Electronic structure of TiSe2 from a quasi-self-consistent G0W0 approach

n a previous work, it was shown that the inclusion of exact exchange is essential for a first-principles description of both the electronic and the vibrational properties of TiSe2, M. Hellgren et al. [Phys. Rev. Lett. 119, 176401 (2017)]. The GW approximation provides a parameter-free description of screened exchange but is usually employed perturbatively (G0W0), making results more or less dependent on the starting point. In this work, we develop a quasi-self-consistent extension of G0W0 based on the random phase approximation (RPA) and the optimized effective potential of hybrid density functional theory. This approach generates an optimal G0W0 starting point and a hybrid exchange parameter consistent with the RPA. While self-consistency plays a minor role for systems such as Ar, BN, and ScN, it is shown to be crucial for TiS2 and TiSe2. We find the high-temperature phase of TiSe2 to be a semimetal with a band structure in good agreement with experiment. Furthermore, the optimized hybrid functional agrees well with our previous estimate and therefore accurately reproduces the low-temperature charge-density-wave phase

ABINIT: Overview and focus on selected capabilities

Paper published as part of the special topic on Electronic Structure SoftwareABINIT is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe–Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the “temperaturedependent effective potential” approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which ABINIT relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The ABINIT DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library LIBPAW. ABINIT has strong links with many other software projects that are briefly mentioned.This work (A.H.R.) was supported by the DMREF-NSF Grant No. 1434897, National Science Foundation OAC-1740111, and U.S. Department of Energy DE-SC0016176 and DE-SC0019491 projects. N.A.P. and M.J.V. gratefully acknowledge funding from the Belgian Fonds National de la Recherche Scientifique (FNRS) under Grant No. PDR T.1077.15-1/7. M.J.V. also acknowledges a sabbatical “OUT” grant at ICN2 Barcelona as well as ULiège and the Communauté Française de Belgique (Grant No. ARC AIMED G.A. 15/19-09). X.G. and M.J.V. acknowledge funding from the FNRS under Grant No. T.0103.19-ALPS. X.G. and G.-M. R. acknowledge support from the Communauté française de Belgique through the SURFASCOPE Project (No. ARC 19/24-057). X.G. acknowledges the hospitality of the CEA DAM-DIF during the year 2017. G.H. acknowledges support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05-CH11231 (Materials Project Program No. KC23MP). The Belgian authors acknowledge computational resources from supercomputing facilities of the University of Liège, the Consortium des Equipements de Calcul Intensif (Grant No. FRS-FNRS G.A. 2.5020.11), and Zenobe/CENAERO funded by the Walloon Region under Grant No. G.A. 1117545. M.C. and O.G. acknowledge support from the Fonds de Recherche du Québec Nature et Technologie (FRQ-NT), Canada, and the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant No. RGPIN-2016-06666. The implementation of the libpaw library (M.T., T.R., and D.C.) was supported by the ANR NEWCASTLE project (Grant No. ANR-2010-COSI-005-01) of the French National Research Agency. M.R. and M.S. acknowledge funding from Ministerio de Economia, Industria y Competitividad (MINECO-Spain) (Grants Nos. MAT2016-77100-C2-2-P and SEV-2015-0496) and Generalitat de Catalunya (Grant No. 2017 SGR1506). This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation program (Grant Agreement No. 724529). P.G. acknowledges support from FNRS Belgium through PDR (Grant No. HiT4FiT), ULiège and the Communauté française de Belgique through the ARC project AIMED, the EU and FNRS through M.ERA.NET project SIOX, and the European Funds for Regional Developments (FEDER) and the Walloon Region in the framework of the operational program “Wallonie-2020.EU” through the project Multifunctional thin films/LoCoTED. The Flatiron Institute is a division of the Simons Foundation. A large part of the data presented in this paper is available directly from the Abinit Web page www.abinit.org. Any other data not appearing in this web page can be provided by the corresponding author upon reasonable request.Peer reviewe

Periodic states of jellium in two and three dimensions : Hartree-Fock approximation

