A Quantum-Chemical Bonding Database for Solid-State Materials.

An in-depth insight into the chemistry and nature of the individual chemical bonds is essential for understanding materials. Bonding analysis is thus expected to provide important features for large-scale data analysis and machine learning of material properties. Such chemical bonding information can be computed using the LOBSTER software package, which post-processes modern density functional theory data by projecting the plane wave-based wave functions onto an atomic orbital basis. With the help of a fully automatic workflow, the VASP and LOBSTER software packages are used to generate the data. We then perform bonding analyses on 1520 compounds (insulators and semiconductors) and provide the results as a database. The projected densities of states and bonding indicators are benchmarked on standard density-functional theory computations and available heuristics, respectively. Lastly, we illustrate the predictive power of bonding descriptors by constructing a machine learning model for phononic properties, which shows an increase in prediction accuracies by 27% (mean absolute errors) compared to a benchmark model differing only by not relying on any quantum-chemical bonding features.

Automated Bonding Analysis with Crystal Orbital Hamilton Populations.

Invited for this month's cover are researchers from Bundesanstalt für Materialforschung und -prüfung (Federal Institute for Materials Research and Testing) in Germany, Friedrich Schiller University Jena, Université catholique de Louvain, University of Oregon, Science & Technology Facilities Council, RWTH Aachen University, Hoffmann Institute of Advanced Materials, and Dartmouth College. The cover picture shows a workflow for automatic bonding analysis with Python tools (green python). The bonding analysis itself is performed with the program LOBSTER (red lobster). The starting point is a crystal structure, and the results are automatic assessments of the bonding situation based on Crystal Orbital Hamilton Populations (COHP), including automatic plots and text outputs. Coordination environments and charges are also assessed. More information can be found in the Research Article by J. George, G. Hautier, and co-workers.

Automated Bonding Analysis with Crystal Orbital Hamilton Populations.

Understanding crystalline structures based on their chemical bonding is growing in importance. In this context, chemical bonding can be studied with the Crystal Orbital Hamilton Population (COHP), allowing for quantifying interatomic bond strength. Here we present a new set of tools to automate the calculation of COHP and analyze the results. We use the program packages VASP and LOBSTER, and the Python packages atomate and pymatgen. The analysis produced by our tools includes plots, a textual description, and key data in a machine-readable format. To illustrate those capabilities, we have selected simple test compounds (NaCl, GaN), the oxynitrides BaTaO2 N, CaTaO2 N, and SrTaO2 N, and the thermoelectric material Yb14 Mn1 Sb11 . We show correlations between bond strengths and stabilities in the oxynitrides and the influence of the Mn-Sb bonds on the magnetism in Yb14 Mn1 Sb11 . Our contribution enables high-throughput bonding analysis and will facilitate the use of bonding information for machine learning studies.

Ferroelectricity and multiferroicity in anti-Ruddlesden-Popper structures.

Combining ferroelectricity with other properties such as visible light absorption or long-range magnetic order requires the discovery of new families of ferroelectric materials. Here, through the analysis of a high-throughput database of phonon band structures, we identify a structural family of anti-Ruddlesden-Popper phases [Formula: see text]O (A=Ca, Sr, Ba, Eu, X=Sb, P, As, Bi) showing ferroelectric and antiferroelectric behaviors. The discovered ferroelectrics belong to the new class of hyperferroelectrics that polarize even under open-circuit boundary conditions. The polar distortion involves the movement of O anions against apical A cations and is driven by geometric effects resulting from internal chemical strains. Within this structural family, we show that [Formula: see text]O combines coupled ferromagnetic and ferroelectric order at the same atomic site, a very rare occurrence in materials physics.

ChemEnv: a fast and robust coordination environment identification tool.

Coordination or local environments have been used to describe, analyze and understand crystal structures for more than a century. Here, a new tool called ChemEnv, which can identify coordination environments in a fast and robust manner, is presented. In contrast to previous tools, the assessment of the coordination environments is not biased by small distortions of the crystal structure. Its robust and fast implementation enables the analysis of large databases of structures. The code is available open source within the pymatgen package and the software can also be used through a web app available on http://crystaltoolkit.org through the Materials Project.

