Search

The nature of chemical bonding in actinide compounds (molecular complexes and materials) remains elusive in many respects. A thorough analysis of their electron charge distribution can prove decisive in elucidating bonding trends and oxidation states along the series. However, the accurate determination and robust analysis of the charge density of actinide compounds pose several challenges from both experimental and theoretical perspectives. Significant advances have recently been made on the experimental reconstruction and topological analysis of the charge density of actinide materials [Gianopoulos et al. IUCrJ, 2019, 6, 895 [PMC free article] [PubMed]]. Here, we discuss complementary advances on the theoretical side, which allow for the accurate determination of the charge density of actinide materials from quantum-mechanical simulations in the bulk. In particular, the extension of the Topond software implementing Bader’s quantum theory of atoms in molecules and crystals (QTAIMAC) to f- and g-type basis functions is introduced, which allows for an effective study of lanthanides and actinides in the bulk and in vacuo, on the same grounds. Chemical bonding of the tetraphenyl phosphate uranium hexafluoride cocrystal [PPh4+][UF6–] is investigated, whose experimental charge density is available for comparison. Crystal packing effects on the charge density and chemical bonding are quantified and discussed. The methodology presented here allows reproducing all subtle features of the topology of the Laplacian of the experimental charge density. Such a remarkable qualitative and quantitative agreement represents a strong mutual validation of both approaches—experimental and computational—for charge density analysis of actinide compounds.

We study pressure-induced isostructural electronic phase transitions in the prototypical mixed valence and strongly correlated material EuO using the global-hybrid density functional theory. The simultaneous presence in the valence of highly localized $d$- and $f$-type bands and itinerant $s$- and $p$-type states, as well as the half-filled $f$-type orbital shell with seven unpaired electrons on each Eu atom, have made the description of the electronic features of this system a challenge. The electronic band structure, density of states, and atomic oxidation states of EuO are analyzed in the 0--50 GPa pressure range. An insulator-to-metal transition at about 12 GPa of pressure was identified. The second isostructural transition at approximately 30--35 GPa, previously believed to be driven by an oxidation from Eu(II) to Eu(III), is shown instead to be associated with a change in the occupation of the Eu $d$ orbitals, as can be determined from the analysis of the corresponding atomic orbital populations. The Eu $d$ band is confined by the surrounding oxygens and split by the crystal field, which results in orbitals of ${e}_{g}$ symmetry (i.e., ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{2{z}^{2}\ensuremath{-}{x}^{2}\ensuremath{-}{y}^{2}}$, pointing along the Eu-O direction) being abruptly depopulated at the transition as a means to alleviate electron-electron repulsion in the highly compressed structures.

The chemistry of f-electrons in lanthanide and actinide materials is yet to be fully rationalized. Quantum-mechanical simulations can provide useful complementary insight to that obtained from experiments. The quantum theory of atoms in molecules and crystals (QTAIMAC), through thorough topological analysis of the electron density (often complemented by that of its Laplacian) constitutes a general and robust theoretical framework to analyze chemical bonding features from a computed wave function. Here, we present the extension of the Topond module (previously limited to work in terms of s-, p- and d-type basis functions only) of the Crystal program to f- and g-type basis functions within the linear combination of atomic orbitals (LCAO) approach. This allows for an effective QTAIMAC analysis of chemical bonding of lanthanide and actinide materials. The new implemented algorithms are applied to the analysis of the spatial distribution of the electron density and its Laplacian of the cesium uranyl chloride, Cs2UO2Cl4, crystal. Discrepancies between the present theoretical description of chemical bonding and that obtained from a previously reconstructed electron density by experimental X-ray diffraction are illustrated and discussed.

International audience; We revise formal and numerical aspects of collinear and non-collinear density functional theories in the context of a two-component self-consistent treatment of spin–orbit coupling. Theoretical and numerical analyses of the non-collinear approaches confirm their ability to yield the proper collinear limit and provide rotational invariance of the total energy for functionals in the local-density or generalized-gradient approximations (GGAs). Calculations on simple molecules corroborate the formal considerations and highlight the importance of an effective screening algorithm to provide the sufficient level of numerical stability required for a rotationally invariant implementation of non-collinear GGA functionals. The illustrative calculations provide a first numerical comparison of both previously proposed non-collinear formulations for GGA functionals. The proposed screening procedure allows us to effectively deal with points of small magnetization, which would otherwise be problematic for the evaluation of the exchange–correlation energy and/or potential for non-collinear GGA functionals. Both previously suggested formulations for the non-collinear GGA are confirmed to be adequate for total energy calculations, provided that the screening is achieved on a sufficiently fine grid. All methods are implemented in the Crystal program.

International audience; A noncanonical coupled perturbed Kohn–Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment of spin–orbit coupling (SOC) is provided. We take the scalar-relativistic KS-DFT/HF solution, obtained with a relativistic effective core potential, as the zeroth-order approximation. Explicit expressions are given for the total energy through the 4th order, which satisfy the 2n + 1 rule. Second-order expressions are provided for orbital energies and density variables of spin-current DFT. Test calculations are carried out on the halogen homonuclear diatomic and hydride molecules, including 6p and 7p elements, as well as open-shell negative ions. The computed properties through second or third order match well with those from reference two-component self-consistent field calculations for total and orbital energies as well as spin-current densities. In only one case (At2–) did a significant deviation occur for the remaining density variables. Our coupled perturbation theory approach provides an efficient way of adding the effect of SOC to a scalar-relativistic single-reference KS-DFT/HF treatment, in particular because it does not require diagonalization in the two-component spinor basis, leading to saving factors on the number of required floating-point operations that may exceed one order of magnitude.

