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In the framework of density functional theory (DFT) simulations of molecules and materials, anharmonic terms of the potential energy surface are commonly computed numerically, with an associated cost that rapidly increases with the size of the system. Recently, an efficient approach to calculate cubic and quartic interatomic force constants in the basis of normal modes [Theor. Chem. Acc., 120, 23 (2008)] was implemented in the Crystal program [J. Chem. Theory Comput., 15, 3755-3765 (2019)]. By applying group theory, we are able to further reduce the associated computational cost, as the exploitation of point symmetry can significantly reduce the number of distinct atomically displaced nuclear configurations to be explicitly explored for energy and forces calculations. Our strategy stems from Wigner's theorem and the fact that normal modes are bases of the irreducible representations (irreps) of the point group. The proposed group theoretical approach is implemented in the Crystal program and its efficiency assessed on six test case systems: four molecules (methane, CH4; tetrahedrane, C4H4; cyclo-exasulfur, S6; cubane, C8H8), and two three-dimensional crystals (Magnesium oxide, MgO; and a prototypical Zinc-imidazolate framework, ZIF-8). The speedup imparted by this approach is consistently very large in all high-symmetry molecular and periodic systems, peaking at 76% for MgO.

International audience; The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

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 anharmonicity of O-H stretching vibrations of water ice is characterized by use of a periodic implementation of the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, which take phonon-phonon couplings explicitly into account through numerical evaluation of high-order terms of the nuclear potential. The low-temperature, proton-ordered phase of water ice (namely, ice XI) is investigated. The net effect of a coupled anharmonic treatment of stretching modes is not just a rigid blue-shift of the respective harmonic spectral frequencies but rather a complex change of their relative spectral positions, which cannot be captured by simple scaling strategies based on harmonic calculations. The adopted techniques allow for a hierarchical treatment of anharmonic terms of the nuclear potential, which is key to an effective identification of leading factors. We show that the anharmonic independent-mode approximation─only describing the "intrinsic anharmonicity" of the O-H stretches─is unable to capture the correct physics, and that couplings among O-H stretches must be described. Inspection of harmonic normal coordinates allows identification of specific features of the O-H stretching motions which most likely enable strong mode-mode couplings. Finally, by coupling O-H stretches to all other possible modes of ice XI (THz collective vibrations, molecular librations, bendings), we identify specific types of motion which significantly affect O-H stretching states: in particular, molecular librations are found to affect the stretching states more than molecular bendings.

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...

The anharmonicity of O-H stretching vibrations of water ice is characterized by use of a periodic implementation of the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, which take phonon-phonon couplings explicitly into account through numerical evaluation of high-order terms of the nuclear potential. The low-temperature, proton-ordered phase of water ice (namely, ice-XI) is investigated. The net effect of a coupled anharmonic treatment of stretching modes is not just a rigid blue-shift of the respective harmonic spectral frequencies but rather a complex change of their relative spectral positions, which can not be captured by simple scaling strategies based on harmonic calculations. The adopted techniques allow for a hierarchical treatment of anharmonic terms of the nuclear potential, which is key to an effective identification of leading factors. We show that an anharmonic independent-mode approximation only describing the "intrinsic anharmonicity" of the O-H stretches is unable to capture the correct physics and that couplings among O-H stretches must be described. Inspection of harmonic normal coordinates allows to identify specific features of the O-H stretching motions which most likely enable strong mode-mode couplings. Finally, by coupling O-H stretches to all other possible modes of ice-XI (THz collective vibrations, molecular librations, bendings), we identify specific types of motion which significantly affect O-H stretching states: in particular, molecular librations are found to affect the stretching states more than molecular bendings.

