VAMPyR-A high-level Python library for mathematical operations in a multiwavelet representation.

Wavelets and multiwavelets have lately been adopted in quantum chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few), they provide a framework that narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for multiwavelet calculations (algebra and integral and differential operator application) and exposes the required functionality to write a simple Python code to solve, among others, the Hartree-Fock equations, the generalized Poisson equation, the Dirac equation, and the time-dependent Schrödinger equation up to any predefined precision. In this study, we will outline the main features of multiresolution analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms.

Ultrafast Polarization Switching in BaTiO3 Nanomaterials: Combined Density Functional Theory and Coupled Oscillator Study.

The challenge of achieving ultrafast switching of electric polarization in ferroelectric materials remains unsolved as there is no experimental evidence of such switching to date. In this study, we developed an enhanced model that describes switching within a two-dimensional space of generalized coordinates at THz pulses. Our findings indicate that stable switching in barium titanate cannot be achieved through a single linearly polarized pulse. When the intensity of the linearly polarized pulse reaches a certain threshold, the sample experiences depolarization but not stable switching. Our study also reveals that phonon friction plays a minor role in the switching dynamics and provides an estimate of the optimal parameters for the perturbing pulse with the lowest intensity that results in the depolarization of an initially polarized sample.

Full Breit Hamiltonian in the Multiwavelets Framework.

New techniques in core-electron spectroscopy are necessary to resolve the structures of oxides of f-elements and other strongly correlated materials that are present only as powders and not as single crystals. Thus, accurate quantum chemical methods must be developed to calculate core spectroscopic properties in such materials. In this contribution, we present an important development in this direction, extending our fully adaptive real-space multiwavelet basis framework to tackle the four-component Dirac-Coulomb-Breit Hamiltonian. We show that multiwavelets can reproduce one-dimensional grid-based approaches. They are however a fully three-dimensional approach which can later be extended to molecules and materials. Our multiwavelet implementation attained precise results irrespective of the chosen nuclear model, provided that the error threshold is tight enough and that the chosen polynomial basis is sufficiently large. Furthermore, our results confirmed that in two-electron species, the magnetic and Gauge contributions from s-orbitals are identical in magnitude and can account for the experimental evidence from K and L edges.

Scalar Relativistic Effects with Multiwavelets: Implementation and Benchmark.

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effects are strongest in the nuclear region, where the description of electrons through a linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared with lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcoming this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows one to achieve a proper description of the nuclear region. In this work, we extended the multiwavelet-based code MRChem to the scalar zero-order regular approximation framework. We validated our implementation by comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave-based code EXCITING.

Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of Fe-Al.

We propose a machine-learning interatomic potential for multi-component magnetic materials. In this potential we consider magnetic moments as degrees of freedom (features) along with atomic positions, atomic types, and lattice vectors. We create a training set with constrained DFT (cDFT) that allows us to calculate energies of configurations with non-equilibrium (excited) magnetic moments and, thus, it is possible to construct the training set in a wide configuration space with great variety of non-equilibrium atomic positions, magnetic moments, and lattice vectors. Such a training set makes possible to fit reliable potentials that will allow us to predict properties of configurations in the excited states (including the ones with non-equilibrium magnetic moments). We verify the trained potentials on the system of bcc Fe-Al with different concentrations of Al and Fe and different ways Al and Fe atoms occupy the supercell sites. Here, we show that the formation energies, the equilibrium lattice parameters, and the total magnetic moments of the unit cell for different Fe-Al structures calculated with machine-learning potentials are in good correspondence with the ones obtained with DFT. We also demonstrate that the theoretical calculations conducted in this study qualitatively reproduce the experimentally-observed anomalous volume-composition dependence in the Fe-Al system.

Electronic Properties of Zn2V(1-x)NbxN3 Alloys to Model Novel Materials for Light-Emitting Diodes.

We propose the Zn2V(1-x)NbxN3 alloy as a new promising material for optoelectronic applications, in particular for light-emitting diodes (LEDs). We perform accurate electronic-structure calculations of the alloy for several concentrations x using density-functional theory with meta-GGA exchange-correlation functional TB09. The band gap is found to vary between 2.2 and 2.9 eV with varying V/Nb concentration. This range is suitable for developing bright LEDs with tunable band gap as potential replacements for the more expensive Ga(1-x)In(x)N systems. Effects of configurational disorder are taken into account by explicitly considering all possible distributions of the metal ions within the metal sublattice for the chosen supercells. We have evaluated the band gap's nonlinear behavior (bowing) with variation of V/Nb concentration for two possible scenarios: (i) only the structure with the lowest total energy is present at each concentration and (ii) the structure with minimum band gap is present at each concentration, which corresponds to experimental conditions when also metastable structures are presents. We found that the bowing is about twice larger in the latter case. However, in both cases, the bowing parameter is found to be lower than 1 eV, which is about twice smaller than that in the widely used Ga(1-x)In(x)N alloy. Furthermore, we found that both crystal volume changes due to alloying and local effects (atomic relaxation and the V-N/Nb-N bonding difference) have important contributions to the band gap bowing in Zn2V(1-x)NbxN3.

