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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.

The effect of nanosize and structural disorder on the MgCl2 support of Ziegler–Natta catalysts has been investigated in terms of induced changes to their vibrational spectroscopic fingerprint. In p...

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.

Quasi-harmonic lattice-dynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal-organic framework material: MOF-5. The softening upon compression of an A2g phonon mode at the gamma point in the high-symmetry Fm3m structure is identified, which leads to a symmetry reduction and a group subgroup phase transition to a low-symmetry Fm3 phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equation-of-state of MOF-5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of K0 (pressure derivative of K) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analysed. The evolution of the mechanical anisotropy of MOF-5 as a function of pressure is also determined, which allows us to identify the occurrence of a shear-induced mechanical instability at 0.45 GPa.

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.

Quasi-harmonic lattice-dynamical calculations are performed to investigate the combined effect of temperature and pressure on the structural and mechanical properties of a prototypical metal-organic framework material: MOF-5. The softening upon compression of an A2g phonon mode at the gamma point in the high-symmetry Fm3m structure is identified, which leads to a symmetry reduction and a group subgroup phase transition to a low-symmetry Fm3 phase for compressions larger than 0.8%. The effect of the symmetry reduction on the equation-of-state of MOF-5 is investigated, which provides a static bulk modulus K reducing from 17 to 14 GPa and a corresponding change of K0 (pressure derivative of K) from positive to negative. The effect of pressure on the negative thermal expansion of the framework and on its mechanical response is analysed. The evolution of the mechanical anisotropy of MOF-5 as a function of pressure is also determined, which allows us to identify the occurrence of a shear-induced mechanical instability at 0.45 GPa.

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.

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).

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.

We use ab initio density functional theory (DFT) to elucidate the mechanical properties of two topologically distinct zeolitic imidazolate framework (ZIF) materials: ZIF-4 and ZIF-zni, both of which have the same chemical composition of Zn(Im)2 [Im = C3H3N2-] and are constructed from an identical Zn - Im - Zn basic building block. The CRYSTAL code was used to compute the single-crystal elastic constants Cij of the (orthorhombic) ZIF-4 and (tetragonal) ZIF-zni structures at the PBE level of theory. Through tensorial analysis of the Cij, we reveal the three-dimensional representation surfaces of the Young's modulus, shear modulus, Poisson's ratio and linear compressibility, which enable us to describe the detailed elasticity behaviour and to pinpoint basic crystal structure-property correlations. Notably, we discover that ZIF-4 can potentially exhibit a negative Poisson's ratio, thereby representing the first example of an 'auxetic-ZIF' to be identified to date. Furthermore, we show that our DFT predictions are consistent with recently reported experimental measurements of the Young's and bulk moduli of such complex ZIF structures We use ab initio density functional theory (DFT) to elucidate the mechanical properties of two topologically distinct zeolitic imidazolate framework (ZIF) materials: ZIF-4 and ZIF-zni, both of which have the same chemical composition of Zn(Im)2 [Im = C3H3N2-] and are constructed from an identical Zn - Im - Zn basic building block. The CRYSTAL code was used to compute the single-crystal elastic constants Cij of the (orthorhombic) ZIF-4 and (tetragonal) ZIF-zni structures at the PBE level of theory. Through tensorial analysis of the Cij, we reveal the three-dimensional representation surfaces of the Young's modulus, shear modulus, Poisson's ratio and linear compressibility, which enable us to describe the detailed elasticity behaviour and to pinpoint basic crystal structure-property correlations. Notably, we discover that ZIF-4 can potentially exhibit a negative Poisson's ratio, thereby representing the first example of an 'auxetic-ZIF' to be identified to date. Furthermore, we show that our DFT predictions are consistent with recently reported experimental measurements of the Young's and bulk moduli of such complex ZIF structures.

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.

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.