Le modèle du jellium est l'un des modèles fondamentaux de la matière condensée.Il est constitué d'un ensemble d'électrons et d'un fond uniforme qui assure la neutralité globale.À température nulle et sans champ extérieur, la densité électronique est le seul paramètre du système.Malgré la simplicité de ce modèle, l'état fondamental du jellium en fonction de la densité reste un problème ouvert.Nous avons étudié le modèle du jellium à 2 et 3 dimensions dans l'approximation de Hartree-Fock par une méthode numérique de descente.En utilisant des états périodiques, le nombre d’inconnues est grandement réduit et le nombre d’électrons peut atteindre le million.À type de réseau et polarisation fixés, nous montrons que le système forme un cristal de Wigner à basse densité puis, au dessus d'une densité de transition, occupe des états «métalliques» caractérisés par une structure cristalline avec une maille plus petite que celle du cristal de Wigner.Les états métalliques interpolent entre le cristal de Wigner et le gaz de Fermi, ce dernier n'étant retrouvé qu'à densité infinie.Ce comportement se retrouve à deux et trois dimensions, pour un gaz polarisé et non polarisé, et pour les différents type de réseaux considérés dans nos travaux.Le diagramme de phase à deux ou trois dimensions est alors très riche et comprend à basse densité diverses phases «cristal de Wigner» avec des symétries et polarisations différentes.À haute densité, les états métalliques non-polarisées déstabilisent le cristal de Wigner et le gaz de Fermi. Ces états métalliques s’interprètent comme une superposition d’ondes de densité de spin, prédite par Overhauser en 1962.The jellium model is a fundamental model in condensed matter. It is formed by a set of electrons and a uniform background insuring global neutrality. At zero temperature and without external field, the ground-state depends only on the electronic density. Despite its simplicity, the jellium ground-state is still an open problem. We studied the jellium model in 2 and 3 dimensions within the Hartree-Fock approximation using a numerical descent method. Assuming periodic states, we greatly reduce the number of unknowns and the system may contain up to one million of electrons. At fixed lattice symmetry and polarization, the ground-state is a Wigner crystal at low density, and a «metallic state» above a critical density value. These metallic states are crystals with a lattice constant smaller than in Wigner phase, and interpolate between the latter and the Fermi gas. The metallic states exists in two and three dimensions, for a polarized and unpolarized gas, and for various lattice symmetries. Therefore, the jellium phase diagram at zero temperature is rich : it contains several Wigner crystal phases at low density, polarized and unpolarized, and an unpolarized metallic state at high density. These states are well described by a superposition of spin-density waves, as predicted by Overhauser in 1962

États périodiques du jellium à deux et trois dimensions : approximation de Hartree-Fock

The jellium model is a fundamental model in condensed matter. It is formed by a set of electrons and a uniform background insuring global neutrality. At zero temperature and without external field, the ground-state depends only on the electronic density. Despite its simplicity, the jellium ground-state is still an open problem. We studied the jellium model in 2 and 3 dimensions within the Hartree-Fock approximation using a numerical descent method. Assuming periodic states, we greatly reduce the number of unknowns and the system may contain up to one million of electrons. At fixed lattice symmetry and polarization, the ground-state is a Wigner crystal at low density, and a «metallic state» above a critical density value. These metallic states are crystals with a lattice constant smaller than in Wigner phase, and interpolate between the latter and the Fermi gas. The metallic states exists in two and three dimensions, for a polarized and unpolarized gas, and for various lattice symmetries. Therefore, the jellium phase diagram at zero temperature is rich : it contains several Wigner crystal phases at low density, polarized and unpolarized, and an unpolarized metallic state at high density. These states are well described by a superposition of spin-density waves, as predicted by Overhauser in 1962.Le modèle du jellium est l'un des modèles fondamentaux de la matière condensée.Il est constitué d'un ensemble d'électrons et d'un fond uniforme qui assure la neutralité globale.À température nulle et sans champ extérieur, la densité électronique est le seul paramètre du système.Malgré la simplicité de ce modèle, l'état fondamental du jellium en fonction de la densité reste un problème ouvert.Nous avons étudié le modèle du jellium à 2 et 3 dimensions dans l'approximation de Hartree-Fock par une méthode numérique de descente.En utilisant des états périodiques, le nombre d’inconnues est grandement réduit et le nombre d’électrons peut atteindre le million.À type de réseau et polarisation fixés, nous montrons que le système forme un cristal de Wigner à basse densité puis, au dessus d'une densité de transition, occupe des états «métalliques» caractérisés par une structure cristalline avec une maille plus petite que celle du cristal de Wigner.Les états métalliques interpolent entre le cristal de Wigner et le gaz de Fermi, ce dernier n'étant retrouvé qu'à densité infinie.Ce comportement se retrouve à deux et trois dimensions, pour un gaz polarisé et non polarisé, et pour les différents type de réseaux considérés dans nos travaux.Le diagramme de phase à deux ou trois dimensions est alors très riche et comprend à basse densité diverses phases «cristal de Wigner» avec des symétries et polarisations différentes.À haute densité, les états métalliques non-polarisées déstabilisent le cristal de Wigner et le gaz de Fermi. Ces états métalliques s’interprètent comme une superposition d’ondes de densité de spin, prédite par Overhauser en 1962

Periodic states of jellium in two and three dimensions : Hartree-Fock approximation