Electronic Properties of Functionalized Diamanes for Field-Emission Displays.

Ultrathin diamond films, or diamanes, are promising quasi-2D materials that are characterized by high stiffness, extreme wear resistance, high thermal conductivity, and chemical stability. Surface functionalization of multilayer graphene with different stackings of layers could be an interesting opportunity to induce proper electronic properties into diamanes. Combination of these electronic properties together with extraordinary mechanical ones will lead to their applications as field-emission displays substituting original devices with light-emitting diodes or organic light-emitting diodes. In the present study, we focus on the electronic properties of fluorinated and hydrogenated diamanes with (111), (110), (0001), (101̅0), and (2̅110) crystallographic orientations of surfaces of various thicknesses by using first-principles calculations and Bader analysis of electron density. We see that fluorine induces an occupied surface electronic state, while hydrogen modifies the occupied bulk state and also induces unoccupied surface states. Furthermore, a lower number of layers is necessary for hydrogenated diamanes to achieve the convergence of the work function in comparison with fluorinated diamanes, with the exception of fluorinated (110) and (2̅110) films that achieve rapid convergence and have the same behavior as other hydrogenated surfaces. This induces a modification of the work function with an increase of the number of layers that makes hydrogenated (2̅110) diamanes the most suitable surface for field-emission displays, better than the fluorinated counterparts. In addition, a quasi-quantitative descriptor of surface dipole moment based on the Tantardini-Oganov electronegativity scale is introduced as the average of bond dipole moments between the surface atoms. This new fundamental descriptor is capable of predicting a priori the bond dipole moment and may be considered as a new useful feature for crystal structure prediction based on artificial intelligence.

Translucency and Color Stability of a Simplified Shade Nanohybrid Composite after Ultrasonic Scaling and Air-Powder Polishing.

We aimed to assess the influence of professional dental prophylaxis on the translucency and color stability of a novel simplified shade nanohybrid composite material. Sixty composite disks (5 mm in diameter and 2 mm thick) of light (n = 30) and dark (n = 30) shades were prepared. The specimens were randomly divided into the following three groups (n = 10) according to the prophylaxis procedure used: ultrasonic scaling, air-powder polishing with sodium bicarbonate, and controls. The specimens were submitted to translucency and color analysis based on the CIELab system. Two measurements were performed before and after 48-h storage in coffee. Translucency values of untreated light and dark specimens were 9.15 ± 0.38 and 5.28 ± 1.10, respectively. Air-powder polishing decreased the translucency of the light composite specimens. Storage in coffee resulted in color changes (∆E) ranging between 2.69 and 12.05 and a mean translucency decrease ranging between -0.88 and -6.91. The samples in the light group tended to exhibit greater staining; the treatment method had no effect on ∆E. It can be concluded that light-shade composite restorations are more prone to translucency and color changes resulting from air-powder polishing and contact with staining media. However, further research using other composites and powders is required.

Constrained Density Functional Theory: A Potential-Based Self-Consistency Approach.