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.

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.

The thermomechanical response of organic semiconducting solids is an essential aspect to consider in the design of materials for advanced applications, and in particular, flexible electronics. The non-covalent intermolecular forces that exist in organic solids not only result in a diverse set of mechanical properties, but also a critical dependence of those same properties on temperature. However, studying the thermoelastic response of solids is experimentally challenging, often requiring large single-crystals and sensitive experimental apparatus. An alternative contactless approach involves using low-frequency vibrational spectroscopy to characterize the underlying intermolecular forces, and then combining this information with solid-state density functional theory simulations to retrieve the mechanical response of materials. This methodology, which only requires poly-micro-crystalline sample (compared to large single-crystals), leverages recent advances in the quasi-harmonic approximation to predict the temperature evolution of crystalline structures, dynamics, and associated forces, and then utilizes this information to determine the elastic tensor as a function of temperature. Here, this methodology is illustrated for two prototypical organic semiconducting crystals, rubrene and BTBT, and suggests a new alternative means to characterizing the thermoelastic response of organic materials.

The spin-current density functional theory (SCDFT), when formulated in a basis of Pauli spinors, provides a proper theoretical framework for the study of materials in an arbitrarily oriented external magnetic field and/or upon inclusion of spin-dependent relativistic effects, such as spin-orbit coupling. The SCDFT is formulated in terms of the particle-number density $n$, the Cartesian components of the magnetization ${m}_{x},$ ${m}_{y},$ and ${m}_{z}$, the orbital-current density $\mathbit{j}$, and the three spin-current densities ${\mathbit{J}}^{x},$ ${\mathbit{J}}^{y},$ and ${\mathbit{J}}^{z}$, where each of these density variables depends on specific blocks of the density matrix. Exchange-correlation (xc) functionals within the SCDFT should therefore depend on all of these eight fundamental density variables: ${F}_{xc}[n,{m}_{x},{m}_{y},{m}_{z},\mathbit{j},{\mathbit{J}}^{x},{\mathbit{J}}^{y},{\mathbit{J}}^{z}]$, which makes their parametrization a formidable task. Here, we formulate the adiabatic connection of the SCDFT for a treatment of exact Fock exchange in the theory. We show how the inclusion of a fraction of Fock exchange in standard functionals of the (spin) DFT (either in their collinear or noncollinear versions: ${F}_{xc}[n],$ ${F}_{xc}[n,{m}_{z}]$ and ${F}_{xc}[n,{m}_{x},{m}_{y},{m}_{z}]$) allows for the two-electron potential to depend on all those blocks of the density matrix that correspond to the eight density variables of the SCDFT, in a sensible and yet practical way. In particular, in the local-density and generalized-gradient approximations of the SCDFT, the treatment of the current densities solely from the Fock exchange term is formally justified by the short-range behavior of the exchange hole. We discuss that the adiabatic coupling strength parameter modulates the two-electron coupling of the orbital- and spin-current densities with the particle-number density and magnetization. Formal considerations are complemented by numerical tests on a periodic model system in the presence of spin-orbit coupling and in the absence of an external magnetic field.

Cubic cuprous oxide, Cu2O, is characterized by a peculiar structural response to temperature: it shows a relatively large negative thermal expansion below 250 K, then followed by a positive thermal expansion at higher temperatures. The two branches of its thermal expansion (negative and positive) are almost perfectly symmetric at low temperatures, with the minimum of its lattice parameter at about 250 K and with the lattice parameter at 500 K almost coinciding with that at 0 K. We perform lattice-dynamical quantum-mechanical calculations to investigate the thermal expansion of Cu2O. Phonon mode-specific Gruneisen parameters are computed, which allows us to identify different spectral regions of atomic vibrations responsible for the two distinct regimes of thermal expansion. Two different computational approaches are explored, their results compared, and their numerical aspects critically assessed: a well-established method based on the quasiharmonic approximation, where harmonic frequencies are computed at different lattice volumes, and an alternative approach, where quadratic and cubic interatomic force-constants are computed at a single volume. The latter scheme has only recently become computationally feasible in the context of lattice thermal conductivity simulations. When proper numerical parameters are used (phonon sampling, tolerances, etc.), the two approaches are here shown to provide a very consistent description, yet at a rather different computational cost. All of the experimentally observed features of the complex thermal expansion of Cu2O are correctly reproduced up to 500 K, with a slight overall underestimation of the volume contraction.Cubic cuprous oxide, Cu2O, is characterized by a peculiar structural response to temperature: it shows a relatively large negative thermal expansion below 250 K, then followed by a positive thermal expansion at higher temperatures. The two branches of its thermal expansion (negative and positive) are almost perfectly symmetric at low temperatures, with the minimum of its lattice parameter at about 250 K and with the lattice parameter at 500 K almost coinciding with that at 0 K. We perform lattice-dynamical quantum-mechanical calculations to investigate the thermal expansion of Cu2O. Phonon mode-specific Gruneisen parameters are computed, which allows us to identify different spectral regions of atomic vibrations responsible for the two distinct regimes of thermal expansion. Two different computational approaches are explored, their results compared, and their numerical aspects critically assessed: a well-established method based on the quasiharmonic approximation, where harmonic frequencies are computed a...

We perform a formal analysis of relativistic density functional theory for the treatment of spin-orbit coupling (SOC), noncollinear magnetization (NCM), and orbital current density (OCD). We identify specific components of the spinors (namely, those mapped onto imaginary diagonal spin-blocks of the density matrix) that arise from the SOC operator and define the OCD. We show that these pieces of the spinors only enter in the bielectronic part of the potential through the exact Fock exchange (FE) operator. The lack of FE therefore leads to a correspondingly incorrect physical description of SOC, NCM, and OCD. This analysis is complemented with an illustrative example, where we show that, while in the absence of FE, the theory fails even at reproducing the expected right-hand relationship between the NCM and OCD, its inclusion provides results that match those from a reference SOC configuration-interaction calculation.

