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Members of the DFT+U family of functionals are increasingly prevalent methods of addressing errors intrinsic to (semi-) local exchange-correlation functionals at minimum computational cost, but require their parameters U and J to be calculated in situ for a given system of interest, simulation scheme, and runtime parameters. The SCF linear response approach offers ab initio acquisition of the U and has recently been extended to compute the J analogously, which measures localized errors related to exchange-like effects. We introduce a renovated post-processor, the lrUJ utility, together with this detailed best-practices guide, to enable users of the popular, open-source Abinit first-principles simulation suite to engage easily with in situ Hubbard parameters and streamline their incorporation into material simulations of interest. Features of this utility, which may also interest users and developers of other DFT codes, include $n$-degree polynomial regression, error analysis, Python plotting facilities, didactic documentation, and avenues for further developments. In this technical introduction and guide, we place particular emphasis on the intricacies and potential pitfalls introduced by the projector augmented wave (PAW) method, SCF mixing schemes, and non-linear response, several of which are translatable to DFT+U(+J) implementations in other packages., Comment: 46 pages, 6 figures (+3 figures in appendix), 2 tables (+1 table in appendix)

Electronic structure calculations based on many-body perturbation theory (e.g. GW or the random-phase approximation (RPA)) require function evaluations in the complex time and frequency domain, for example inhomogeneous Fourier transforms or analytic continuation from the imaginary axis to the real axis. For inhomogeneous Fourier transforms, the time-frequency component of the GreenX library provides time-frequency grids that can be utilized in low-scaling RPA and GW implementations. In addition, the adoption of the compact frequency grids provided by our library also reduces the computational overhead in RPA implementations with conventional scaling. In this work, we present low-scaling GW and conventional RPA benchmark calculations using the GreenX grids with different codes (FHI-aims, CP2K and ABINIT) for molecules, two-dimensional materials and solids. Very small integration errors are observed when using 30 time-frequency points for our test cases, namely $<10^{-8}$ eV/electron for the RPA correlation energies, and 10 meV for the GW quasiparticle energies., Comment: 15 pages, 6 figures

Machine-learning interatomic potentials have revolutionized materials modeling at the atomic scale. Thanks to these, it is now indeed possible to perform simulations of \abinitio quality over very large time and length scales. More recently, various universal machine-learning models have been proposed as an out-of-box approach avoiding the need to train and validate specific potentials for each particular material of interest. In this paper, we review and evaluate five different universal machine-learning interatomic potentials (uMLIPs), all based on graph neural network architectures which have demonstrated transferability from one chemical system to another. The evaluation procedure relies on data both from a recent verification study of density-functional-theory implementations and from the Materials Project. Through this comprehensive evaluation, we aim to provide guidance to materials scientists in selecting suitable models for their specific research problems, offer recommendations for model selection and optimization, and stimulate discussion on potential areas for improvement in current machine-learning methodologies in materials science., Comment: 7 figures

In the last decades, material discovery has been a very active research field driven by the need to find new materials for many different applications. This has also included materials with heavy elements, beyond the stable isotopes of lead, as most actinides exhibit unique properties that make them useful in various applications. Furthermore, new heavy elements beyond actinides, collectively referred to as super-heavy elements (SHEs), have been synthesized, filling previously empty space of Mendeleev periodic table. Their chemical bonding behavior, of academic interest at present, would also benefit of state-of-the-art modeling approaches. In particular, in order to perform first-principles calculations with planewave basis sets, one needs corresponding pseudopotentials. In this work, we present a series of scalar- and fully-relativistic optimized norm-conserving Vanderbilt pseudopotentials (ONCVPs) for thirty-four actinides and super-heavy elements, for three different exchange-correlation functionals (PBE, PBEsol and LDA). The scalar-relativistic version of these ONCVPs is tested by comparing equations of states for crystals, obtained with \textsc{abinit} 9.6, with those obtained by all-electron zeroth-order regular approximation (ZORA) calculations, without spin-orbit coupling, performed with the Amsterdam Modeling Suite \textsc{band} code. $\Delta$-Gauge and $\Delta_1$-Gauge indicators are used to validate these pseudopotentials. This work is a contribution to the PseudoDojo project, in which pseudopotentials for the whole periodic table are developed and systematically tested. The pseudopotential files are available on the PseudoDojo web-interface pseudo-dojo.org in psp8 and UPF2 formats, both suitable for \textsc{abinit}, the latter being also suitable for Quantum ESPRESSO.