Chemical reactions, charge transfer reactions, and magnetic materials are notoriously difficult to describe within Kohn-Sham density functional theory, which is strictly a ground-state technique. However, over the last few decades, an approximate method known as constrained density functional theory (cDFT) has been developed to model low-lying excitations linked to charge transfer or spin fluctuations. Nevertheless, despite becoming very popular due to its versatility, low computational cost, and availability in numerous software applications, none of the previous cDFT implementations is strictly similar to the corresponding ground-state self-consistent density functional theory: the target value of constraints (e.g., local magnetization) is not treated equivalently with atomic positions or lattice parameters. In the present work, by considering a potential-based formulation of the self-consistency problem, the cDFT is recast in the same framework as Kohn-Sham DFT: a new functional of the potential that includes the constraints is proposed, where the constraints, the atomic positions, or the lattice parameters are treated all alike, while all other ingredients of the usual potential-based DFT algorithms are unchanged, thanks to the formulation of the adequate residual. Tests of this approach for the case of spin constraints (collinear and noncollinear) and charge constraints are performed. Expressions for the derivatives with respect to constraints (e.g., the spin torque) for the atomic forces and the stress tensor in cDFT are provided. The latter allows one to study striction effects as a function of the angle between spins. We apply this formalism to body-centered cubic iron and first reproduce the well-known magnetization amplitude as a function of the angle between local magnetizations. We also study stress as a function of such an angle. Then, the local collinear magnetization and the local atomic charge are varied together. Since the atomic spin magnetizations, local atomic charges, atomic positions, and lattice parameters are treated on an equal footing, this formalism is an ideal starting point for the generation of model Hamiltonians and machine-learning potentials, computation of second or third derivatives of the energy as delivered from density-functional perturbation theory, or for second-principles approaches.

GIPAW Pseudopotentials of d Elements for Solid-State NMR.

Computational methods are increasingly used to support interpreting, assigning and predicting the solid-state nuclear resonance magnetic spectra of materials. Currently, density functional theory is seen to achieve a good balance between efficiency and accuracy in solid-state chemistry. To be specific, density functional theory allows the assignment of signals in nuclear resonance magnetic spectra to specific sites and can help identify overlapped or missing signals from experimental nuclear resonance magnetic spectra. To avoid the difficulties correlated to all-electron calculations, a gauge including the projected augmented wave method was introduced to calculate nuclear resonance magnetic parameters with great success in organic crystals in the last decades. Thus, we developed a gauge including projected augmented pseudopotentials of 21 d elements and tested them on, respectively, oxides or nitrides (semiconductors), calculating chemical shift and quadrupolar coupling constant. This work can be considered the first step to improving the ab initio prediction of nuclear magnetic resonance parameters, and leaves open the possibility for inorganic compounds to constitute an alternative standard compound, with respect to tetramethylsilane, to calculate the chemical shift. Furthermore, this work represents the possibility to obtain results from first-principles calculations, to train a machine-learning model to solve or refine structures using predicted nuclear magnetic resonance spectra.

Sr-Doped Superionic Hydrogen Glass: Synthesis and Properties of SrH22.

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Despite notable progress, detecting superconductivity in compressed hydrogen remains an unsolved problem. Following the mainstream of extensive investigations of compressed metal polyhydrides, here small doping of molecular hydrogen by strontium is demonstrated to lead to a dramatic reduction in the metallization pressure to ≈200 GPa. Studying the high-pressure chemistry of the Sr-H system, the formation of several new phases is observed: C2/m-Sr3 H13 , pseudocubic SrH6 , SrH9 with cubic F 4 ¯ 3 m $F\bar{4}3m$ -Sr sublattice, and pseudo tetragonal superionic P1-SrH22 , the metal hydride with the highest hydrogen content (96 at%) discovered so far. High diffusion coefficients of hydrogen in the latter phase DH  = 0.2-2.1 × 10-9 m2 s-1 indicate an amorphous state of the H-sublattice, whereas the strontium sublattice remains solid. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-TC superconductors with an atomic H sublattice. The discovered SrH22 , a kind of hydrogen sponge, opens a new class of materials with ultrahigh content of hydrogen.

Thermochemical electronegativities of the elements.

Electronegativity is a key property of the elements. Being useful in rationalizing stability, structure and properties of molecules and solids, it has shaped much of the thinking in the fields of structural chemistry and solid state chemistry and physics. There are many definitions of electronegativity, which can be roughly classified as either spectroscopic (these are defined for isolated atoms) or thermochemical (characterizing bond energies and heats of formation of compounds). The most widely used is the thermochemical Pauling's scale, where electronegativities have units of eV-1/2. Here we identify drawbacks in the definition of Pauling's electronegativity scale-and, correcting them, arrive at our thermochemical scale, where electronegativities are dimensionless numbers. Our scale displays intuitively correct trends for the 118 elements and leads to an improved description of chemical bonding (e.g., bond polarity) and thermochemistry.

Computational Modeling of 2D Materials under High Pressure and Their Chemical Bonding: Silicene as Possible Field-Effect Transistor.

