We compare the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical dference in their overall performance although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large large band gap materials --without affecting that of semiconductors-- by including a larger portion of Hartree-Fock exchange in its short range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option for the black box prediction of band gaps.
Density functional theory within the local or semilocal density approximations (DFT-LDA/GGA) has become a workhorse in electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. Accurate prediction of band gaps using firstprinciples methods is time consuming, requiring hybrid functionals, quasi-particle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in …
A meta generalized gradient level screened range-separated hybrid functional is developed for solid-state electronic structure theory. Assessment of the present range-separated hybrid functional for solid-state lattice constants and band gaps indicate that the present functional can be used for describing those properties efficiently in meta-GGA level. Specifically, the performance of the present functional for band gap of solids indicates that the present meta-GGA level screened hybrids functional is quite productive beyond the GGA level. The most appealing feature of the present formalism is…
Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and othe…
A Unified Dielectric-Dependent Hybrid Functional for Accurate Band Gaps across Dimensions
Nicolaus Copernicus University in Toruń（托伦哥白尼大学）；Paderborn University（帕德博恩大学）；Indian Institute of Technology, Hyderabad（海德拉巴印度理工学院）；National Institute of Science Education and Research（国家科学教育与研究机构）
Accurate prediction of fundamental band gaps of crystalline solid state systems entirely within density functional theory is a long standing challenge. Here, we present a simple and inexpensive method that achieves this by means of non-empirical optimal tuning of the parameters of a screened range-separated hybrid functional. The tuning involves the enforcement of an ansatz that generalizes the ionization potential theorem to the removal of an electron in an occupied state described by a localized Wannier function in a modestly sized supercell calculation. The method is benchmarked against exp…
We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrodinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several physically justified constraints, including the generalized Koopmans' theorem. We find that hybrid functionals yield strikingly accurate electron densities and gaps in both exchange-dominated and correlated systems. We also discuss the role of the s…
We describe a first open-access database of experimentally investigated hybrid organic-inorganic materials with two-dimensional (2D) perovskite-like crystal structure. The database includes 515 compounds, containing 180 different organic cations, 10 metals (Pb, Sn, Bi, Cd, Cu, Fe, Ge, Mn, Pd, Sb) and 3 halogens (I, Br, Cl) known so far and will be regularly updated. The database contains a geometrical and crystal chemical analysis of the structures, which are useful to reveal quantitative structure-property relationships for this class of compounds. We show that the penetration depth of spacer…
Hybrid density functional (HDF) approximations usually deliver higher accuracy than local and semilocal approximations to the exchange-correlation functional, but this comes with drastically increased computational cost. Practical implementations of HDFs inevitably involve numerical approximations -- even more so than their local and semilocal counterparts due to the additional numerical complexity arising from treating the exact-exchange component. This raises the question regarding the reproducibility of the HDF results yielded by different implementations. In this work, we benchmark the num…
Accurate and efficient prediction of the band gaps and optical spectra of chalcopyrite semiconductors from a non-empirical range-separated dielectric-dependent hybrid: Comparison with many-body perturbation theory
Recently, two nonempirical hybrid functionals, dielectric-dependent range-separated hybrid functional based on the Coulomb-attenuating method (DD-RSH-CAM) and doubly screened hybrid functional (DSH), have been suggested by [Chen et al, Phys. Rev. Mater. 2, 073803 (2018)] and [Cui et al, J. Phys. Chem. Lett. 9, 2338 (2018)], respectively. These two hybrid functionals are both based on a common model dielectric function approach, but differ in the way how to non-empirically obtain the range-separation parameter. By retaining the full short-range Fock exchange and a fraction of the long-range Foc…
A Hybrid Machine Learning Framework for Predicting Hydrogen Storage Capacities in Metal Hydrides: Unsupervised Feature Learning with Deep Neural Networks
Halide perovskites constitute a chemically-diverse class of crystals with great promise as photovoltaic absorber materials, featuring band gaps between about 1 and 3.5 eV depending on composition. Their diversity calls for a general computational approach to predicting their band gaps. However, such an approach is still lacking. Here, we use density functional theory (DFT) and many-body perturbation theory within the GW approximation to compute the quasiparticle or fundamental band gap of a set of ten representative halide perovskites: CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$), MAPbBr$_3$, CsSnBr$_3$, (…
Electronic structure and phase stability of oxide semiconductors: Performance of dielectric-dependent hybrid functional DFT, benchmarked against $GW$ band structure calculations and experiments
Accurately modeling the electronic structure of materials is a persistent challenge to high-throughput 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…
Resolving Contradictory Estimates of Band Gaps of Bulk PdSe$_2$: A Wannier-Localized Optimally-Tuned Screened Range-Separated Hybrid Density Functional Theory Study