Combining phonon accuracy with high transferability in Gaussian approximation potential models.

Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that accurately predict vibrational properties in specific regions of configuration space while retaining flexibility and transferability to others. We use an adaptive regularization of the GAP fit that scales with the absolute force magnitude on any given atom, thereby exploring the Bayesian interpretation of GAP regularization as an "expected error" and its impact on the prediction of physical properties for a material of interest. The approach enables excellent predictions of phonon modes (to within 0.1 THz-0.2 THz) for structurally diverse silicon allotropes, and it can be coupled with existing fitting databases for high transferability across different regions of configuration space, which we demonstrate for liquid and amorphous silicon. These findings and workflows are expected to be useful for GAP-driven materials modeling more generally.

LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory.

We present an update on recently developed methodology and functionality in the computer program Local Orbital Basis Suite Toward Electronic-Structure Reconstruction (LOBSTER) for chemical-bonding analysis in periodic systems. LOBSTER is based on an analytic projection from projector-augmented wave (PAW) density-functional theory (DFT) computations (Maintz et al., J. Comput. Chem. 2013, 34, 2557), reconstructing chemical information in terms of local, auxiliary atomic orbitals and thereby opening the output of PAW-based DFT codes to chemical interpretation. We demonstrate how LOBSTER has been improved by taking into account time-reversal symmetry, thereby speeding up the DFT and LOBSTER calculations by a factor of 2. Over the recent years, the functionalities have also been continually expanded, including accurate projected densities of states (DOSs), crystal orbital Hamilton population (COHP) analysis, atomic and orbital charges, gross populations, and the recently introduced k-dependent COHP. The software is offered free-of-charge for non-commercial research.

The Limited Predictive Power of the Pauling Rules.

The Pauling rules have been used for decades to rationalise the crystal structures of ionic compounds. Despite their importance, there has been no statistical assessment of the performances of these five empirical rules so far. Here, we rigorously and automatically test all five Pauling rules for a large data set of around 5000 known oxides. We discuss each Pauling rule separately, stressing their limits and range of application in terms of chemistries and structures. We conclude that only 13 % of the oxides simultaneously satisfy the last four rules, indicating a much lower predictive power than expected.

The many flavours of halogen bonds - message from experimental electron density and Raman spectroscopy.

Experimental electron-density studies based on high-resolution diffraction experiments allow halogen bonds between heavy halogens to be classified. The topological properties of the electron density in Cl...Cl contacts vary smoothly as a function of the interaction distance. The situation is less straightforward for halogen bonds between iodine and small electronegative nucleophiles, such as nitrogen or oxygen, where the electron density in the bond critical point does not simply increase for shorter distances. The number of successful charge-density studies involving iodine is small, but at least individual examples for three cases have been observed. (a) Very short halogen bonds between electron-rich nucleophiles and heavy halogen atoms resemble three-centre-four-electron bonds, with a rather symmetric heavy halogen and without an appreciable σ hole. (b) For a narrow intermediate range of halogen bonds, the asymmetric electronic situation for the heavy halogen with a pronounced σ hole leads to rather low electron density in the (3,-1) critical point of the halogen bond; the properties of this bond critical point cannot fully describe the nature of the associated interaction. (c) For longer and presumably weaker contacts, the electron density in the halogen bond critical point is only to a minor extent reduced by the presence of the σ hole and hence may be higher than in the aforementioned case. In addition to the electron density and its derived properties, the halogen-carbon bond distance opposite to the σ hole and the Raman frequency for the associated vibration emerge as alternative criteria to gauge the halogen-bond strength. We find exceptionally long C-I distances for tetrafluorodiiodobenzene molecules in cocrystals with short halogen bonds and a significant red shift for their Raman vibrations.

Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene.

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.

Plane-Wave Density Functional Theory Meets Molecular Crystals: Thermal Ellipsoids and Intermolecular Interactions.