A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations. The approach, based on symbolic computation with computer algebra systems and automated generation of optimized subroutines, takes full advantage of sparsity and is here applied to first energy derivatives with respect to nuclear displacements and lattice parameters of molecules and materials. The implementation in the Crystal code is presented, and the considerably improved computational efficiency over the previous implementation is illustrated. For this purpose, three different tasks involving the use of analytical forces are considered: (i) geometry optimization; (ii) harmonic frequency calculation; and (iii) elastic tensor calculation. Three test case materials are selected as representatives of different classes: (i) a metallic 2D model of the Cu(111) surface; (ii) a wide-gap semiconductor ZnO crystal, with a wurtzite-type structure; and (iii) a porous metal-organic crystal, namely the ZIF-8 zinc-imidazolate framework. Finally, it is argued that the present symbolic approach is particularly amenable to generalizations, and its potential application to other derivatives is sketched.

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.

The OPC UA protocol is an upcoming de-facto standard for building Industry 4.0 processes in Europe, and one of the few industrial protocols that promises security features to prevent attackers from manipulating and damaging critical infrastructures. Despite the importance of the protocol, challenges in the adoption of OPC UA's security features by product vendors, libraries implementing the standard, and end-users were not investigated so far. In this work, we systematically investigate 48 publicly available artifacts consisting of products and libraries for OPC UA and show that 38 out of the 48 artifacts have one (or more) security issues. In particular, we show that 7 OPC UA artifacts do not support the security features of the protocol at all. In addition, 31 artifacts that partially feature OPC UA security rely on incomplete libraries and come with misleading instructions. Consequently, relying on those products and libraries will result in vulnerable implementations of OPC UA security features. To verify our analysis, we design, implement, and demonstrate attacks in which the attacker can steal credentials exchanged between victims, eavesdrop on process information, manipulate the physical process through sensor values and actuator commands, and prevent the detection of anomalies.

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.

In recent years, several schemes have been proposed to detect anomalies and attacks on Cyber-Physical Systems (CPSs) such as Industrial Control Systems (ICSs). Based on the analysis of sensor data, unexpected or malicious behavior is detected. Those schemes often rely on (implicit) assumptions on temporally stable sensor data distributions and invariants between process values. Unfortunately, the proposed schemes often perform not optimally with Recall scores lower than 70% (e.g., missing 3 alarms every 10 anomalies) for some ICS datasets, with unclear root issues.In this work, we propose a general framework to check whether a given ICS dataset has specific properties (stable sensor distributions in normal operations, potentially state-dependent), which then allows to determine whether certain Anomaly Detection approaches can be expected to perform well. We apply our framework to three datasets showing that the behavior of actuators and sensors are very different between Training set and Test set. In addition, we present high-level guides to consider when designing an Anomaly Detection System.

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.

Recently, reconstruction-based anomaly detection was proposed as an effective technique to detect attacks in dynamic industrial control networks. Unlike classical network anomaly detectors that observe the network traffic, reconstruction-based detectors operate on the measured sensor data, leveraging physical process models learned a priori. In this work, we investigate different approaches to evade prior-work reconstruction-based anomaly detectors by manipulating sensor data so that the attack is concealed. We find that replay attacks (commonly assumed to be very strong) show bad performance (i.e., increasing the number of alarms) if the attacker is constrained to manipulate less than 95% of all features in the system, as hidden correlations between the features are not replicated well. To address this, we propose two novel attacks that manipulate a subset of the sensor readings, leveraging learned physical constraints of the system. Our attacks feature two different attacker models: A white box attacker, which uses an optimization approach with a detection oracle, and a black box attacker, which uses an autoencoder to translate anomalous data into normal data. We evaluate our implementation on two different datasets from the water distribution domain, showing that the detector's Recall drops from 0.68 to 0.12 by manipulating 4 sensors out of 82 in WADI dataset. In addition, we show that our black box attacks are transferable to different detectors: They work against autoencoder-, LSTM-, and CNN-based detectors. Finally, we implement and demonstrate our attacks on a real industrial testbed to demonstrate their feasibility in real-time., Proceedings of the Annual Computer Security Applications Conference (ACSAC) 2020

Cubic cuprous oxide, Cu

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.

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.

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.