The band gap is an important parameter of semiconductor materials that influences several functional properties, in particular optical properties. However, a fast and reliable first-principles prediction of band gaps remains a challenging problem. Standard DFT approximations tend to strongly underestimate band gaps, while the more accurate $GW$ and hybrid functionals are much more computationally demanding and unsuitable for high-throughput screening. In this work, we have performed an extensive benchmark of several approximations with different computational complexity ($G_{0}W_{0}$@PBEsol, H…
This work is aimed to study mixed-cation (hybrid methyl ammonium plus inorganic cations) halide perovskites using first principles Density Functional Theory (DFT) formalism in order to find their potential applications in perovskite based photovoltaics. This is an addition to the two previous studies performed by the author on high-throughput screening of hybrid halide and inorganic halide perovskites. This work involves mixing certain amounts of the inorganic cation to the organic site (methyl ammonium) and study the electronic structure of the resultant. 63 perovskites have been simulated in…
A finite electronic band gap is a standard filter in high-throughput screening of materials using density functional theory (DFT). However, because of the systematic underestimation of band gaps in standard DFT approximations, a number of compounds may incorrectly be predicted metallic. In a more accurate treatment, such materials may instead appear as low band gap materials and could e.g. have good thermoelectric properties if suitable doping is feasible. To explore this possibility, we performed hybrid functional calculations on 1093 cubic materials listed in the MaterialsProjects database w…
For fast and accurate calculations of band gaps of solids, we present an {\it ab initio} method that extends the density functional theory plus on-site Hubbard interaction (DFT+$U$) to include inter-site Hubbard interaction ($V$). This formalism is appropriate for considering various interactions such as a local Coulomb repulsion, covalent hybridizations, and their coexistence in solids. To achieve self-consistent evaluations of $U$ and $V$, we adapt a recently proposed Agapito-Curtarolo-Buongiorno Nardelli pseudohybrid functional for DFT$+U$ to implement a density functional of $V$ and obtain…
In$_2$Se$_3$ is a semiconductor material that can be stabilized in different crystal structures (at least one 3D and several 2D layered structures have been reported) with diverse electrical and optical properties. This feature has plagued its characterization over the years, with reported band gaps varying in an unacceptable range of 1 eV. Using first-principles calculations based on density functional theory and the HSE06 hybrid functional, we investigated the structural and electronic properties of four layered phases of In$_2$Se$_3$, addressing their relative stability and the nature of th…
We perform hybrid functional and quasi-particle band structure calculations with spin-orbit interaction to investigate the band structures of Mg2Si, Mg2Ge, and Mg2Sn. For all Mg2X materials, where X = Si, Ge, and Sn, the characteristics of band edge states, i.e., band and valley degeneracies, and orbital characters, are found to be conserved, independent of the computational schemes such as density functional generalized gradient approximation, hybrid functionals, or quasi-particle calculations. However, the magnitude of the calculated band gap varies significantly with the computational schem…
Dispersion Corrected Structural Properties and Quasiparticle Band Gaps of Several Organic Energetic Solids
我们对一系列含能固体进行了{ \it ab initio}计算，探索了它们的结构和电子性质。为了计算这些分子固体的基态体积，在DFT中采用了不同的色散校正方法，即Tkartchenko-Scheffler方法（有和没有自洽屏蔽），Grimme方法（D2，D3（BJ））和vdw-DF方法。我们的研究结果表明，色散校正方法是必不可少的，在理解这些复杂的结构与范德华相互作用和氢键。计算的基态体积和体积模量表明，每种方法的性能是不是唯一的，因此，仔细检查是强制性的解释理论预测。这项工作还强调了准粒子计算的重要性，在预测的带隙，这是在这里得到的GW近似。我们发现，所获得的带隙的范围从4至7 eV的不同的化合物，表明它们的绝缘性质。此外，我们显示准粒子能带结构计算的重要作用，相关的间隙与能量特性。
We derive a dielectric-dependent hybrid functional which accurately describes the electronic properties of heterogeneous interfaces and surfaces, as well as those of three- and two-dimensional bulk solids. The functional, which does not contain any adjustable parameter, is a generalization of self-consistent hybrid functionals introduced for homogeneous solids, where the screened Coulomb interaction is defined using a spatially varying, local dielectric function. The latter is determined self-consistently using density functional calculations in finite electric fields. We present results for t…
Hybrid density functional calculations of the band gap of Ga$_x$In$_{1-x}$N
最近的理论工作提供的证据表明，混合泛函，其中包括一小部分的确切（Hartree Fock）交换在密度泛函理论（DFT）的交换和相关条款，显着改善半导体带隙的描述相比，本地和半本地的近似。基于最近发展的计算扩展绝缘体系中精确交换的有序$N$方法，我们实现了一个有效的方案来确定混合泛函带隙。我们使用这个方案来研究的带隙和其他电子性质的三元化合物在$_{1-x}$ Ga $_{x}$ N使用64原子的超原胞模型。
Electronic structure and optical properties of halide double perovskites from a Wannier-localized optimally-tuned screened range-separated hybrid functional
The electronic properties graphene nanoflakes (GNFs) with embedded hexagonal boron nitride (hBN) domains are investigated by combined {\it ab initio} density functional theory calculations and machine learning techniques. The energy gaps of the quasi-0D graphene based systems, defined as the differences between LUMO and HOMO energies, depend on the sizes of the hBN domains relative to the size of the pristine graphene nanoflake, but also on the position of the hBN domain. The range of the energy gaps for different configurations is increasing as the hBN domains get larger. We develop two artif…
Giant spin Nernst effect in a two-dimensional antiferromagnet due to magnetoelastic coupling-induced gaps and interband transitions between magnon-like bands
On the origin of energy gaps in quasicrystalline potentials
University of Cambridge（剑桥大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Ludwig-Maximilians-Universität München（慕尼黑大学）