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.

Piezo-optical and elasto-optical properties of lead molibdate (PbMoO4) crystals are investigated, as determined by the quantum-mechanical ab initio calculation of the full set of elasto-optic, piezo-optic and elastic tensor components. Indicative surfaces are built, which describe the anisotropy of these stress- and strain-optical effects and allow for its rigorous analysis. Maximum values of these properties are determined as well as the geometries of acousto-optic interaction displaying the maximum efficiency. Lead molibdate crystals are found to be characterized by a large piezo-optic efficiency, the maximum change of the optical path (per unit of mechanical stress and specimen length) being calculated to 24.9 Br, which is a much larger value than previously reported for other well-known piezo-optic materials such as LiNbO3, CaWO4 and GaP. It is also shown that a significant rotation (up to several tens of degrees) of the optical indicatrix about the X3 optical axis is induced by uniaxial pressure or deformation, depending only on pressure (or deformation) direction, which has relevant implications in the design of acousto-optic cells.

International audience; A large out-of-plane piezoelectricity can be induced in graphene by carbon substitution. Several simple substitutions are considered where C atoms are replaced by heavier group-IV elements (Si, Ge, and Sn). A more complex functionalization (namely, pyrrolic N-doped graphene) is also investigated where different functional groups, such as F, Cl, H3C, and H2N, are studied. Piezoelectric and elastic response properties of all systems are determined quantum mechanically at the ab initio level of theory. A rationalization of the physical and chemical parameters which most affect the out-of-plane piezoelectricity of functionalized graphene is reported, which reveals the dominant character of the nuclear over electronic contribution. The combination of an out-of-plane symmetry-breaking defect and a soft infrared-active phonon mode, with a large cell-deformation coupling, is shown to constitute the necessary prerequisite to induce a large out-of-plane piezoelectric response into functionalized graphene. © 2016 American Chemical Society.

The combination of quantum-mechanical simulations and infrared absorption spectroscopy measurements provides a clear picture for a long standing puzzle in surface science: the actual structure and vibrational dynamics of the low-temperature ordered CO monolayer adsorbed on (001) MgO surfaces. The equilibrium structure of the commensurate (4 × 2) adsorbed phase consists of three CO molecules per primitive cell (surface coverage of 75%) located at two inequivalent sites: one molecule seats upright on top of a Mg site while two molecules, tilted off the normal to the surface, are symmetrically positioned relative to the upright one with anti-parallel projections on the surface. This configuration, long believed to be incompatible with measured polarization infrared spectra, is shown to reproduce all observed spectral features, including a new, unexpected one: the vanishing anharmonicity of CO stretching modes in the monolayer.

We revise formal and numerical aspects of collinear and noncollinear density functional theory (DFT) in the context of a two-component self-consistent treatment of spin-orbit coupling (SOC). While the extension of the standard one-component theory to a noncollinear magnetization is formally well-defined within the local density approximation, and therefore results in a numerically stable theory, this is not the case within the generalized gradient approximation (GGA). Previously reported formulations of noncollinear DFT based on GGA exchange-correlation potentials have several limitations: (i) they fail at reducing (either formally or numerically) to the proper collinear limit (i.e., when the magnetization is parallel or antiparallel to the z axis everywhere in space); (ii) they fail at ensuring a quantitative rotational invariance of the total energy and even a qualitative rotational invariance of the spatial distribution of the magnetization when a SOC operator is included in the Hamiltonian; (iii) they are numerically very unstable in regions of small magnetization. All of the above-mentioned problems are here shown (both formally and through test examples) to be solved by using instead a new formulation of noncollinear DFT for GGA functionals, which we call the "signed canonical" theory, as combined with an effective screening algorithm for unstable terms of the exchange-correlation potential in regions of small magnetization. All methods are implemented in the CRYSTAL program and tests are performed on simple molecules to compare the different formulations of noncollinear DFT.

An effective algorithm for the quasi-harmonic calculation of thermo-elastic stiffness constants of materials is discussed and implemented into the Crystal program for quantum-mechanical simulations of extended systems. Two different approaches of increasing complexity and accuracy are presented. The first one is a quasi-static approximation where the thermal dependence of elastic constants is assumed to be due only to the thermal expansion of the system. The second one is fully quasi-harmonic, takes into account thermal expansion, and explicitly computes Helmholtz free energy derivatives with respect to strain. The conversion of isothermal into adiabatic thermo-elastic constants is also addressed. The algorithm is formally presented and applied to the description of the thermo-elastic response of the forsterite mineral.

Metal-organic frameworks are an important class of porous materials exhibiting a variety of promising properties that are related to the unique atomic-level structural features found in the solids. Using terahertz time-domain spectroscopy, the relationship between the large-amplitude low-frequency vibrations and the mechanochemical features found in these materials can be elucidated, providing deep insight into the origins of the favourable phenomena.