Molecular compounds, organic and inorganic, crystallize in diverse and complex structures. They continue to inspire synthetic efforts and "crystal engineering", with implications ranging from fundamental questions to pharmaceutical research. The structural complexity of molecular solids is linked with diverse intermolecular interactions: hydrogen bonding with all its facets, halogen bonding, and other secondary bonding mechanisms of recent interest (and debate). Today, high-resolution diffraction experiments allow unprecedented insight into the structures of molecular crystals. Despite their usefulness, however, these experiments also face problems: hydrogen atoms are challenging to locate, and thermal effects may complicate matters. Moreover, even if the structure of a crystal is precisely known, this does not yet reveal the nature and strength of the intermolecular forces that hold it together. In this Account, we show that periodic plane-wave-based density functional theory (DFT) can be a useful, and sometimes unexpected, complement to molecular crystallography. Initially developed in the solid-state physics communities to treat inorganic solids, periodic DFT can be applied to molecular crystals just as well: theoretical structural optimizations "help out" by accurately localizing the elusive hydrogen atoms, reaching neutron-diffraction quality with much less expensive measurement equipment. In addition, phonon computations, again developed by physicists, can quantify the thermal motion of atoms and thus predict anisotropic displacement parameters and ORTEP ellipsoids "from scratch". But the synergy between experiment and theory goes much further than that. Once a structure has been accurately determined, computations give new and detailed insights into the aforementioned intermolecular interactions. For example, it has been debated whether short hydrogen bonds in solids have covalent character, and we have added a new twist to this discussion using an orbital-based theory that once more had been developed for inorganic solids. However, there is more to a crystal structure than a handful of short contacts between neighboring residues. We hence have used dimensionally resolved analyses to dissect crystalline networks in a systematic fashion, one spatial direction at a time. Initially applied to hydrogen bonding, these techniques can be seamlessly extended to halogen, chalcogen, and pnictogen bonding, quantifying bond strength and cooperativity in truly infinite networks. Finally, these methods promise to be useful for (bio)polymers, as we have recently exemplified for α-chitin. At the interface of increasingly accurate and popular DFT methods, ever-improving crystallographic expertise, and new challenging, chemical questions, we believe that combined experimental and theoretical studies of molecular crystals are just beginning to pick up speed.

Tetrel Bonds in Infinite Molecular Chains by Electronic Structure Theory and Their Role for Crystal Stabilization.

Intermolecular bonds play a crucial role in the rational design of crystal structures, dubbed crystal engineering. The relatively new term tetrel bonds (TBs) describes a long-known type of such interactions presently in the focus of quantum chemical cluster calculations. Here, we energetically explore the strengths and cooperativity of these interactions in infinite chains, a possible arrangement of such tetrel bonds in extended crystals, by periodic density functional theory. In the chains, the TBs are amplified due to cooperativity by up to 60%. Moreover, we computationally take apart crystals stabilized by infinite tetrel-bonded chains and assess the importance of the TBs for the crystal stabilization. Tetrel bonds can amount to 70% of the overall interaction energy within some crystals, and they can also be energetically decisive for the taken crystal structure; their individual strengths also compete with the collective packing within the crystal structures.

Lattice thermal expansion and anisotropic displacements in 𝜶-sulfur from diffraction experiments and first-principles theory.

Thermal properties of solid-state materials are a fundamental topic of study with important practical implications. For example, anisotropic displacement parameters (ADPs) are routinely used in physics, chemistry, and crystallography to quantify the thermal motion of atoms in crystals. ADPs are commonly derived from diffraction experiments, but recent developments have also enabled their first-principles prediction using periodic density-functional theory (DFT). Here, we combine experiments and dispersion-corrected DFT to quantify lattice thermal expansion and ADPs in crystalline α-sulfur (S8), a prototypical elemental solid that is controlled by the interplay of covalent and van der Waals interactions. We begin by reporting on single-crystal and powder X-ray diffraction measurements that provide new and improved reference data from 10 K up to room temperature. We then use several popular dispersion-corrected DFT methods to predict vibrational and thermal properties of α-sulfur, including the anisotropic lattice thermal expansion. Hereafter, ADPs are derived in the commonly used harmonic approximation (in the computed zero-Kelvin structure) and also in the quasi-harmonic approximation (QHA) which takes the predicted lattice thermal expansion into account. At the PPBE+D3(BJ) level, the QHA leads to excellent agreement with experiments. Finally, more general implications of this study for theory and experiment are discussed.

