Ruddlesden-Popper Oxyfluorides La2Ni1-xCuxO3F2 (0 ≤ x ≤ 1): Impact of the Ni/Cu Ratio on the Thermal Stability and Magnetic Properties.

Ruddlesden-Popper oxyfluorides of the substitution series La2Ni1-xCuxO3F2 (0 ≤ x ≤ 1) were obtained by topochemical fluorination with polyvinylidene fluoride (PVDF) of oxide precursors La2Ni1-xCuxO4. The thermal stability and the temperature-dependent unit cell evolution of the oxyfluorides were investigated by high-temperature XRD measurements. The oxyfluoride with x = 0.6 shows the highest decomposition temperature of θdec ∼ 520 °C, which is significantly higher than the ones found for the end members La2NiO3F2 (x = 0) θdec ∼ 460 °C and La2CuO3F2 (x = 1) θdec ∼ 430 °C. The magnetic properties of all La2Ni1-xCuxO3F2 oxyfluorides were characterized by field- and temperature-dependent measurements as well as DFT calculations of the magnetic ground state. An antiferromagnetic ordering was derived for all substitution levels. For the Néel temperature (TN), a nonlinear dependence on the copper content was found, and comparably high values of TN in the region of 200-250 K were observed in the broad composition range of 0.3 ≤ x ≤ 0.8.

Ruddlesden-Popper Oxyfluorides La2Ni1-xCuxO3F2 (0 ≤ x ≤ 1): Impact of the Ni/Cu Ratio on the Structure.

Ruddlesden-Popper oxyfluorides La2Ni1-xCuxO3F2 (0 ≤ x ≤ 1) were obtained by topochemical reaction of oxide precursors La2Ni1-xCuxO4, prepared by citrate-based soft chemistry synthesis, with polyvinylidene fluoride (PVDF) as the fluorine source. Systematic changes of the crystal structure in the oxide as well as the oxyfluoride substitution series were investigated. For 0.2 ≤ x ≤ 0.9, the oxyfluorides adopt the monoclinic (C2/c) structural distortion previously solved for the x = 0.8 compound based on neutron powder diffraction data, whereas the sample with a lower Cu content of x = 0.1 crystallizes in the orthorhombic (Cccm) structure variant of La2NiO3F2. The orthorhombic-to-monoclinic structural transition was found to be the result of an additional tilt component of the Jahn-Teller elongated CuO4F2 octahedra. The structural transitions were additionally studied by DFT calculations, confirming the monoclinic space group symmetry. The "channel-like" anionic ordering of the endmembers La2NiO3F2 and La2CuO3F2 was checked by 19F MAS NMR experiments and was found to persist throughout the entire substitution series.

Sampling the Materials Space for Conventional Superconducting Compounds.

A large scale study of conventional superconducting materials using a machine-learning accelerated high-throughput workflow is performed, starting by creating a comprehensive dataset of around 7000 electron-phonon calculations performed with reasonable convergence parameters. This dataset is then used to train a robust machine learning model capable of predicting the electron-phonon and superconducting properties based on structural, compositional, and electronic ground-state properties. Using this machine, the transition temperatures (Tc ) of approximately 200 000 metallic compounds are evaluated, all of which are on the convex hull of thermodynamic stability (or close to it) to maximize the probability of synthesizability. Compounds predicted to have Tc values exceeding 5 K are further validated using density-functional perturbation theory. As a result, 541 compounds with Tc values surpassing 10 K, encompassing a variety of crystal structures and chemical compositions, are identified. This work is complemented with a detailed examination of several interesting materials, including nitrides, hydrides, and intermetallic compounds. Particularly noteworthy is LiMoN2 , which is predicted to be superconducting in the stoichiometric trigonal phase, with a Tc exceeding 38 K. LiMoN2 has previously been synthesized in this phase, further heightening its potential for practical applications.

Two-Dimensional Noble Metal Chalcogenides in the Frustrated Snub-Square Lattice.

We study two-dimensional noble metal chalcogenides, with compositions {Cu, Ag, Au}2{S, Se, Te}, crystallizing in a snub-square lattice. This is a semiregular two-dimensional tesselation formed by triangles and squares that exhibits geometrical frustration. We use for comparison a square lattice, from which the snub-square tiling can be derived by a simple rotation of the squares. The monolayer snub-square chalcogenides are very close to thermodynamic stability, with the most stable system (Ag2Se) a mere 7 meV/atom above the convex hull of stability. All compounds studied in the square and snub-square lattice are semiconductors, with band gaps ranging from 0.1 to more than 2.5 eV. Excitonic effects are strong, with an exciton binding energy of around 0.3 eV. We propose the Cu (001) surface as a possible substrate to synthesize Cu2Se, although many other metal and semiconducting surfaces can be found with very good lattice matching.