In the past decades many density-functional theory methods and codes adopting periodic boundary conditions have been developed and are now extensively used in condensed matter physics and materials science research. Only in 2016, however, their precision (i.e., to which extent properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. We discuss here general recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z=1 to 96 and characterizing 10 prototypical cubic compounds for each element: 4 unaries and 6 oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Such effort is facilitated by deploying AiiDA common workflows that perform automatic input parameter selection, provide identical input/output interfaces across codes, and ensure full reproducibility. Finally, we discuss the extent to which the current results for total energies can be reused for different goals (e.g., obtaining formation energies)., Comment: Main text: 23 pages, 4 figures. Supplementary: 68 pages. Nature Review Physics 2023

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing., Comment: Submitted as a roadmap article to Modelling and Simulation in Materials Science and Engineering; Address any correspondence to Vikram Gavini (vikramg@umich.edu) and Danny Perez (danny_perez@lanl.gov)

The electronic structure of condensed matter can be significantly affected by the electron-phonon interaction, leading to important phenomena such as electrical resistance, superconductivity or the formation of polarons. This interaction is often neglected in band structure calculations but can have a strong impact on band gaps or optical spectra. Commonly used frameworks for electron-phonon energy corrections are the Allen-Heine-Cardona theory and the Fr\"ohlich model. While the latter shows qualitative agreement with experiment for many polar materials, its simplicity should bring hard limits to its applicability in real materials. Improvements can be made by introducing a generalized version of the model, which considers anisotropic and degenerate electronic bands, and multiple phonon branches. In this work, we search for trends and outliers on over a thousand materials in existing databases of phonon and electron band structures. We use our results to identify the limits of applicability of the standard Fr\"olich model by comparing to the generalized version, and by testing its basic hypothesis of a large radius for the polaronic wavefunction and the corresponding atomic displacement cloud. Among our extended set of materials, most exhibit large polaron behavior as well as validity of the perturbative treatment. For the valence band, there is also a significant fraction of the materials for which the perturbative treatment cannot be applied and/or for which the size of the self-trapping region is close to the atomic repetition distance. We find a large variety of behaviors, and employ much more accurate, fully ab initio Allen-Heine-Cardona calculations to understand extreme cases, where the Fr\"ohlich model should fail and unusually large zero-point renormalization energies occur.

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interaction in ionic systems, that induces associated spectroscopic and optical signatures of such quasi-particles in these materials. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows characteristic signatures of polarons, better denoted "nonpolarons" in this case. The polaronic effects are produced by short-range crystal fields with only a small influence of long-range quadrupoles. The many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fr\"{o}hlich case. The temperature-dependent spectral function of diamond is determined by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges., Comment: 10 pages 16 Figures + Subfigures 2 Tables 82 References Supplementary Information (SI) at the end: SI 10 pages SI 14 Figures + Subfigures SI 1 Table

The mobility of carriers, as limited by their scattering with phonons, can now routinely be obtained from first-principles electron-phonon coupling calculations. However, so far, most computations have relied on some form of simplification of the linearized Boltzmann transport equation based on either the self-energy, the momentum- or constant relaxation time approximations. Here, we develop a high-throughput infrastructure and an automatic workflow and we compute 69 phonon-limited mobilities in semiconductors. We compare the results resorting to the approximations with the exact iterative solution. We conclude that the approximate values may deviate significantly from the exact ones and are thus not reliable. Given the minimal computational overhead, our work encourages to rely on this exact iterative solution and warns on the possible inaccuracy of earlier results reported using relaxation time approximations., Comment: 6 pages, 2 figures

Polarons, that is, charge carriers correlated with lattice deformations, are ubiquitous quasiparticles in semiconductors, and play an important role in electrical conductivity. To date most theoretical studies of so-called large polarons, in which the lattice can be considered as a continuum, have focused on the original Fr\"ohlich model: a simple (non-degenerate) parabolic isotropic electronic band coupled to one dispersionless longitudinal optical phonon branch. The Fr\"ohlich model allows one to understand characteristics such as polaron formation energy, radius, effective mass and mobility. Real cubic materials, instead, have electronic band extrema that are often degenerate or anisotropic and present several phonon modes. In the present work, we address such issues. We keep the continuum hypothesis inherent to the large polaron Fr\"ohlich model, but waive the isotropic and non-degeneracy hypotheses, and also include multiple phonon branches. For polaron effective masses, working at the lowest order of perturbation theory, we provide analytical results for the case of anisotropic electronic energy dispersion, with two distinct effective masses (uniaxial) and numerical simulations for the degenerate 3-band case, typical of III-V and II-VI semiconductor valence bands. We also deal with the strong-coupling limit, using a variational treatment: we propose trial wavefunctions for the above-mentioned cases, providing polaron radii and energies. Then, we evaluate the polaron formation energies, effective masses and localisation lengths using parameters representative of a dozen II-VI, III-V and oxide semiconductors, for both electron and hole polarons...In the non-degenerate case, we compare the perturbative approach with the Feynman path integral approach in characterisizing polarons in the weak coupling limit..., Comment: 18 pages, 10 figures in main text; 11 pages, 1 figure in supplementary material