Anisotropic thermal motion in transition-metal carbonyls from experiments and ab initio theory.

The thermal motion of atoms in crystals is quantified by anisotropic displacement parameters (ADPs). Here we show that dispersion-corrected periodic density-functional theory can be used to compute accurate ADPs for transition metal carbonyls, which serve as model systems for crystalline organometallic and coordination compounds.

Ammonothermal Synthesis, Crystal Structure, and Properties of the Ytterbium(II) and Ytterbium(III) Amides and the First Two Rare-Earth-Metal Guanidinates, YbC(NH)3 and Yb(CN3H4)3.

We report the oxidation-controlled synthesis of the ytterbium amides Yb(NH2)2 and Yb(NH2)3 and the first rare-earth-metal guanidinates YbC(NH)3 and Yb(CN3H4)3 from liquid ammonia. For Yb(NH2)2, we present experimental atomic displacement parameters from powder X-ray diffraction (PXRD) and density functional theory (DFT)-derived hydrogen positions for the first time. For Yb(NH2)3, the indexing proposal based on PXRD arrives at R3̅, a = 6.2477(2) Å, c = 17.132(1) Å, V = 579.15(4) Å(3), and Z = 6. The oxidation-controlled synthesis was also applied to make the first rare-earth guanidinates, namely, the doubly deprotonated YbC(NH)3 and the singly deprotonated Yb(CN3H4)3. YbC(NH)3 is isostructural with SrC(NH)3, as derived from PXRD (P63/m, a = 5.2596(2) Å, c = 6.6704(2) Å, V = 159.81(1) Å(3), and Z = 2). Yb(CN3H4)3 crystallizes in a structure derived from the [ReO3] type, as studied by powder neutron diffraction (Pn3̅, a = 13.5307(3) Å, V = 2477.22(8) Å(3), and Z = 8 at 10 K). Electrostatic and hydrogen-bonding interactions cooperate to stabilize the structure with wide and empty channels. The IR spectra of the guanidinates are compared with DFT-calculated phonon spectra to identify the vibrational modes. SQUID magnetometry shows that Yb(CN3H4)3 is a paramagnet with isolated Yb(3+) (4f(13)) ions. A CONDON 2.0 fit was used to extract all relevant parameters.

Synthesis, structure, and properties of SrC(NH)3 , a nitrogen-based carbonate analogue with the trinacria motif.

Strontium guanidinate, SrC(NH)3 , the first compound with a doubly deprotonated guanidine unit, was synthesized from strontium and guanidine in liquid ammonia and characterized by X-ray and neutron diffraction, IR spectroscopy, and density-functional theory including harmonic phonon calculations. The compound crystallizes in the hexagonal space group P63 /m, constitutes the nitrogen analogue of strontium carbonate, SrCO3 , and its structure follows a layered motif between Sr(2+) ions and complex anions of the type C(NH)3 (2-) ; the anions adopt the peculiar trinacria shape. A comparison of theoretical phonons with experimental IR bands as well as quantum-chemical bonding analyses yield a first insight into bonding and packing of the formerly unknown anion in the crystal.

On the DFT ground state of crystalline bromine and iodine.

We report on an erroneous ground state within common density functional theory (DFT) methods for the solid elements bromine and iodine. Phonon computations at the GGA level for both molecular crystals yield imaginary vibrational modes, erroneously indicating dynamic instability-that fact alone could easily pass as a computational artefact, but these imaginary modes lead to energetically more favorable and dynamically stable structures, made up of infinite monoatomic chains. In contrast, meta-GGA and hybrid functionals yield the correct energetic order for bromine, while for iodine, most global hybrids do not improve the GGA result significantly. The qualitatively correct answer, in both cases, is given by the long-range corrected hybrid LC-ωPBE, the Minnesota functionals M06L and M06, and by periodic Hartree-Fock and MP2 theory. This poor performance of economic DFT functionals should be kept in mind, for example, during global structure optimizations of systems with significant contributions from halogen bonds.