The combination of new experimental and theoretical techniques provides evidence of instantaneous electron correlation effects in directional Compton profiles of crystalline silicon, which cannot be reproduced when reference is made to a density matrix obtained from a single-determinantal wavefunction. These effects are instead accounted for by a recently implemented post-Hartree-Fock periodic scheme, which gives results in quite good agreement with the high-quality experimental data.

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

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.

We report accurate ab initio theoretical predictions of the elastic, seismic, and structural anisotropy of the orthorhombic Mg2SiO4 forsterite crystal at high pressures (up to 20 GPa) and temperatures (up to its melting point, 2163 K), which constitute earth's upper mantle conditions. Single-crystal elastic stiffness constants are evaluated up to 20 GPa and their first- and second-order pressure derivatives reported. Christoffel's equation is solved at several pressures: directional seismic wave velocities and related properties (azimuthal and polarization seismic anisotropies) discussed. Thermal structural and average elastic properties, as computed within the quasi-harmonic approximation of the lattice potential, are predicted at high pressures and temperatures: directional thermal expansion coefficients, first- and second-order pressure derivatives of the isothermal bulk modulus, and P-V-T equation-of-state. The effect on computed properties of five different functionals, belonging to three different classes of approximations, of the density functional theory is explicitly investigated.

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.

cited By 20; International audience; A complete theoretical characterization of dielectric, elastic, photoelastic, and piezoelectric tensors of the low-temperature rhombohedral phase of BaTiO3 was performed by accurate ab initio simulations within periodic boundary conditions, using one-electron Hamiltonians and atom-centered Gaussian-type-function basis sets as in the crystal program. Because this phase is stable only at very low temperature, experimental characterization is difficult, and none of such tensorial properties have been measured. For this reason, we validated our method by comparing structural, electronic, and vibrational properties of the other three phases of BaTiO3 (cubic, tetragonal, and orthorhombic) with available experimental data. The effect of the adopted one-electron Hamiltonian on the considered tensorial properties, beyond the simple local density approximation and the dependence on the electric field frequency of dielectric and photoelastic constants, is explicitly investigated. © 2014 American Physical Society.

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.

A computational strategy is devised for the accurate ab initio simulation of elastic properties of crystalline materials under pressure. The proposed scheme, based on the evaluation of the analytical stress tensor and on the automated computation of pressure-dependent elastic stiffness constants, is implemented in the CRYSTAL solid state quantum-chemical program. Elastic constants and related properties (bulk, shear and Young moduli, directional seismic wave velocities, elastic anisotropy index, Poisson's ratio, etc.) can be computed for crystals of any space group of symmetry. We apply such a technique to the study of high-pressure elastic properties of three silicate garnet end-members (namely, pyrope, grossular, and andradite) which are of great geophysical interest, being among the most important rock-forming minerals. The reliability of this theoretical approach is proved by comparing with available experimental measurements. The description of high-pressure properties provided by several equations of state is also critically discussed.

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${}_{3}$.

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.

We have investigated the transition from molecular to fully covalent phases of solid nitrogen with an advanced ab initio quantum-mechanical method for crystals that rigorously describes weak dispersive interactions. It is demonstrated that the thermodynamic domain of stability of the cubic gauche phase (a promising high-energy- density material) extends down to pressures of about 60 GPa and that the high experimental transition pressure of 110 GPa is largely due to kinetic barriers which prevent the dissociation of triply bonded ${\mathrm{N}}_{2}$ molecules. The role of temperature is complex: it helps the kinetics of the transition to fully covalent phases while it stabilizes the molecular phases through the entropic term.

This chapter deals with the charge, spin and momentum densities of electrons in crystalline solids as obtained from ab-initio simulations. It describes state-of-the-art approaches using plane waves or local basis functions, and comments on their main advantages and drawbacks. The influence of computational parameters on densities is demonstrated by way of examples. Ongoing developments are briefly discussed: thermal effects, response to external perturbations, post-Hartree Fock treatment of electron correlation.

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