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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.

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.

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.

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

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.

FSG acknowledges the CINECA award under the ISCRA initiative (HP10BJO47B) for the availability of high-performance computing resources and support., The phase transitions between paraelectric (PE) and ferroelectric (FE) isomorph phases of LiNbO3 have been investigated quantum mechanically by using a Gaussian-type basis set, the B3LYP hybrid functional and the CRYSTAL17 code. The structural, electronic and vibrational properties of the two phases are analyzed. The vibrational frequencies evaluated at the Γ point indicate that the paraelectric phase is unstable, with a complex saddle point with four negative eigenvalues. The energy scan of the A2u mode at −215 cm−1 (i215) shows a dumbbell potential with two symmetric minima. The isotopic substitution, performed on the Li and Nb atoms, allows interpretation of the nontrivial mechanism of the phase transition. The ferroelectric phase is more stable than the paraelectric one by 0.32 eV. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.--//-- Published under CC BY 4.0 licence., CINECA HP10BJO47B; Institute of Solid State Physics, University of Latvia as the Center of Excellence is supported through the Framework Program for European universities Union Horizon 2020, H2020-WIDESPREAD-01–2016–2017-TeamingPhase2 under Grant Agreement No. 739508, CAMART2 project.

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.

International audience; The way quantum mechanical ab initio computer codes allow to compute, through perturbation theory (the so-called SC-CP, self-consistent coupled-perturbed scheme), many properties resulting from the interaction of the electric field with a crystalline system is illustrated. The polarizability, which leads to the dielectric tensors as well as to the refractive indices and to the birefringence of materials, is the simplest on this list. Higher order tensors, like the first and second hyperpolarizabilities, can be obtained as well with the CRYSTAL code here used. These properties, resulting from the Taylor expansion of the total energy of the solid as a function of the electric field, belong to a large family of phenomena generated by combining in different ways the frequencies of the fields. Second-harmonic generation (SHG), Pockels effect, intensity-dependent refractive index (IDRI), and other quantities now accessible to experiment can be computed at a relatively low cost and with high accuracy.

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.

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.

The vibrational features of eight interstitial nitrogen related defects in silicon have been investigated at the first principles quantum mechanical level by using a periodic supercell approach, a hybrid functionals, an all electron Gaussian type basis set and the Crystal code. The list includes defects that will be indicated as Ni (one N atom forming a bridge between two Si atoms), Ni-Ns (one interstitial and one substitutional N atom linked to the same Si atom), Ni-Ni (two Ni defects linked to the same couple of silicon atoms) and Ni-Sii-Ni (two Ni defects linked to the same interstitial silicon atom). Four 〈0 0 1〉 split interstitial (dumbbell) defects have also been considered, in which one lattice atom splits in two, and as a result the two interstitial atoms are three fold coordinated: they are two N (indicated as IN-N), one N and one Si (IN-Si), one N and one C (IC-N). For comparison, also the case with two Si atoms (ISi-Si) has been included. Four of these eight defects have unpaired electrons, and have been described through the UHF (Unrestricted Hartree-Fock like) computational scheme. The local defect geometry and the charge and spin density distributions have been analyzed. For the first time, intensities of IR and Raman spectra were calculated along with the frequencies, and this is crucial for the comparison of theoretical simulations with experiments. All these defects present very characteristic features in their IR spectrum, dominated by one or two very intense peaks. It has been possible to find a simulated counterpart to each one of the five peaks reported by Stein in 1985 (Applied Physics Letters, 47, 1339), and then to establish a correspondence between the microscopic structure of the defects and the IR intense peaks. The Raman spectra are in all cases dominated by the perfect silicon peak at about 530 cm−1, and are then not very useful for the characterization of the defects., Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART²

Made available in DSpace on 2021-06-26T05:08:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-06-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) The development of new technologies in the search for efficient energy storage systems is combined with the development of materials that are efficient in this type of application, such as carbon-based nanosheets, a promising alternative to be applied in Na-based batteries. Computational simulations founded on the density functional theory have been carried out to describe the graphenylene (GP) as a promising and versatile 2D material to be applied as a Na-anode material. A complete scan was made to determine the energy profile when a sodium atom travels over the GP, to explain the mechanism of Na interaction and the maximum Na saturation. The theoretical storage capacity of GP reaches 450 mAh/g and 650 mAh/g for up and up-down saturations and (NaC3) and (NaC1.5) ratio respectively. Therefore, the GP appears to be a suitable alternative to be used as a layered material to be applied to Na-based batteries. Univ Fed Rio Grande do Norte, Dept Mat Engn, Mat Sci & Engn Postgrad Program, BR-59078970 Natal, RN, Brazil Univ Fed Rio Grande do Norte, Chem Inst, BR-59078970 Natal, RN, Brazil Univ Torino, Dipartimento Chim, Via Giuria 5, I-10125 Turin, Italy Sao Paulo State Univ, Modeling & Mol Simulat Grp, BR-17033360 Bauru, SP, Brazil Sao Paulo State Univ, Modeling & Mol Simulat Grp, BR-17033360 Bauru, SP, Brazil FAPESP: 2019/08928-9 FAPESP: 2013/07296-2 CAPES: 001 CAPES: 88887.467334/2019-00 CNPq: 420062/2016-5