To study the possibility for silicene to be employed as a field-effect transistor (FET) pressure sensor, we explore the chemistry of monolayer and multilayered silicene focusing on the change in hybridization under pressure. Ab initio computations show that the effect of pressure depends greatly on the thickness of the silicene film, but also reveals the influence of real experimental conditions, where the pressure is not hydrostatic. For this purpose, we introduce anisotropic strain states. With pure uniaxial stress applied to silicene layers, a path for sp3 silicon to sp3d silicon is found, unlike with pure hydrostatic pressure. Even with mixed-mode stress (in-plane pressure half of the out-of-plane one), we find no such path. In addition to introducing our theoretical approach to study 2D materials, we show how the hybridization change of silicene under pressure makes it a good FET pressure sensor.

The Volumetric Source Function: Looking Inside van der Waals Interactions.

The study of van der Waals interactions plays a central role in the understanding of bonding across a range of biological, chemical and physical phenomena. The presence of van der Waals interactions can be identified through analysis of the reduced density gradient, a fundamental parameter at the core of Density Functional Theory. An extension of Bader's Quantum Theory of Atoms in Molecules is developed here through combination with the analysis of the reduced density gradient. Through this development, a new quantum chemical topological tool is presented: the volumetric source function. This technique allows insight into the atomic composition of van der Waals interactions, offering the first route towards applying the highly successful source function to these disperse interactions. A new algorithm has been implemented in the open-source code, CRITIC2, and tested on acetone, adipic and maleic acids molecular crystals, each stabilized by van der Waals interactions. This novel technique for studying van der Waals interactions at an atomic level offers unprecedented opportunities in the fundamental study of intermolecular interactions and molecular design for crystal engineering, drug design and bio-macromolecular processes.

Exotic Two-Dimensional Structure: The First Case of Hexagonal NaCl.

NaCl is one of the simplest compounds and was thought to be well-understood, and yet, unexpected complexities related to it were uncovered at high pressure and in low-dimensional states. Here, exotic hexagonal NaCl thin films on the (110) diamond surface were crystallized in the experiment following a theoretical prediction based on ab initio evolutionary algorithm USPEX. State-of-the-art calculations and experiments showed the existence of a hexagonal NaCl thin film, which is due to the strong chemical interaction of the NaCl film with the diamond substrate.

When does a hydrogen bond become a van der Waals interaction? a topological answer.

The hydrogen bond (H-bond) is among the most important noncovalent interaction (NCI) for bioorganic compounds. However, no "energy border" has yet been identified to distinguish it from van der Waals (vdW) interaction. Thus, classifying NCIs and interpreting their physical and chemical importance remain open to great subjectivity. In this work, the "energy border" between vdW and H-bonding interactions was identified using a dimer of water, as well as for a series of classical and nonclassical H-bonding systems. Through means of the quantum theory of atoms in molecules and in particular the source function, it was possible to clearly identify the transition from H-bonding to vdW bonding via analysis of the electronic structure. This "energy border" was identified both on elongating the interatomic interaction and by varying the contact angle. Hence, this study also redefines the "critic angle" previously proposed by Galvão et al. (J. Phys. Chem. A 2013, 117, 12668). Consequently, such "energy border" through an analysis of atomic basins volume variation was possible to identify the end of long-range interactions. © 2019 Wiley Periodicals, Inc.

Crystal structure resolution of an insulator due to the cooperative Jahn-Teller effect through Bader's theory: the challenging case of cobaltite oxide Y114.

Cobaltite YBaCo4O7, abbreviated as Y114, is one of the most thoroughly investigated perovskites, owing largely to its interesting magnetic properties. Y114 is an insulator as a result of the cooperative Jahn-Teller effect, where one electron jumps quickly from one cobalt site to another, making it impossible to experimentally assign the correct oxidation state for each of the two cobalt sites. The present study solved the ambiguity by means of state-of-the-art DFT calculations. The two cobalt sites were differentiated through an analysis of charge density within the framework of the quantum theory of atoms in molecules.

Topology vs. thermodynamics in chemical reactions: the instability of PH5.

The topological approach, based on Bader theory, is compared to the common thermodynamical methodology to study chemical reactivity. It is shown how the former indeed has numerous advantages and provides a more detailed description with respect to the latter about the course of the reaction. The comparison between the two approaches is performed by considering a classical reaction, i.e. the decomposition of PX5 (X = H, F). The topological investigation was supported by using different state-of-the-art topological tools, such as the source function, Espinosa indexes, delocalisation indexes, and domain-averaged Fermi hole analysis. Furthermore, in this work a new topological descriptor, the Bader energy density, PBADER, is introduced and applied to the study case. For the first time since Bader theory was introduced, the distribution of atomic energies in the atomic basins was analysed in detail and used to explain the chemical reactivity a priori.