find that the same behavior emerges when comparing with pressure–volume datasets from the experimental literature, where it has been so far overlooked due to the misleading use of a fourth-order Birch–Murnaghan equation of state. Indeed, we show that the equation of state must be extended up to at least the sixth power of the Eulerian strain to approximate the complex elastic behavior of feldspars. The low albite structure softens under increasing pressure between 5 and 8 GPa, as a result of the initiation of auxiliary compression mechanisms—notably, the squeezing of the crankshaft chains along b—and then abruptly resumes a stiffening trend in association with a displacive transformation of the O–O pair interactions. Whether this is an isosymmetric phase transition or a supercritical crossover, it suggests a compatibility with seismological profiles indicating a low wave-velocity anomaly in correspondence of the upper portion of the subducting Pacific plate and the disappearance of such anomaly at greater depths, assuming the alkali feldspar survives as a metastable phase. The data and methodology described here can enable the exploration of important, potentially overlooked features in other minerals, and inspire future high-pressure research in mineral physics.

The NV0 defect in diamond has been investigated quantum-mechanically, by analyzing its structural, electronic, vibrational and magnetic properties. The possible spin states for NV0 are a quartet N V q 0 (4A2 symmetry) and a doublet (2E symmetry). In the latter state a single electron occupies a double degenerate level producing a Jahn Teller distortion that removes the degeneracy and lowers the total energy. The symmetry reduces from C3v to CS and two local minima are indeed identified, to be indicated as N V d 1 0 (2A′ symmetry) and N V d 2 0 (2A″ symmetry). N V d 1 0 is the ground state, and is more stable than N V q 0 by ~ 0.5 eV, and than N V d 2 0 by ~ 0.2 eV, irrespective of the functional or basis set adopted. The EPR hyperfine coupling tensor has been computed for N V q 0 and has been found to be in excellent agreement with available experimental data. The IR spectra of the NV defects (the three neutral cases and also the negatively charged one, for comparison) show specific peaks and shape that characterize each system and differentiate the spectra according to the spin and charge state. The Raman spectra of the NV0 defects shows a single peak, redshifted with respect to the single peak of pristine diamond by 2 cm−1 only, but in turn well separated from the negatively charged form of the defect.