Le modèle du jellium est l'un des modèles fondamentaux de la matière condensée.Il est constitué d'un ensemble d'électrons et d'un fond uniforme qui assure la neutralité globale.À température nulle et sans champ extérieur, la densité électronique est le seul paramètre du système.Malgré la simplicité de ce modèle, l'état fondamental du jellium en fonction de la densité reste un problème ouvert.Nous avons étudié le modèle du jellium à 2 et 3 dimensions dans l'approximation de Hartree-Fock par une méthode numérique de descente.En utilisant des états périodiques, le nombre d’inconnues est grandement réduit et le nombre d’électrons peut atteindre le million.À type de réseau et polarisation fixés, nous montrons que le système forme un cristal de Wigner à basse densité puis, au dessus d'une densité de transition, occupe des états «métalliques» caractérisés par une structure cristalline avec une maille plus petite que celle du cristal de Wigner.Les états métalliques interpolent entre le cristal de Wigner et le gaz de Fermi, ce dernier n'étant retrouvé qu'à densité infinie.Ce comportement se retrouve à deux et trois dimensions, pour un gaz polarisé et non polarisé, et pour les différents type de réseaux considérés dans nos travaux.Le diagramme de phase à deux ou trois dimensions est alors très riche et comprend à basse densité diverses phases «cristal de Wigner» avec des symétries et polarisations différentes.À haute densité, les états métalliques non-polarisées déstabilisent le cristal de Wigner et le gaz de Fermi. Ces états métalliques s’interprètent comme une superposition d’ondes de densité de spin, prédite par Overhauser en 1962.The jellium model is a fundamental model in condensed matter. It is formed by a set of electrons and a uniform background insuring global neutrality. At zero temperature and without external field, the ground-state depends only on the electronic density. Despite its simplicity, the jellium ground-state is still an open problem. We studied the jellium model in 2 and 3 dimensions within the Hartree-Fock approximation using a numerical descent method. Assuming periodic states, we greatly reduce the number of unknowns and the system may contain up to one million of electrons. At fixed lattice symmetry and polarization, the ground-state is a Wigner crystal at low density, and a «metallic state» above a critical density value. These metallic states are crystals with a lattice constant smaller than in Wigner phase, and interpolate between the latter and the Fermi gas. The metallic states exists in two and three dimensions, for a polarized and unpolarized gas, and for various lattice symmetries. Therefore, the jellium phase diagram at zero temperature is rich : it contains several Wigner crystal phases at low density, polarized and unpolarized, and an unpolarized metallic state at high density. These states are well described by a superposition of spin-density waves, as predicted by Overhauser in 1962

Random phase approximation with exchange for an accurate description of crystalline polymorphism

International audienceWe determine the correlation energy of BN, SiO2 and ice polymorphs employing a recently developed RPAx (random phase approximation with exchange) approach. The RPAx provides larger and more accurate polarizabilities as compared to the RPA, and captures effects of anisotropy. In turn, the correlation energy, defined as an integral over the density-density response function, gives improved binding energies without the need for error cancellation. Here, we demonstrate that these features are crucial for predicting the relative energies between low-and high-pressure polymorphs of different coordination number as, e.g., between α-quartz and stishovite in SiO2, and layered and cubic BN. Furthermore, a reliable (H2O)2 potential energy surface is obtained, necessary for describing the various phases of ice. The RPAx gives results comparable to other high-level methods such as coupled cluster and quantum Monte Carlo, also in cases where the RPA breaks down. Although higher computational cost than RPA we observe a faster convergence with respect to the number of eigenvalues in the response function

Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations

We investigate the adiabatic approximation to the exact-exchange kernel for calculating correlation energies within the adiabatic-connection fluctuation-dissipation framework of time-dependent density functional theory. A numerical study is performed on a set of systems having bonds of different character (H$_2$ and N$_2$ molecules, H-chain, H$_2$-dimer, solid-Ar and the H$_2$O-dimer). We find that the adiabatic kernel can be sufficient in strongly bound covalent systems, yielding similar bond lengths and binding energies. However, for non-covalent systems the adiabatic kernel introduces significant errors around equilibrium geometry, systematically overestimating the interaction energy. The origin of this behaviour is investigated by studying a model dimer composed of one-dimensional closed-shell atoms interacting via soft-Coulomb potentials. The kernel is shown to exhibit a strong frequency dependence at small to intermediate atomic separation that affects both the low-energy spectrum and the exchange-correlation hole obtained from the corresponding diagonal of the two-particle density matrix.Comment: 10 pages, 8 figure

ABINIT: Overview and focus on selected capabilities

Abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe–Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the “temperature-dependent effective potential” approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned