Improved band gaps and structural properties from Wannier–Fermi–Löwdin self-interaction corrections for periodic systems (original) (raw)
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Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 1998
A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron anities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies nonzero o-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an eective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to in®nite order in the o-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to in®nite periodic systems.
2020
We present a scheme to construct atomic Wannier orbitals which maximally hybridizes naturally by construction through a self-consistently chosen gauge, and capable of incorporating the effects of local atomic environment. These orbitals not only allow accurate extraction of multi-orbital tight-binding(TB) parameters well beyond the nearest neighbourhood, but more importantly, facilitate easy multi-orbital mapping of electronic structure from smaller reference systems to larger target systems with similar variety of atomic neighbourhood, based on projected Wannier centres learned from reference systems. The mapping renders electronic structure of large systems not only at the mean-field level of Kohn-Sham density functional theory(DFT), but also facilitate effective transfer of self-energy correction estimated within the GW approximation of many-body perturbation theory, from smaller reference systems to larger target systems, explicit computation of which would otherwise be prohibitively expensive. Such a bottom-up transferability of TB parameters at the DFT+GW level in the multi-orbital basis made of the proposed maximally hybridized atomic Wannier orbitals demonstrated in a representative variety of two and three dimensional systems, is expected to substantially reduce the computational cost of accurate estimation of electronic structure of large systems with hundreds of atoms.
A Hartree-Fock ab initio band-structure calculation employing Wannier-type orbitals
An ab initio Wannier-function-based approach to electronic ground-state calculations for crystalline solids is outlined. In the framework of the linear combination of atomic orbitals method the infinite character of the solid is rigorously taken into account. The Hartree-Fock ground-state energy, cohesive energy, lattice constant and bulk modulus are calculated in a fully ab initio manner as it is demonstrated for sodium chloride, NaCl, using basis sets close to the Hartree-Fock limit. It is demonstrated that the Hartree-Fock band-structure can easily be recovered with the current approach and agrees with the one obtained from a more conventional Bloch-orbital-based calculation. It is argued that the advantage of the present approach lies in its capability to include electron correlation effects for crystalline insulators by means of well-established quantum chemical procedures.
First-principles Wannier functions and effective lattice fermion models for narrow-band compounds
Physical Review B, 2006
We propose a systematic procedure for constructing effective lattice fermion models for narrowband compounds on the basis of first-principles electronic-structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO3, YTiO3, V2O3, and Y2Mo2O7, whose low-energy properties are linked exclusively to the electronic structure of an isolated t2g band. The method consists of three parts, starting from the electronic structure in the local-density approximation (LDA). (i) construction of the kinetic-energy Hamiltonian using formal downfolding method. It allows to describe the band structure close to the Fermi level in terms of a limited number of (unknown yet) Wannier functions (WFs), and eliminate the rest of the basis states. (ii) solution of an inverse problem and construction of WFs for the given kinetic-energy Hamiltonian. Here, we closely follow the construction of the basis functions in the liner-muffin-tin-orbital (LMTO) method, and enforce the orthogonality of WFs to other band. In this approach, one can easily control the contributions of the kinetic energy to the WFs. (iii) calculation of screened Coulomb interactions in the basis of auxiliary WFs. The latter are defined as the WFs for which the kinetic-energy term is set to be zero. Meanwhile, the hybridization between TM d and other atomic states is well preserved by the orthogonality condition to other bands. The use of auxiliary WFs is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly in the model Hamiltonian. In order to calculate the screened Coulomb interactions we employed a hybrid approach. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization connecting the TM d orbitals and other orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening of on-site Coulomb interactions associated with the change of this hybridization in the random-phase approximation. The second channel of screening appears to be very important, and results in relatively small value of the effective Coulomb interaction for isolated t2g bands (about 2-3 eV, depending on the material). We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, as well as the effect of dimensionality of the model Hamiltonian. PACS numbers: 71.10.Fd; 71.15.Mb; 71.28.+d; 71.15.Ap In this paper we will discuss the first part of this project and show how results of conventional LDA calculations for the t 2g bands can be mapped onto the multi-orbital Hubbard model:
Physical Review B, 2006
A versatile method for combining density functional theory (DFT) in the local density approximation (LDA) with dynamical mean-field theory (DMFT) is presented. Starting from a general basis-independent formulation, we use Wannier functions as an interface between the two theories. These functions are used for the physical purpose of identifying the correlated orbitals in a specific material, and also for the more technical purpose of interfacing DMFT with different kinds of band-structure methods (with three different techniques being used in the present work). We explore and compare two distinct Wannier schemes, namely the maximally-localized-Wannier-function (MLWF) and the N-th order muffin-tin-orbital (NMTO) methods. Two correlated materials with different degrees of structural and electronic complexity, SrVO3 and BaVS3, are investigated as case studies. SrVO3 belongs to the canonical class of correlated transition-metal oxides, and is chosen here as a test case in view of its simple structure and physical properties. In contrast, the sulfide BaVS3 is known for its rich and complex physics, associated with strong correlation effects and low-dimensional characteristics. New insights into the physics associated with the metal-insulator transition of this compound are provided, particularly regarding correlation-induced modifications of its Fermi surface. Additionally, the necessary formalism for implementing self-consistency over the electronic charge density in a Wannier basis is discussed.