Local charged defects in periodic systems are usually investigated by adopting the supercell charge compensated (CC) model, which consists of two main ingredients: (i) the periodic supercell, hopefully large enough to reduce to negligible values the interaction among defects belonging to different cells; (ii) a background of uniform compensating charge that restores the neutrality of the supercell and then avoids the "Coulomb catastrophe". Here, an alternative approach is proposed and compared to CC, the double defect (DD) model, in which another point defect is introduced in the supercell that provides (or accept) the electron to be transferred (subtracted) to the defect of interest. The DD model requires obviously a (much) larger supercell than CC, and the effect of the relative position of the two defects must be explored. A third possible option, the cluster approach, is not discussed here. The two models have been compared with reference to the VN

International audience; A computational approach is presented to compute anharmonic vibrational states of solids from quantum-mechanical DFT calculations by taking into explicit account phonon–phonon couplings via the vibrational configuration interaction (VCI) method. The Born–Oppenheimer potential energy surface (PES) is expanded in a Taylor’s series in terms of harmonic normal coordinates, centered at the equilibrium nuclear configuration, is truncated to quartic order, and contains one-mode, two-mode, and three-mode interatomic force constants. The description of the anharmonic terms of the PES involves the numerical evaluation of high-order energy derivatives (cubic and quartic in our case) with respect to nuclear displacements and constitutes the most computationally demanding step in the characterization of anharmonic vibrational states of materials. Part I is devoted to the description of the PES. Four different numerical approaches are presented for the description of the potential, all based on a grid representation of the PES in the basis of the normal coordinates, that require different ingredients (energy and/or forces) to be evaluated at each point (i.e., nuclear configuration) of the grid. The numerical stability and relative computational efficiency of the various schemes for the description of the PES are discussed on two molecular systems (water and methane) and two extended solids (Ice-XI and MgH2). All the presented algorithms are implemented into a developmental version of the Crystal program.

International audience; Two methods are implemented in the Crystal program for the calculation of anharmonic vibrational states of solids: the vibrational self-consistent field (VSCF) and the vibrational configuration-interaction (VCI). While the former is a mean-field approach, where each vibrational mode interacts with the average potential of the others, the latter allows for an explicit and complete account of mode–mode correlation. Both schemes are based on the representation of the adiabatic potential energy surface (PES) discussed in Part I, where the PES is expanded in a Taylor’s series so as to include up to cubic and quartic terms. The VSCF and VCI methods are formally presented and their numerical parameters discussed. In particular, the convergence of computed anharmonic vibrational states, within the VCI method, is investigated as a function of the truncation of the expansion of the nuclear wave function. The correctness and effectiveness of the implementation is discussed by comparing with available theoretical and experimental data on both molecular and periodic systems. The effect of the adopted basis set and exchange-correlation functional in the description of the PES on computed anharmonic vibrational states is also addressed.

Local charged defects in periodic systems are usually investigated by adopting the supercell charge compensated (CC) model, which consists of two main ingredients: (i) the periodic supercell, hopef...

The lattice structures, electronic characteristics and spectroscopic features of the three vicinal substitutional, spin zero defects, Ns-Ns (A-centre), Bs-Bs, and Bs-Ns in diamond are reported. They are derived from all-electron B3LYP calculations based on Gaussian basis sets, within a periodic supercell scheme, including both 64- and 216-atom cells. The local geometry reflects the differences between the strong C-C bond of the host lattice and the weaker impurity-impurity bonding in the defective systems. The band structures show two occupied bands 1.06 eV above the VBE for Ns-Ns, and empty bands 3.36 eV and 0.25 eV below the CBE for Bs-Bs and for Bs-Ns respectively. The IR spectra of Bs-Bs and Ns-Ns contain sharp peaks at 631 cm−1, 692 cm−1 and 1373 cm−1, and 451 cm−1, 571 cm−1 and 1276 cm−1, respectively, which might reasonably be considered as ‘finger prints’ for these systems. For Bs-Ns, a set of medium intensity absorptions are predicted at 890 cm−1, 945 cm−1, 1018 cm−1, 1078 cm−1 and 1281 cm−1. However, numerous peaks in this region have been predicted for other defective systems, so that the firm identification of Bs-Ns based on these frequencies is much less certain than Bs-Bs and Ns-Ns.