Lanthanide sesquioxides are strongly correlated materials characterized by highly localized unpaired electrons in the $f$ band. Theoretical descriptions based on standard density functional theory (DFT) formulations are known to be unable to correctly describe their peculiar electronic and magnetic features. In this study, electronic and magnetic properties of the first four lanthanide sesquioxides in the series are characterized through a reliable description of spin localization as ensured by hybrid functionals of the DFT, which include a fraction of nonlocal Fock exchange. Because of the high localization of the $f$ electrons, multiple metastable electronic configurations are possible for their ground state depending on the specific partial occupation of the $f$ orbitals: the most stable configuration is here found and characterized for all systems. Magnetic ordering is explicitly investigated, and the higher stability of an antiferromagnetic configuration with respect to the ferromagnetic one is predicted. The critical role of the fraction of exchange on the description of their electronic properties (notably, on spin localization and on the electronic band gap) is addressed. In particular, a recently proposed theoretical approach based on a self-consistent definition---through the material dielectric response---of the optimal fraction of exchange in hybrid functionals is applied to these strongly correlated materials.

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; 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.

An ab initio quantum-mechanical theoretical framework is presented to compute the thermal properties of molecular crystals. The present strategy combines dispersion-corrected density-functional-theory (DFT-D), harmonic phonon dispersion, quasi-harmonic approximation to the lattice dynamics for thermal expansion and thermodynamic functions, and quasi-static approximation for anisotropic thermo-elasticity. The proposed scheme is shown to reliably describe thermal properties of the urea molecular crystal by a thorough comparison with experimental data.

Structural and energetic properties of the grossular-katoite solid solution are studied with a full ab initio quantum chemical approach. An all-electron basis set and the hybrid B3LYP functional are used. Calculations are performed within the primitive cell of cubic garnets. The hydrogarnet substitution, SiO 4 ↔ H 4 O 4 , yields 136 symmetry-independent configurations ranging from triclinic to cubic symmetry. All of them have been structurally optimized, the relaxed geometries being characterized by pseudo-cubic conventional cells. At the present level of approximation, the most stable configurations constitute by far the largest contributions to the system properties. Considering only the most stable configurations, average geometrical features of the actual solid solution are closely approximated. The excess volume displays a highly non-ideal behavior that is favorably compared with carefully analyzed and selected experimental data. The excess enthalpy deviates from the regular model; it draws an asymmetric function of composition with two minima that can be associated to structures or compositions observed in nature. Geometrical variations and distribution of the tetrahedra are analyzed. Calculations provide independent support to the use of a split-atom model for experimental refinements on these compounds. The asymmetry of the enthalpy of mixing can be associated with two distinct distribution patterns of the tetrahedra. Hydrogen interactions also contribute to the asymmetry of the excess enthalpy, as it turns out by comparison between compositions close to fully hydrated katoite and those close to grossular. Hydrogen interactions in Si-free katoite are found to be weak as suggested by dramatic changes in the H environment associated with the introduction of SiO 4 tetrahedra.

The Linear Combination of Atomic Orbitals approach implemented into the public Crystal program for quantum-chemical simulations of n-dimensional periodic systems ( $$n = 0,1,2,3$$ ) is here extended to g-type basis functions. A general algorithmic procedure is devised for the calculation of the coefficients needed for the analytical evaluation of one- and two-electron integrals for energy and forces within the recursive McMurchie–Davidson strategy, up to arbitrarily high quantum numbers. Explicit routines are generated for the calculation of all the coefficients needed for g-type functions, which ensure a very high computational efficiency. The code has been generalized in many respects so as to allow for the use of g-type functions for: (1) Hartree–Fock energy and forces; (2) density functional theory energy and forces (in either a local density, generalized gradient, meta-GGA or various hybrid approximations); (3) all-electron and pseudo-potential basis sets; (4) spin-restricted and unrestricted calculations; (5) coupled-perturbed Hartree–Fock/Kohn–Sham (hyper)-polarizability calculations; (6) projected density-of-states. The g-type basis functions are expected to play an important role in (1) the description of the electronic structure of heavy elements and in particular of lanthanides and actinides with occupied 4f and 5f bands, respectively, where they represent the first polarization, (2) those calculations requiring an accurate description of the electronic polarization.

In this study we explore the implications of oxygen vacancy formation and of copper doping in the orthorhombic CaSnO3 perovskite, by means of density functional theory, focusing on energetic and electronic properties. In particular, the electronic charge distribution is analyzed by Mulliken, Hirshfeld-I, Bader and Wannier approaches. Calculations are performed at the PBE and the PBE0 level (for doping with Cu, only PBE0), with both spin-restricted and spin-unrestricted formulations; unrestricted calculations are used for spin-polarized cases and for the naturally open-shell cases (Cu doping). An oxygen vacancy is found to have the tendency to reduce Sn neighbors by giving rise to an energy band within the energy band-gap of the pristine system, close to the valence band. At variance with what happens in the CaTiO3 perovskite (also investigated here), an oxygen vacancy in the CaSnO3 perovskite is found to lose two valence electrons and thus to be positively charged so that no F-center is formed. Regarding Cu doping, when one Sn atom is substituted by a Cu one, the most stable configuration corresponds to having the Cu atom as a first neighbor to the vacancy. These findings shed some light on the catalytic and phosphorous host properties of this perovskite.