Reproducibility of density functional approximations: How new functionals should be reported.

Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations are published every year. To become available in program packages, the novel density functional approximations (DFAs) need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al., SoftwareX 7, 1 (2018)], a constant problem in this task is verification due to the lack of reliable reference data. As we discuss in this work, this lack has led to several non-equivalent implementations of functionals such as Becke-Perdew 1986, Perdew-Wang 1991, Perdew-Burke-Ernzerhof, and Becke's three-parameter hybrid functional with Lee-Yang-Parr correlation across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs. DFAs must be verifiable in order to prevent the reappearance of the above-mentioned errors and incompatibilities. A common framework for verification and testing is, therefore, needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters-especially the quadrature grid-need to be converged to guarantee a ≲0.1 µEh precision in the total energy, which is nowadays routinely achievable in fully numerical calculations. Moreover, as such sub-µEh level agreement can only be achieved when fully equivalent implementations of the DFA are used, the source code of the reference implementation should also be made available in any publication describing a new DFA.

Machine-Learning-Assisted Determination of the Global Zero-Temperature Phase Diagram of Materials.

Crystal-graph attention neural networks have emerged recently as remarkable tools for the prediction of thermodynamic stability. The efficacy of their learning capabilities and their reliability is however subject to the quantity and quality of the data they are fed. Previous networks exhibit strong biases due to the inhomogeneity of the training data. Here a high-quality dataset is engineered to provide a better balance across chemical and crystal-symmetry space. Crystal-graph neural networks trained with this dataset show unprecedented generalization accuracy. Such networks are applied to perform machine-learning-assisted high-throughput searches of stable materials, spanning 1 billion candidates. In this way, the number of vertices of the global T = 0 K phase diagram is increased by 30% and find more than ≈150 000 compounds with a distance to the convex hull of stability of less than 50 meV atom-1 . The discovered materials are then accessed for applications, identifying compounds with extreme values of a few properties, such as superconductivity, superhardness, and giant gap-deformation potentials.

Many recent density functionals are numerically ill-behaved.

Most computational studies in chemistry and materials science are based on the use of density functional theory. Although the exact density functional is unknown, several density functional approximations (DFAs) offer a good balance of affordable computational cost and semi-quantitative accuracy for applications. The development of DFAs still continues on many fronts, and several new DFAs aiming for improved accuracy are published every year. However, the numerical behavior of these DFAs is an often-overlooked problem. In this work, we look at all 592 DFAs for three-dimensional systems available in Libxc 5.2.2 and examine the convergence of the density functional total energy based on tabulated atomic Hartree-Fock wave functions. We show that several recent DFAs, including the celebrated SCAN family of functionals, show impractically slow convergence with typically used numerical quadrature schemes, making these functionals unsuitable both for routine applications and high-precision studies, as thousands of radial quadrature points may be required to achieve sub-µEh accurate total energies for these functionals, while standard quadrature grids like the SG-3 grid only contain O(100) radial quadrature points. These results are both a warning to users to always check the sufficiency of the quadrature grid when adopting novel functionals, as well as a guideline to the theory community to develop better-behaved density functionals.

Efficient and improved prediction of the band offsets at semiconductor heterojunctions from meta-GGA density functionals: A benchmark study.

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations, efficient, accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk bandgaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (two times revised strongly constrained and appropriately normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and local modified Becke-Johnson exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the density functional theory framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy.

A dataset of 175k stable and metastable materials calculated with the PBEsol and SCAN functionals.

In the past decade we have witnessed the appearance of large databases of calculated material properties. These are most often obtained with the Perdew-Burke-Ernzerhof (PBE) functional of density-functional theory, a well established and reliable technique that is by now the standard in materials science. However, there have been recent theoretical developments that allow for increased accuracy in the calculations. Here, we present a dataset of calculations for 175k crystalline materials obtained with two functionals: geometry optimizations are performed with PBE for solids (PBEsol) that yields consistently better geometries than the PBE functional, and energies are obtained from PBEsol and from SCAN single-point calculations at the PBEsol geometry. Our results provide an accurate overview of the landscape of stable (and nearly stable) materials, and as such can be used for reliable predictions of novel compounds. They can also be used for training machine learning models, or even for the comparison and benchmark of PBE, PBEsol, and SCAN.

Crystal graph attention networks for the prediction of stable materials.