International audience; 97 Total downloads11 citation on Dimensions.Turn on MathJaxGet permission to re-use this articleShare this article Share this content via email Share on Facebook Share on Twitter Share on Google+ Share on MendeleyArticle informationAbstractThis paper reports calculated energies and electronic structures of O(2p), O(2s) and Al(2p) excited states in bulk -Al2O3, at the and surfaces and in the presence of O vacancy defects, obtained from all-electron HF, B3LYP, GGA and LDA calculations based on a recently described direct -SCF approach (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). The closely related frequency-dependent optical constants derived from B3LYP calculations within the CPHF/DF framework are also reported, where both sets of results are shown to compare favourably with the experimental spectra. The differences between the directly calculated excited state energies, which in -Al2O3 are equal to the leading excitation edges, based on the four functionals, are substantially less than the differences between the corresponding (ground state) band gaps, as reported previously for AFII NiO (Mackrodt et al 2018 J. Phys.: Condens. Matter 30 495901). For the B3LYP functional, these energies are 8.7 eV, 12.5 eV and 73.7 eV for the O(2p), O(2s) and Al(2p) excitations respectively. The O(2p) edge is predicted to be degenerate, with distinct excitations from O(2p) states that are parallel to and perpendicular to the c-axis, in agreement with the reported spectra (Tomiki et al 1993 J. Phys. Soc. Japan 62 573). Detailed analyses of the charge and spin distributions in the four bulk excited states indicate that these are essentially charge-transfer excitonic, with acceptor sites at the nearest neighbour positions. Despite the close proximity of the O() and O(2p) excited state energies, the charge and spin distributions are predicted to be quite different.

The calculation of the full vibrational spectrum (Infrared or Raman) of very large systems (say larger than one thousand atoms) is not only very expensive, but also of relatively low interest, as in many (most of the) cases only a subset of modes, well separated from the large, diffuse bands resulting from the superposition of thousands of peaks, is used for the spectroscopic characterization of the specific system under study. Here, a fragment strategy, consisting in computing and diagonalizing a reduced (in size) Hessian matrix centered around the zone of interest, is illustrated, and its accuracy and efficiency documented, by comparison with the full Hessian diagonalization (FHD) scheme. Three test cases are considered, showing different vibrational features. They are defects in diamond: the $${\hbox {VN}}_3$$ H defect (V stands for the vacancy), where the interesting point is the characterization of the bending and stretching modes of H, well separated from the large band resulting from the perturbation of the diamond manifold; the $${\hbox {VH}}_4$$ defect (four H atoms in the vacancy, with vibrational modes related to H appearing both at high and low wave numbers); and the $${\hbox {I}}_{2{\mathrm{N}}}$$ interstitial defect, with modes in which the N atoms are involved, appearing at wave numbers not far from the manifold of the perfect diamond modes. So the three cases, apparently similar, explore three different situations of interest for the fragment strategy: (1) localized modes very well separated from the large diamond continuous band ( $${\hbox {VN}}_3$$ H); (2) modes at upper border of the large diamond continuous band ( $${\hbox {I}}_{2{\mathrm{N}}}$$ ): a case in which the modes of interest appear both as separated from and merged with the large continuous band ( $${\hbox {VH}}_4$$ ). It turns out that in all cases relatively small fragments, containing from 2 to 40 atoms, permit to reproduce with high accuracy (the difference with respect to the FHD being always smaller than 5 cm $$^{-1}$$ for the wave numbers, and a few percent for the IR intensity) the spectral feature(s) of interest, at a computational cost that is only a small fraction of the one required by the FHD.

International audience; Quantum-mechanical calculations are performed to investigate the structural, electronic, and infrared (IR) and Raman spectroscopic features of one of the most common radiation-induced defects in diamond: the “dumb-bell” 〈100〉 split self-interstitial. A periodic super-cell approach is used in combination with all-electron basis sets and hybrid functionals of density-functional-theory (DFT), which include a fraction of exact non-local exchange and are known to provide a correct description of the electronic spin localization at the defect, at variance with simpler formulations of the DFT. The effects of both defect concentration and spin state are explicitly addressed. Geometrical constraints are found to prevent the formation of a double bond between the two three-fold coordinated carbon atoms. In contrast, two unpaired electrons are fully localized on each of the carbon atoms involved in the defect. The open-shell singlet state is slightly more stable than the triplet (the energy difference being just 30 meV, as the unpaired electrons occupy orthogonal orbitals) while the closed-shell solution is less stable by about 1.55 eV. The formation energy of the defect from pristine diamond is about 12 eV. The Raman spectrum presents only two peaks of low intensity at wave-numbers higher than the pristine diamond peak (characterized by normal modes extremely localized on the defect), whose positions strongly depend on defect concentration as they blue shift up to 1550 and 1927 cm−1 at infinite defect dilution. The first of these peaks, also IR active, is characterized by a very high IR intensity, and might then be related to the strong experimental feature of the IR spectrum occurring at 1570 cm−1. A second very intense IR peak appears at about 500 cm−1, which, despite being originated from a “wagging” motion of the self-interstitial defect, exhibits a more collective, less localized character.