International audience; The latest release of the Crystal program for solid-state quantum-mechanical ab initio simulations is presented. The program adopts atom-centered Gaussian-type functions as a basis set, which makes it possible to perform all-electron as well as pseudopotential calculations. Systems of any periodicity can be treated at the same level of accuracy (from 0D molecules, clusters and nanocrystals, to 1D polymers, helices, nanorods, and nanotubes, to 2D monolayers and slab models for surfaces, to actual 3D bulk crystals), without any artificial repetition along nonperiodic directions for 0–2D systems. Density functional theory calculations can be performed with a variety of functionals belonging to several classes: local-density (LDA), generalized-gradient (GGA), meta-GGA, global hybrid, range-separated hybrid, and self-consistent system-specific hybrid. In particular, hybrid functionals can be used at a modest computational cost, comparable to that of pure LDA and GGA formulations, because of the efficient implementation of exact nonlocal Fock exchange. Both translational and point-symmetry features are fully exploited at all steps of the calculation, thus drastically reducing the corresponding computational cost. The various properties computed encompass electronic structure (including magnetic spin-polarized open-shell systems, electron density analysis), geometry (including full or constrained optimization, transition-state search), vibrational properties (frequencies, infrared and Raman intensities, phonon density of states), thermal properties (quasi-harmonic approximation), linear and nonlinear optical properties (static and dynamic [hyper]polarizabilities), strain properties (elasticity, piezoelectricity, photoelasticity), electron transport properties (Boltzmann, transport across nanojunctions), as well as X-ray and inelastic neutron spectra. The program is distributed in serial, parallel, and massively parallel versions. In this paper, the original developments that have been devised and implemented in the last 4 years (since the distribution of the previous public version, Crystal14, occurred in December 2013) are described.

Nowadays, the efficient exploitation of high-performance computing resources is crucial to extend the applicability of first-principles theoretical methods to the description of large, progressively more realistic molecular and condensed matter systems. This can be achieved only by devising effective parallelization strategies for the most time-consuming steps of a calculation, which requires some effort given the usual complexity of quantum-mechanical algorithms, particularly so if parallelization is to be extended to all properties and not just to the basic functionalities of the code. In this Article, the performance and capabilities of the massively parallel version of the Crystal17 package for first-principles calculations on solids are discussed. In particular, we present: (i) recent developments allowing for a further improvement of the code scalability (up to 32 768 cores); (ii) a quantitative analysis of the scaling and memory requirements of the code when running calculations with several thousands (up to about 14 000) of atoms per cell; (iii) a documentation of the high numerical size consistency of the code; and (iv) an overview of recent ab initio studies of several physical properties (structural, energetic, electronic, vibrational, spectroscopic, thermodynamic, elastic, piezoelectric, topological) of large systems investigated with the code.

Anharmonicity in solid materials is a critical factor that dictates a number of observable phenomena, especially those that depend on temperature. However, characterising such interactions is difficult due to the nature in which they combine with other effects, both experimentally and theoretically. This work details how terahertz time-domain and low-frequency Raman spectroscopy, when combined with state-of-the-art computational techniques, can be used to extract critical anharmonic information that enhances understanding the temperature-dependant thermochemical and thermomechanical properties of crystalline solids.

A fully-automated algorithm for the determination of the system-specific optimal fraction of exact exchange in self-consistent hybrid functionals of the density-functional-theory is illustrated, as implemented into the public Crystal program. The exchange fraction of this new class of functionals is self-consistently updated proportionally to the inverse of the dielectric response of the system within an iterative procedure (Skone et al 2014 Phys. Rev. B 89, 195112). Each iteration of the present scheme, in turn, implies convergence of a self-consistent-field (SCF) and a coupled-perturbed-Hartree-Fock/Kohn-Sham (CPHF/KS) procedure. The present implementation, beside improving the user-friendliness of self-consistent hybrids, exploits the unperturbed and electric-field perturbed density matrices from previous iterations as guesses for subsequent SCF and CPHF/KS iterations, which is documented to reduce the overall computational cost of the whole process by a factor of 2.

cited By 0; International audience; The VN3H defect in diamond (a vacancy surrounded by three nitrogen and one carbon atoms, the latter being saturated by a hydrogen atom) is investigated quantum-mechanically by use of a periodic supercell approach, an all-electron Gaussian-type basis set, "hybrid" functionals of density functional theory, and the Crystal program. Three fully optimized structural models (supercells containing 32, 64, and 128 atoms) are considered to investigate the effect of defect concentration. The electronic configuration of the defect is reported along with a description of its structural features. In particular, the influence of the lone-pair electrons of the three nitrogen atoms on the C-H bond is discussed. A thorough characterization of the vibrational spectroscopic features of the VN3H defect is also presented, where the anharmonicity of the most relevant normal modes is discussed. The infrared and Raman spectra show specific peaks, which allow for the identification of this particular defect among the many defects that are commonly present in both natural and irradiation-damaged diamonds. In particular, the main feature of the spectral fingerprint of the defect (i.e. the C-H stretching mode), experimentally observed at 3107 cm-1, is here computed at 3094 cm-1 with the B3LYP "hybrid" functional (with an anharmonic redshift of 157 cm-1 with respect to its harmonic value). The role played by the three nitrogen atoms on the spectral features of the defect is clearly identified through the redshift due to the 14N → 15N isotopic substitution. © 2017 the Owner Societies.

Many thanks to M. Maček-Kržmanc, R. A. Evarestov, D. Gryaznov and D. Fuks for fruitful discussions. This study was supported by the ERA-NET HarvEnPiez project., An enhancement of the piezoelectric properties of lead-free materials, which allow conversion of mechanical energy into electricity, is a task of great importance and interest. Results of first-principles calculations of piezoelectric/electromechanical properties of the Ba(1–x)SrxTiO3 (BSTO) ferroelectric solid solution with a perovskite structure are presented and discussed. Calculations are performed within the linear combination of atomic orbitals (LCAO) approximation and periodic-boundary conditions, using the advanced hybrid functionals of density functional theory (DFT). A supercell model allows the investigation of multiple chemical compositions x. In particular, three BSTO solid solutions with x = 0, 0.125, 0.25 are considered within the experimental stability domain of the ferroelectric tetragonal phase of the solid solution (x < 0.3). The configurational disorder with x = 0.25 composition is also investigated explicitly considering the seven possible atomic configurations corresponding to this composition. It is predicted that Sr-doping of BaTiO3 makes it mechanically harder and enhances its electromechanical/piezoelectric properties, which are important for relevant applications., ERA-NET HarvEnPiez project; 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

Two alternative approaches for the quantum-mechanical calculation of the nuclear-relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi-analytical approach based on the evaluation of the force- and displacement-response internal-strain tensors as combined with the interatomic force-constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi-Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc.