Graph neural networks for crystal structures typically use the atomic positions and the atomic species as input. Unfortunately, this information is not available when predicting new materials, for which the precise geometrical information is unknown. We circumvent this problem by replacing the precise bond distances with embeddings of graph distances. This allows our networks to be applied directly in high-throughput studies based on both composition and crystal structure prototype without using relaxed structures as input. To train these networks, we curate a dataset of over 2 million density functional calculations of crystals with consistent calculation parameters. We apply the resulting model to the high-throughput search of 15 million tetragonal perovskites of composition ABCD2. As a result, we identify several thousand potentially stable compounds and demonstrate that transfer learning from the newly curated dataset reduces the required training data by 50%.

Structure, Magnetism, and Thermal Stability of La2NiO2.5F3: A Ruddlesden-Popper Oxyfluoride Crystallizing in Space Group P42/nnm.

We report on the new Ruddlesden-Popper (RP) oxyfluoride La2NiO2.5F3 containing an unprecedented high amount of fluorine and Ni2+. This oxyfluoride was prepared by topochemical low-temperature fluorination of La2NiO4, which was obtained by a soft chemistry synthesis, with poly(vinylidene difluoride) (PVDF) as fluorinating agent. La2NiO2.5F3 is the first n = 1 RP compound crystallizing in the tetragonal space group P42/nnm (a = 5.7297(6) Å and c = 13.0106(2) Å). The crystal structure shows a unique tilting scheme of the NiO4F2 octahedra that has so far been only theoretically predicted. Combined neutron and X-ray powder diffraction experiments together with bond-valence-sum and DFT+U calculations reveal an unusual anion ordering with fluoride being located on the apical anion sites of the NiO4F2 octahedra. Excess fluorine ions were found to populate two of the four interstitial anion sites in an ordered fashion. A third interstitial anion position is occupied by oxygen ions while the fourth site remains unoccupied. This hitherto unobserved ordering scenario in RP oxyfluorides promotes a strong layerwise alternating tilting of the NiO4F2 octahedra. Magnetic measurements show strong antiferromagnetic interactions with a high Néel temperature of about 225 K and a pronounced ZFC/FC splitting most likely as the result of a small ferromagnetic moment arising from spin canting. The electronic structure was characterized by DFT and UV-vis spectroscopy, and a strong increase of Eg was found compared to La2NiO4 (3.4 eV vs 1.3 eV).

Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals.

The density-functional theory (DFT) approximations that are the most accurate for the calculation of bandgap of bulk materials are hybrid functionals, such as HSE06, the modified Becke-Johnson (MBJ) potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGAs), such as HLE16, or meta-GGAs, such as (m)TASK, have also proven to be quite accurate for the bandgap. Here, the focus is on two-dimensional (2D) materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [T. Rauch, M. A. L. Marques, and S. Botti, Phys. Rev. B 101, 245163 (2020); Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the bandgap of 2D systems, G0W0 results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the bandgaps that are the closest to G0W0. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.

Bishop's hat silicene: a planar square silicon bilayer decorated with adatoms.

We investigate a family of free-standing quasi-two-dimensional silicon structures based on a planar square bilayer with adatom decorations. When attached to the bilayer, these adatoms form local reconstructions which resemble either a bishop's hat or elongated square bipyramids. We systematically constructed members of this family via exhaustive enumeration and then studied them using tight-binding and density-functional theory. We find that this geometry contributes significantly to the stability of the resulting structures, with some squared bilayers energetically more stable than the honeycomb bilayers. The most interesting phases were then characterized in more detail, and they all turned out metallic. Finally, we propose the [100] surface of ZrO2 as the most suitable substrate for the synthesis of these two-dimensional phases.

Electronic Structure of Molecules, Surfaces, and Molecules on Surfaces with the Local Modified Becke-Johnson Exchange-Correlation Potential.

The knowledge of electronic properties of matter is the key to the understanding of its properties and to propose useful applications. To model hybrid organic/inorganic systems with the plane-wave approach, large supercells with many atoms are usually necessary to minimize artificial interactions between periodic images. For such systems, accurate approximations to the exchange-correlation functional of density functional theory, such as hybrid functionals, become computationally expensive, and cheaper approaches need to be considered. Here, we apply the local modified Becke-Johnson exchange-correlation potential to free molecules and surfaces and study its accuracy for calculated ionization potentials. This quantity being important to understand the band alignment of composite heterogeneous systems, we demonstrate the application of the potential to the electronic structure calculation of an exemplary composite semiconductor/molecule system, namely, a F6-TCNNQ molecule adsorbed on a hydrogenated Si(111) surface.