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.

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 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.

This paper reports calculated energies and electronic structures of nineteen excited states in NiO based on a Δ-SCF approach reported previously for the [Formula: see text] transitions in NiO and Sr2CuO2Cl2. They are the spin-flip: [Formula: see text]; eight [Formula: see text]: (one electron) 3A2g → 3 T 2g , (two electron) 3A2g → 3 T 1g , 3A2g → a 1 E g , 3A2g → 1 T 2g , 3A2g → 1 T 1g , 3A2g → b1 E g , 3A2g → b1 T 2g ; two O(2p) → Ni(3d); seven Ni(3d) → O(2p) (including two spin-flip) and the O(2s) → Ni(3d) charge transfer excitations, which span an energy range from 0.25 eV to 17.53 eV, and include the fundamental band gap associated with an excitonic O(2p) → Ni(3d) transition at 4.23 eV. These are compared to absorption and emission spectra, and previous calculations. In the case of the O(2p) → Ni(3d) excitations, comparisons are given for gap and Γ-point energies derived from HF, PBE0, HSE06, B3LYP, B1WC, GGA and LDA one-electron approximations. Finally, the directly calculated Stokes shifts and associated luminescence energies for the two O(2p) → Ni(3d) transitions are reported, where the excitonic value is found to be in good agreement with the recently reported experimental value.

International audience; When a slab includes an increasing number of layers, some of its properties evolve naturally toward the corresponding ones of the bulk. In other cases, however, this correspondence must be established, as is the case, for example, of the elastic constants involving the lattice parameter orthogonal to the basal plane in the bulk, which in the latter is not defined. Other properties as the first and second hyperpolarizabilities, of the piezoelectricity and elastic tensors, in both the electronic and ionic contributions, are also included in the present work. In all cases, the corresponding property in the bulk is identified. The good agreement between the slab and bulk results documents the convergence of the former with the number of layers. It represents also an important check of the numerical accuracy of the CRYSTAL code in computing this large set of properties.

The six possible VNxHy defects in diamond (a vacancy surrounded by x = 1 to 3 a vacancy surrounded by x = 1 to 3 nitrogens and y = 1 to 4-x hydrogens) are investigated at the quantum mechanical level by using the periodic supercell approach (64 atoms), an all electron Gaussian-type basis set, and hybrid functionals. It turns out that steric hindrance and short range repulsion is not such to prevent hydrogen atoms (up to 3 in VNH3) from fitting in the V cavity and saturating the dangling bonds of the carbon atoms first neighbors of the vacancy. All the investigated systems present specific IR spectra, with bending and stretching peaks above the nearly continuous band (from 400 to about 1340 cm−1) resulting from the perturbation of the perfect diamond spectrum by the vacancy and the nitrogen substitutions. These peaks, ranging from 1340 to 1700 cm−1 (bending; data refer to the harmonic approximation) and from 3100 to nearly 4000 cm−1 (stretching), might be considered fingerprints of the various defects. The C–H anharmonicity, evaluated numerically, turns out to be very sensitive to the N and H load, ranging from −202 cm−1 (redshift of the triplet state of VNH) to +57 cm−1 (blueshift of the symmetric stretching in VNH3).

International audience; The aim of this work is to investigate the consequences of lattice distortion on the vibrational features of rare-earth perovskites. To this end, a series of REMO3 compounds has been synthesized with different rare earths (RE = La, Pr, Nd, Sm) and different transition metals (M = Fe, Co) to evaluate their respective role on lattice distortion. Thin films of these materials have been deposited by magnetron cosputtering in the reactive mode and followed by annealing in air with the same experimental conditions. Characterizations including energy-dispersive X-ray spectroscopy, X-ray diffraction, and Fourier transform infrared spectroscopy have been completed by density functional theory periodic calculations to investigate the octahedra tilt angles and to assign the vibrational spectra. The decrease of RE radius enhances the distortion of the chains of octahedra that can be followed both through the calculated mean tilt angle and experimentally by the profile of the M–O–M bending region. The magnitude of the distortion depends on the dimension of the cuboctahedric site hosting the RE that is controlled by the M radius.