ß-CuN3: the overlooked ground-state polymorph of copper azide with heterographene-like layers.

An unexpected polymorph of the highly energetic phase CuN3 has been synthesized and crystallizes in the orthorhombic space group Cmcm with a=3.3635(7), b=10.669(2), c=5.5547(11) Šand V=199.34(7) Å(3). The layered structure resembles graphite with an interlayer distance of 2.777(1) Š(=1/2 c). Within a single layer, considering N3(-) as one structural unit, there are 10-membered almost hexagonal rings with a heterographene-like motif. Copper and nitrogen atoms are covalently bonded with Cu-N bonds lengths of 1.91 and 2.00 Å, and the N3(-) group is linear but with N-N 1.14 and 1.20 Å. Electronic-structure calculations and experimental thermochemistry show that the new polymorph termed ß-CuN3 is more stable than the established α-CuN3 phase. Also, ß-CuN3 is dynamically, and thus thermochemically, metastable according to the calculated phonon density of states. In addition, ß-CuN3 exhibits negative thermal expansion within the graphene-like layer.

Dimensionality of intermolecular interactions in layered crystals by electronic-structure theory and geometric analysis.

Two-dimensional (2D) and layered structures gained a lot of attention in the recent years ("post-graphene era"). The chalcogen cyanides S(CN)(2) and Se(CN)(2) offer themselves as interesting model systems to study layered inorganic crystal structures; both are built up from cyanide molecules connected by chalcogen bonds (ChBs). Here, we investigate ChBs and their cooperativity directly within the layers of the S(CN)(2) and Se(CN)(2) crystal structures and, furthermore, in putative O(CN)(2) and Te(CN)(2) crystal structures derived therefrom. Moreover, we determine the energetic contributions of ChBs within the layers to the overall stabilization energy. To compare these structures not only energetically but also geometrically, we derive a direction-dependent root mean square of the Cartesian displacement, a possible tool for further computational investigations of layered compounds. The molecular chains connected by ChBs are highly cooperative but do not influence each other when combined to layers: the ChBs are nearly orthogonal in terms of energy when connected to the same chalcogen acceptor atom. Layers built up from ChBs account for 41% to 79% of the overall interaction energy in the crystal. This provides new, fundamental insight into the meaning of ChBs, and therefore directed intermolecular interactions, for the stability of crystal structures.

Cooperativity of halogen, chalcogen, and pnictogen bonds in infinite molecular chains by electronic structure theory.

Halogen bonds (XBs) are intriguing noncovalent interactions that are frequently being exploited for crystal engineering. Recently, similar bonding mechanisms have been proposed for adjacent main-group elements, and noncovalent "chalcogen bonds" and "pnictogen bonds" have been identified in crystal structures. A fundamental question, largely unresolved thus far, is how XBs and related contacts interact with each other in crystals; similar to hydrogen bonding, one might expect "cooperativity" (bonds amplifying each other), but evidence has been sparse. Here, we explore the crucial step from gas-phase oligomers to truly infinite chains by means of quantum chemical computations. A periodic density functional theory (DFT) framework allows us to address polymeric chains of molecules avoiding the dreaded "cluster effects" as well as the arbitrariness of defining a "large enough" cluster. We focus on three types of molecular chains that we cut from crystal structures; furthermore, we explore reasonable substitutional variants in silico. We find evidence of cooperativity in chains of halogen cyanides and also in similar chalcogen- and pnictogen-bonded systems; the bonds, in the most extreme cases, are amplified through cooperative effects by 79% (I···N), 90% (Te···N), and 103% (Sb···N). Two experimentally known organic crystals, albeit with similar atomic connectivity and XB characteristics, show signs of cooperativity in one case but not in another. Finally, no cooperativity is observed in alternating halogen/acetone and halogen/1,4-dioxane chains; in fact, these XBs weaken each other by up to 26% compared to the respective gas-phase dimers.