Atomically Thin Pythagorean Tilings in Two Dimensions.

We perform a theoretical study of an atomically thin, two-dimensional layer obtained by positioning atoms at the vertices of the classical Pythagorean tiling. This leads to an unusual geometrical pattern that is only stable for the three halogens Cl, Br, and I. In this Pythagorean structure, halogen atoms are arranged in strongly bound diatomic units that bind together by weaker electrostatic bonds. The energy of these phases is competitive with those of the low-temperature phase of the halogens and the two-dimensional layer obtained by exfoliating it. The Pythagorean layers are semiconducting, with an unusual band structure composed of very mobile holes and extremely heavy electrons. They are also soft, exhibiting small values of the elastic constants and a very low energy flexural mode. Analysis of the allowed Raman transitions reveals breathing-like modes that might be used to fingerprint, experimentally, the Pythagorean structure. Finally, we present a series of substrates that, due to lattice matching and compatible symmetry, can be used to stabilize these peculiar two-dimensional layers.

Direct insight into the structure-property relation of interfaces from constrained crystal structure prediction.

A major issue that prevents a full understanding of heterogeneous materials is the lack of systematic first-principles methods to consistently predict energetics and electronic properties of reconstructed interfaces. In this work we address this problem with an efficient and accurate computational scheme. We extend the minima-hopping method implementing constraints crafted for two-dimensional atomic relaxation and enabling variations of the atomic density close to the interface. A combination of density-functional and accurate density-functional tight-binding calculations supply energy and forces to structure prediction. We demonstrate the power of this method by applying it to extract structure-property relations for a large and varied family of symmetric and asymmetric tilt boundaries in polycrystalline silicon. We find a rich polymorphism in the interface reconstructions, with recurring bonding patterns that we classify in increasing energetic order. Finally, a clear relation between bonding patterns and electrically active grain boundary states is unveiled and discussed.

First-Principles Identification of Single Photon Emitters Based on Carbon Clusters in Hexagonal Boron Nitride.

A recent study associates carbon with single photon emitters (SPEs) in hexagonal boron nitride (h-BN). This observation, together with the high mobility of carbon in h-BN, suggests the existence of SPEs based on carbon clusters. Here, by means of density functional theory calculations, we studied clusters of substitutional carbon atoms up to tetramers in h-BN. Two different conformations of neutral carbon trimers have zero-point line energies and shifts of the phonon sideband compatible with typical photoluminescence spectra. Moreover, some conformations of two small C clusters next to each other result in photoluminescence spectra similar to those found in the experiments. We also showed that vacancies are unable to reproduce the typical features of the phonon sideband observed in most measurements because of the large spectral weight of low-energy breathing modes, ubiquitous in such defects.

Halogen molecular modifications at high pressure: the case of iodine.

Metallization and dissociation are key transformations in diatomic molecules at high densities particularly significant for modeling giant planets. Using X-ray absorption spectroscopy and atomistic modeling, we demonstrate that in halogens, the formation of a connected molecular structure takes place at pressures well below metallization. Here we show that the iodine diatomic molecule first elongates by ∼0.007 Å up to a critical pressure of Pc ∼ 7 GPa, developing bonds between molecules. Then its length continuously decreases with pressure up to 15-20 GPa. Universal trends in halogens are shown and allow us to predict for chlorine a pressure of 42 ± 8 GPa for molecular bond-length reversal. Our findings contribute to tackling the molecule invariability paradigm in diatomic molecular phases at high pressures and may be generalized to other abundant diatomic molecules in the universe, including hydrogen.

Meta-Local Density Functionals: A New Rung on Jacob's Ladder.

The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density nσ, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a geometric average nσavg(r) = nσ1-x(r)ñσx(r) of the local spin density nσ(r) and the spin density ñσ(r) of a HEG that has the local kinetic energy density τσ(r) of the inhomogeneous system. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG and which form a new rung of Jacob's ladder of density functionals [ AIP Conf. Proc. 2001, 577, 1]. The first functional of this ladder, the local τ approximation (LTA) of Ernzerhof and Scuseria [ J. Chem. Phys. 1999, 111, 911] that corresponds to x = 1 is unfortunately not stable enough to be used in self-consistent field calculations because it leads to divergent potentials, as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of x not only leads to numerical stability of the resulting functional but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional (x = 1/4) of Eich and Hellgren [ J. Chem. Phys. 2014, 141, 224107]. We choose x = 0.50, as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice x = 0.50 also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.

The CECAM electronic structure library and the modular software development paradigm.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.