Full orbital calculation scheme for materials with strongly correlated electrons
Physical Review B, 2005
We propose a computational scheme for the ab initio calculation of Wannier functions (WFs) for correlated electronic materials. The full-orbital HamiltonianĤ is projected into the WF subspace defined by the physically most relevant partially filled bands. The HamiltonianĤ W F obtained in this way, with interaction parameters calculated by constrained LDA for the Wannier orbitals, is used as an ab initio setup of the correlation problem, which can then be solved by many-body techniques, e.g., dynamical mean-field theory (DMFT). In such calculations the self-energy operator Σ(ε) is defined in WF basis which then can be converted back into the full-orbital Hilbert space to compute the full-orbital interacting Green function G(r, r ′ , ε). Using G(r, r ′ , ε) one can evaluate the charge density, modified by correlations, together with a new set of WFs, thus defining a fully selfconsistent scheme. The Green function can also be used for the calculation of spectral, magnetic and electronic properties of the system. Here we report the results obtained with this method for SrVO 3 and V 2 O 3. Comparisons are made with previous results obtained by the LDA+DMFT approach where the LDA DOS was used as input, and with new bulk-sensitive experimental spectra.
Self-consistent band-gap corrections in density functional theory using modified pseudopotentials
Physical Review B, 2007
Density functional calculations based on the local density approximation or generalized gradient approximation have proven their value for predicting ground-state properties of materials. However, the corresponding band structures cannot be directly compared with experiment. We describe an approach based on a modification of pseudopotentials, in the spirit of a technique proposed by Christensen ͓Phys. Rev. B 30, 5753 ͑1984͔͒. These pseudopotentials still accurately describe structural properties and energetics, but they also produce band structures in better agreement with experiment. We establish reliability by performing extensive tests and comparisons with other methods, and illustrate the approach with applications to electronic stucture of bulk, point defects, and surfaces of nitride semiconductors.
Database of Wannier tight-binding Hamiltonians using high-throughput density functional theory
Scientific Data, 2021
Wannier tight-binding Hamiltonians (WTBH) provide a computationally efficient way to predict electronic properties of materials. In this work, we develop a computational workflow for high-throughput Wannierization of density functional theory (DFT) based electronic band structure calculations. We apply this workflow to 1771 materials (1406 3D and 365 2D), and we create a database with the resulting WTBHs. We evaluate the accuracy of the WTBHs by comparing the Wannier band structures to directly calculated spin-orbit coupling DFT band structures. Our testing includes k-points outside the grid used in the Wannierization, providing an out-of-sample test of accuracy. We illustrate the use of WTBHs with a few example applications. We also develop a web-app that can be used to predict electronic properties on-the-fly using WTBH from our database. The tools to generate the Hamiltonian and the database of the WTB parameters are made publicly available through the websites https://github.com...
Accurate determination of band gaps within density functional formalism
In this paper, we report an adaptation of the Harbola-Sahni (HS) exchange potential to the tight-binding linear muffin-tin orbital (TB-LMTO) method to determine band gaps (BGs) of solids accurately. We show that the electrostatic basis of derivation of the Harbola-Sahni potential allows this nonvariational approach to improve substantially over local-density approximation derived BGs, bringing them very close to experimental values. That the accuracy of the HS potential is directly responsible for the determination of correct BGs is demonstrated by performing similar calculations with an accurate model potential that too leads to BGs close to their experimental values. Moreover, ground-state properties like equilibrium lattice parameters and bulk moduli (BM) for various semiconductors like C, Si, AlN, AlP, BP, and 3C-SiC calculated with the HS approach are in close agreement with the experiments. The clear physical interpretation of HS potential leads us to suggest exploring its use for calculating various properties of solids.
Journal of Chemical Theory and Computation, 2020
Accurately modeling the electronic structure of materials is a persistent challenge to highthroughput screening. A promising means of balancing accuracy against computational cost are non-self-consistent calculations with hybrid density-functional theory, where the electronic band energies are evaluated using a hybrid functional from orbitals obtained with a less demanding (semi-)local functional. We have quantified the performance of this technique for predicting the physical properties of sixteen tetrahedral semiconductors with bandgaps from 0.2-5.5 eV. Provided the base functional predicts a non-metallic electronic structure, bandgaps within 5 % of the PBE0 and HSE06 gaps can be obtained with an order of magnitude reduction in computing time. The positions of the valence and conduction band extrema and the Fermi level are well reproduced, further enabling calculation of the band dispersion, density of states, and dielectric properties using Fermi's Golden Rule. While the error in the non-self-consistent total energies is ~50 meV atom-1 , the energy-volume curves are reproduced accurately enough to obtain the equilibrium volume and bulk modulus with minimal error. We also test the dielectric-dependent scPBE0 functional and obtain bandgaps and dielectric constants to within 2.5 % of the self-consistent results, which amount to a significant improvement over self-consistent PBE0 for a similar computational cost. We identify cases where the non-self-consistent approach is expected to perform poorly, and demonstrate that partial self-consistency provides a practical and efficient workaround. Finally, we perform proof-of-concept calculations on CoO and NiO to demonstrate the applicability of the technique to strongly-correlated open-shell transition-metal oxides.