Symmetry features of the internal-strain tensor of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the quantum-mechanical evaluation of the internal-strain tensor of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain tensor is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric tensors of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients.

Quantum-mechanical ab initio calculations are performed to elucidate the vibrational spectroscopic features of a common irradiation-induced defect in diamond, i.e. the neutral vacancy. Raman spectra are computed analytically through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach as a function of both different defect spin states and defect concentration. The experimental Raman features of defective diamond located in the 400-1300 cm-1 spectral range, i.e. below the first-order line of pristine diamond at 1332 cm-1 , are well reproduced, thus corroborating the picture according to which, at low damage densities, this spectral region is mostly affected by non-graphitic sp3 defects. No peaks above 1332 cm-1 are found, thus ruling out previous tentative assignments of different spectral features (at 1450 and 1490 cm-1) to the neutral vacancy. The perturbation introduced by the vacancy to the thermal nuclear motion of carbon atoms in the defective lattice is discussed in terms of atomic anisotropic displacement parameters (ADPs), computed from converged lattice dynamics calculations., Comment: 8 pages, 5 figures, 1 table

Made available in DSpace on 2018-12-11T16:41:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-02-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Structural, elastic and thermodynamic properties of the orthorhombic CaSnO3 perovskite are theoretically investigated at the ab initio level as a function of temperature and pressure. Harmonic and quasi-harmonic lattice dynamical calculations are performed with the Crystal program, by explicitly accounting for thermal expansion effects and by exploring the effect of several DFT functionals. The anisotropic, directional elastic response of the system is characterized up to 20 GPa of pressure. The thermal lattice expansion and elastic bulk modulus are described at simultaneous temperatures up to 2000 K and pressures up to 20 GPa. The Gibbs free energy of formation of CaSnO3 from CaO and SnO2 as a function of temperature is also addressed by means of fully converged phonon dispersion calculations on the three systems. Laboratório de Combustíveis e Materiais INCTMN-UFPB Universidade Federal da Paraíba Grupo de Modelagem e Simulação Molecular INCTMN-UNESP São Paulo State University Dipartimento di Chimica Università di Torino and NIS Nanostructured Interfaces and Surfaces Centre of Excellence, Via Giuria 5 Grupo de Modelagem e Simulação Molecular INCTMN-UNESP São Paulo State University FAPESP: 2013/07296-2 FAPESP: 2013/19289-0

A quasi-analytical theoretical method is devised, and implemented in the Crystal program, for calculation of the direct “proper” piezoelectric tensor of periodic systems including both the clamped-nuclei electronic and nuclear relaxation contributions. It is based on using the analytical Coupled-Perturbed-Hartree–Fock/Kohn–Sham (CPHF/KS) procedure to obtain dipole derivatives with respect to lattice deformations as well as internal coordinates. The sole numerical step required involves building the Hessian matrix through differentiation of analytical energy gradients. Two prototypical piezoelectric, non-ferroelectric, crystals, namely ZnO and α-quartz, are used to demonstrate the accuracy and computational efficiency of our new scheme, which significantly improves upon the commonly used numerical Berry phase approach.

The phonon dispersion and thermodynamic properties of pyrope ( $$\hbox {Mg}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}$$ ) and grossular ( $$\hbox {Ca}_3\hbox {Al}_2\hbox {Si}_3\hbox {O}_{12}$$ ) have been computed by using an ab initio quantum mechanical approach, an all-electron variational Gaussian-type basis set and the B3LYP hybrid functional, as implemented in the Crystal program. Dispersion effects in the phonon bands have been simulated by using supercells of increasing size, containing 80, 160, 320, 640, 1280 and 2160 atoms, corresponding to 1, 2, 4, 8, 16 and 27 $$\mathbf {k}$$ points in the first Brillouin zone. Phonon band structures, density of states and corresponding inelastic neutron scattering spectra are reported. Full convergence of the various thermodynamic properties, in particular entropy (S) and specific heat at constant volume ( $$C_\mathrm{{V}}$$ ), with the number of $$\mathbf {k}$$ points is achieved with 27 $$\mathbf {k}$$ points. The very regular behavior of the S(T) and $$C_\mathrm{{V}}(T)$$ curves as a function of the number of $$\mathbf {k}$$ points, determined by high numerical stability of the code, permits extrapolation to an infinite number of $$\mathbf {k}$$ points. The limiting value differs from the 27- $$\mathbf {k}$$ case by only 0.40 % at 100 K for S (the difference decreasing to 0.11 % at 1000 K) and by 0.29 % (0.05 % at 1000 K) for $$C_\mathrm{{V}}$$ . The agreement with the experimental data is rather satisfactory. We also address the problem of the relative entropy of pyrope and grossular, a still debated question. Our lattice dynamical calculations correctly describe the larger entropy of pyrope than grossular by taking into account merely vibrational contributions and without invoking “static disorder” of the Mg ions in dodecahedral sites. However, as the computed entropy difference is found to be larger than the experimental one by a factor of 2–3, present calculations cannot exclude possible thermally induced structural changes, which could lead to further conformational contributions to the entropy.

The evolution under pressures up to 65 GPa of structural, elastic and vibrational properties of the katoite hydrogarnet, Ca3Al2(OH)12, is investigated with an ab initio simulation performed at the B3LYP level of theory, by using all-electron basis sets with the Crystal periodic program. The high-symmetry Ia3d phase of katoite, stable under ambient conditions, is shown to be destabilized, as pressure increases, by interactions involving hydrogen atoms and their neighbors which weaken the hydrogen bonding network of the structure. The corresponding thermodynamical instability is revealed by anomalous deviations from regularity of its elastic constants and by numerous imaginary phonon frequencies, up to 50 GPa. Interestingly, as pressure is further increased above 50 GPa, the Ia3d structure is shown to become stable again (all positive phonon frequencies and regular elastic constants). However, present calculations suggest that, above about 15 GPa and up to at least 65 GPa, a phase of I4[combining macron]3d symmetry (a non-centrosymmetric subgroup of Ia3d) becomes more stable than the Ia3d one, being characterized by strengthened hydrogen bonds. At low-pressures (between about 5 GPa and 15 GPa), both phases show some instabilities (more so for I4[combining macron]3d than for Ia3d), thus suggesting either the existence of a third phase or a possible phase transition of second order.

cited By 8; International audience; We show that a finite in-plane piezoelectricity can be induced in graphene by breaking its inversion center with any in-plane defect, in the limit of vanishing defect concentration. We first consider different patterns of BN-doped graphene sheets of D3h symmetry, whose electronic and piezoelectric (dominated by the electronic rather than nuclear term) properties are characterized at the ab initio level of theory. We then consider other in-plane defects, such as holes of D3h or C2v point symmetry, and confirm that a common limit value (for low defect concentration) of the piezoelectric response of graphene is obtained regardless of the particular chemical or physical nature of the defects (e11 ≈ 4.5 × 10-10 C/m and d11 ≈ 1.5 pm/V for direct and converse piezoelectricity, respectively). This in-plane piezoelectric response of graphene is one-order of magnitude larger than the out-of-plane previously investigated one. © 2015 American Chemical Society.

For the first time, to the best of our knowledge, we have experimentally determined all of the components of the piezo-optic tensor for monoclinic crystals. This has been implemented on a specific example of triglycine sulfate crystals. Based on the results obtained, the complete elasto-optic tensor has been calculated. Acousto-optic figures of merit (AOFMs) have been estimated for the case of acousto-optic interaction occurring in the principal planes of the optical indicatrix ellipsoid and for geometries in which the highest elasto-optic coefficients are involved as effective parameters. It has been found that the highest AOFM value is equal to 6.8×10−15 s3/kg for the case of isotropic acousto-optic interaction with quasi-longitudinal acoustic waves in the principal planes. This AOFM is higher than the corresponding values typical for canonic acousto-optic materials, which are transparent in the deep ultraviolet spectral range.

We apply first principles quantum mechanical techniques to the study of the solid solution Si1-xGexO2 of α-quartz where silicon atoms are progressively substituted with germanium atoms, to different extents, as a function of the substitutional fraction x. For the first time, the whole range of the substitution (x = 0.0, 0.1[Formula: see text], 0.[Formula: see text], 0.5, 0.[Formula: see text], 0.8[Formula: see text], 1.0), including pure end-members α-SiO2 and α-GeO2, is explored. An elongated supercell (doubled along the c crystallographic axis) is built with respect to the unit cell of pure α-quartz and a set of 13 symmetry-independent configurations is considered. Their structural, energetic, dielectric, elastic and piezoelectric properties are computed and analyzed. All the calculations are performed using the CRYSTAL14 program with a Gaussian-type function basis set with pseudopotentials, and the hybrid functional PBE0; all geometries are fully optimized at this level of theory. In particular, for each configuration, fourth-rank elastic and compliance tensors and third-rank direct and converse piezoelectric tensors are computed. It has already been shown that the structural distortion of the solid solution increases, almost linearly, as the substitutional fraction x increases. The piezoelectric properties of the Si1-xGexO2 solid solution are found to increase with x, with a similar quasi-linear behavior. The electromechanical coupling coefficients are enhanced as well and the linear trend recently predicted by Ranieri et al (2011 Inorg. Chem. 50 4632) can be confirmed from first principles calculations. These doped crystals do represent good candidates for technological applications requiring high piezoelectric coupling and high thermal stability.

International audience; The vibrational properties of CaCO3 aragonite have been investigated both theoretically, by using a quantum mechanical approach (all electron Gaussian type basis set and B3LYP HF-DFT hybrid functional, as implemented in the CRYSTAL code) and experimentally, by collecting polarized infrared (IR) reflectance and Raman spectra. The combined use of theory and experiment permits on the one hand to analyze the many subtle features of the measured spectra, on the other hand to evidentiate limits and deficiencies of both approaches. The full set of TO and LO IR active modes, their intensities, the dielectric tensor (in its static and high frequency components), and the optical indices have been determined, as well as the Raman frequencies. Tools such as isotopic substitution and graphical animation of the modes are available, that complement the analysis of the spectrum.

The complete piezoelectric tensor of ferroelectric SrTiO${}_{3}$ at low temperature is computed by ab initio theoretical simulations. Both direct and converse---coupled with elastic compliance---piezoelectricity are computed and interpreted in terms of electronic and nuclear contributions. The role of the ferroelectric soft phonon mode on this property is found to be dramatic thus leading to a possible giant piezoelectric response at very low temperature. Two possible space groups are considered for the ferroelectric phase of SrTiO${}_{3}$, both compatible with the available experimental data: a tetragonal $I4cm$ and an orthorhombic $Ima2$ one. The piezoelectric response of the two symmetries is predicted to be rather different and could be experimentally detected to clarify the (still unknown) structure of the ferroelectric phase of SrTiO${}_{3}$.

cited By 23; International audience; The vibration spectrum of single-walled zigzag boron nitride (BN) nanotubes is simulated with an ab initio periodic quantum chemical method. The trend towards the hexagonal monolayer (h-BN) in the limit of large tube radius R is explored for a variety of properties related to the vibrational spectrum: vibration frequencies, infrared intensities, oscillator strengths, and vibration contributions to the polarizability tensor. The (n,0) family is investigated in the range from n = 6 (24 atoms in the unit cell and tube radius R = 2.5 Å) to n = 60 (240 atoms in the cell and R = 24.0 Å). Simulations are performed using the CRYSTAL program which fully exploits the rich symmetry of this class of one-dimensional periodic systems: 4n symmetry operators for the general (n,0) tube. Three sets of infrared active phonon bands are found in the spectrum. The first one lies in the 0-600 cm-1 range and goes regularly to zero when R increases; the connection between these normal modes and the elastic and piezoelectric constants of h-BN is discussed. The second (600-800 cm-1) and third (1300-1600 cm-1) sets tend regularly, but with quite different speed, to the optical modes of the h-BN layer. The vibrational contribution of these modes to the two components (parallel and perpendicular) of the polarizability tensor is also discussed. © 2013 American Institute of Physics.

International audience; Fully periodic Hartree-Fock and density functional theory calculations have been used to compute the anisotropic displacement parameters (ADPs) of molecular crystals at different temperatures by using the CRYSTAL code. Crystalline urea was adopted as a benchmark system to investigate the dependence on basis set and Hamiltonian. The results were compared with ADPs derived from neutron diffraction experiments. The approach can estimate the internal ADPs, corresponding to the contributions of high-frequency intramolecular vibrations, and for these internal contributions the results are almost independent of the basis set and Hamiltonian. Much larger variations and discrepancies from neutron diffraction experiments are seen for the external, low-frequency modes, which become dominant at higher temperatures. The approach was then tested on benzene and urotropine. Finally, ADPs of L-alanine were predicted at the B3LYP/6-31G(d,p) level of theory. The total ADPs, including low-frequency external modes, are underestimated, but can be brought into good agreement with the experimental ADPs by introducing a Grüneisen parameter, which partly accounts for anharmonicity of the potential energy surface, but likely also contains contributions from other deficiencies of the calculations.

cited By 29; International audience; Single-walled zigzag beryllium oxide (BeO) nanotubes are simulated with an ab initio quantum chemical method. The (n,0) family is investigated in the range from n = 8 (32 atoms in the unit cell and tube radius R = 3.4 Å) to 64 (256 atoms in the cell and R = 27.1 Å). The trend toward the hexagonal monolayer (h-BeO) in the limit of large tube radius R is explored for a variety of properties: rolling energy, elastic modulus, piezoelectric constant, vibration frequencies, infrared (IR) intensities, oscillator strengths, and electronic and nuclear contributions to the polarizability tensor. Three sets of IR-active phonon bands are found in the spectrum. The first one lies in the 0-300 cm-1 frequency range and exhibits a very peculiar behavior: the vibration frequencies do tend regularly toward zero when R increases while their IR intensities do not; the nature of these normal modes is unveiled by establishing a connection between them and the elastic and piezoelectric constants of h-BeO. The second (680-730 cm-1) and third (1000-1200 cm-1) sets tend regularly, but with quite different slope, to the optical modes of the h-BeO layer. The vibrational contribution of these modes to the two components (parallel and perpendicular) of the polarizability tensor is also discussed. Simulations are performed using the Crystal program which fully exploits the rich symmetry of this class of one-dimensional periodic systems: 4n symmetry operators for the general (n,0) tube. © 2013 American Chemical Society.

International audience; Structural, vibrational, elastic, and dielectric properties of ZnO single-walled nanotubes are investigated theoretically. Calculations are carried out by using a Gaussian basis set and the B3LYP hybrid functional as implemented in the periodic ab initio CRYSTAL code. Nanotubes with increasing radius display asymptotic limits to the infinite monolayer. One soft phonon mode is recognized, whose vibration frequency is shown to be connected to the elastic constant C11 of the monolayer as the 1D → 2D transition is approached. The value of Young's elastic modulus of the nanotubes denotes a remarkable flexibility. Electronic and ionic contributions to the polarizability turn out to be comparable in magnitude. In particular, geometry relaxations at increasing radii show large influence on the transverse vibrational polarizability.

Grossular and andradite are garnet end-members stable under upper mantle conditions. We perform ab initio simulations to investigate the dependence of the bulk modulus on chemical composition of the grossular-andradite solid solution, Ca3Fe(2-2x)Al(2x)(SiO4)3. All-electron local basis sets of Gaussian-type orbitals and the hybrid B3LYP density functional are used. Our calculations predict a linear modulus-composition trend, in contrast to previous conjectures based on "heterogeneous" experimental measurements. We estimate the largest deviation from linearity to be about 0.5 GPa under ambient conditions, and to progressively reduce to less than 0.2 GPa at pressure P = 20 GPa. The bulk modulus is computed over the whole composition range 0 ≤x≤ 1 following two independent approaches: fitting energy-volume data to an equation-of-state and calculating elastic tensors. Results from the two methods are in perfect agreement, assuring consistency and high numerical accuracy of the adopted algorithms.

We have determined ten piezooptic tensor components for monoclinic triglycine sulfate crystals, using an interferometric method. Acoustooptic figure of merit has been...