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification., Comment: 11 pages, 1 table

Electronic and optical properties of materials are affected by atomic motion through the electron-phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fr\"ohlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results., Comment: Note that the supplementary material, included in the main file, is structured differently than in the published version, with a different numbering scheme

Organic molecular crystals are expected to feature appreciable electron-phonon interactions that influence their electronic properties at zero and finite temperature. In this work, we report first-principles calculations and an analysis of the electron-phonon self-energy in naphthalene crystals. We compute the zero-point renormalization and temperature dependence of the fundamental band gap, and the resulting scattering lifetimes of electronic states near the valence- and conduction-band edges employing density functional theory. Further, our calculated phonon renormalization of the $GW$-corrected quasiparticle band structure predicts a fundamental band gap of 5 eV for naphthalene at room temperature, in good agreement with experiments. From our calculated phonon-induced electron lifetimes, we obtain the temperature-dependent mobilities of electrons and holes in good agreement with experimental measurements at room temperatures. Finally, we show that an approximate energy self-consistent computational scheme for the electron-phonon self-energy leads to the prediction of strong satellite bands in the electronic band structure. We find that a single calculation of the self-energy can reproduce the self-consistent results of the band gap renormalization and electrical mobilities for naphthalene, provided that the on-the-mass-shell approximation is used, i.e., if the self-energy is evaluated at the bare eigenvalues., Comment: 12 pages, 7 figures, 3 tables

We include the treatment of quadrupolar fields beyond the Fr\"ohlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense $\mathbf{q}$ meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology.

High-performance $p$-type transparent conducting materials (TCMs) must exhibit a rare combination of properties including high mobility, transparency and $p$-type dopability. The development of high-mobility/conductivity $p$-type TCMs is necessary for many applications such as solar cells, or transparent electronic devices. Oxides have been traditionally considered as the most promising chemical space to dig out novel $p$-type TCMs. However, non-oxides might perform better than traditional $p$-type TCMs (oxides) in terms of mobility. We report on a high-throughput (HT) computational search for non-oxide $p$-type TCMs from a large dataset of more than 30,000 compounds which identified CaTe and Li$_\textrm{3}$Sb as very good candidates for high-mobility $p$-type TCMs. From our calculations, both compounds are expected to be $p$-type dopable: intrinsically for Li$_\textrm{3}$Sb while CaTe would require extrinsic doping. Using electron-phonon computations, we estimate hole mobilities at room-temperature to be about 20 and 70 cm$^2$/Vs for CaTe and Li$_\textrm{3}$Sb, respectively. The computed hole mobility for Li$_\textrm{3}$Sb is quite exceptional and comparable with the electron mobility in the best $n$-type TCMs., Comment: 10 pages, 5 figures

Using density functional theory (DFT) and density functional perturbation theory (DFPT), we investigate the stability and response functions of CsH$_2$PO$_4$, a ferroelectric material at low temperature. This material cannot be described properly by the usual (semi-)local approximations within DFT. The long-range e$^-$-e$^-$ correlation needs to be properly taken into account, using, for instance, Grimme's DFT-D methods, as investigated in this work. We find that DFT-D3(BJ) performs the best for the members of the dihydrogenated alkali phosphate family (KH$_2$PO$_4$, RbH$_2$PO$_4$, CsH$_2$PO$_4$), leading to experimental lattice parameters reproduced with an average deviation of 0.5 %. With these DFT-D methods, the structural, dielectric, vibrational and mechanical properties of CsH$_2$PO$_4$ are globally in excellent agreement with the available experiments ($<$ 2% MAPE for Raman-active phonons). Our study suggests the possible existence of a new low-temperature phase for CsH$_2$PO$_4$, not yet reported experimentally. Finally, we report the implementation of DFT-D contributions to elastic constants within DFPT., Comment: This paper was published in Physical Review B the 25 January 2017 (21 pages, 4 figures)

Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple strongly with phonons in resonance conditions. We design and implement a first-principles methodology to compute second-order Raman scattering, incorporating dielectric responses and phonon eigenstates obtained from density-functional theory and many-body theory. We demonstrate our approach for the case of silicon, relating frequency-dependent relative Raman intensities, that are in excellent agreement with experiment, to different vibrations and regions of the Brillouin zone. We show that exciton-phonon coupling, computed from first principles, indeed strongly affect the spectrum in resonance conditions. The ability to analyze second-order Raman spectra thus provides direct insight into this interaction., Comment: 10 pages, 8 figures

The Bethe-Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe-Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today's standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a double-grid on-the-fly interpolation within the Brillouin zone, combined with the Lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature., Comment: 25 pages, 7 figures, Submitted to Computer Physics Communications

Understanding the physical mechanisms behind thermal effects in phosphors is crucial for white light-emitting diodes (WLEDs) applications, as thermal quenching of their photoluminescence might render them useless. The two chemically close Eu-doped \Hosta and \Hostb crystals are typical phosphors studied for WLEDs. The first one sustains efficient light emission at 100$^{\circ}$C while the second one emits very little light at that temperature. Herein, we analyze from first principles their electronic structure and atomic geometry, before and after absorption/emission of light. Our results, in which the Eu-5d levels are obtained inside the band gap thanks to the removal of an electron from the 4f$^7$ shell, attributes the above-mentioned experimental difference to an auto-ionization model of the thermal quenching, based on the energy difference between Eu$_{\text{5d}}$ and the conduction band minimum. For both Eu-doped phosphors, we identify the luminescent center, and we show that the atomic relaxation in their excited state is of crucial importance for a realistic description of the emission characteristics., Comment: 5 pages and 3 figures

The ab initio prediction of Raman intensities for bulk solids usually relies on the hypothesis that the frequency of the incident laser light is much smaller than the band gap. However, when the photon frequency is a sizeable fraction of the energy gap, or higher, resonance effects appear. In the case of silicon, when excitonic effects are neglected, the response of the solid to light increases by nearly three orders of magnitude in the range of frequencies between the static limit and the gap. When excitonic effects are taken into account, an additional tenfold increase in the intensity is observed. We include these effects using a finite-difference scheme applied on the dielectric function obtained by solving the Bethe-Salpeter equation. Our results for the Raman susceptibility of silicon show stronger agreement with experimental data compared with previous theoretical studies. For the sampling of the Brillouin zone, a double-grid technique is proposed, resulting in a significant reduction in computational effort., Comment: 10 pages, 10 figures, accepted by Physical Review B for publication (http://prb.aps.org/accepted/04072OdeQ2b16026a41081b31f5872037b42287ba)

For a set of ten crystalline materials (oxides and semiconductors), we compute the electronic band structures using the Tran-Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TB09) functional. The band widths and gaps are compared with those from the local-density approximation (LDA) functional, many-body perturbation theory (MBPT), and experiments. At the density-functional theory (DFT) level, TB09 leads to band gaps in much better agreement with experiments than LDA. However, we observe that it globally underestimates, often strongly, the valence (and conduction) band widths (more than LDA). MBPT corrections are calculated starting from both LDA and TB09 eigenenergies and wavefunctions. They lead to a much better agreement with experimental data for band widths. The band gaps obtained starting from TB09 are close to those from quasi-particle self-consistent GW calculations, at a much reduced cost. Finally, we explore the possibility to tune one of the semi-empirical parameters of the TB09 functional in order to obtain simultaneously better band gaps and widths. We find that these requirements are conflicting., Comment: 18 pages, 16 figures

Motivated by the recent discovery of superconductivity in Ca- and Yb-intercalated graphite (CaC$_{6}$ and YbC$_{6}$) and from the ongoing debate on the nature and role of the interlayer state in this class of compounds, in this work we critically study the electron-phonon properties of a simple model based on primitive graphite. We show that this model captures an essential feature of the electron-phonon properties of the Graphite Intercalation Compounds (GICs), namely, the existence of a strong dormant electron-phonon interaction between interlayer and $\pi ^{\ast}$ electrons, for which we provide a simple geometrical explanation in terms of NMTO Wannier-like functions. Our findings correct the oversimplified view that nearly-free-electron states cannot interact with the surrounding lattice, and explain the empirical correlation between the filling of the interlayer band and the occurrence of superconductivity in Graphite-Intercalation Compounds., Comment: 13 pages, 12 figures, submitted to Phys. Rev. B

We report a detailed first-principles study of the structural, electronic and vibrational properties of the superconducting C$_{32}$ phase of the ternary alloy CaAl$_{2-x}$Si$_x$, both in the experimental range $0.6 \leq x \leq 1.2$, for which the alloy has been synthesised, and in the theoretical limits of high aluminium and high silicon concentration. Our results indicate that, in the experimental range, the dependence of the electronic bands on composition is well described by a rigid-band model, which breaks down outside this range. Such a breakdown, in the (theoretical) limit of high aluminium concentration, is connected to the appearance of vibrational instabilities, and results in important differences between CaAl$_2$ and MgB$_2$. Unlike MgB$_2$, the interlayer band and the out-of-plane phonons play a major role on the stability and superconductivity of CaAlSi and related C$_{32}$ intermetallic compounds.