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。
英文摘要：
Recent theoretical work has provided evidence that hybrid functionals, which include a fraction of exact (Hartree Fock) exchange in the density functional theory (DFT) exchange and correlation terms, significantly improve the description of band gaps of semiconductors compared with local and semilocal approximations. Based on a recently developed order-$N$ method for calculating the exact exchange in extended insulating systems, we have implemented an efficient scheme to determine the hybrid functional band gap. We use this scheme to study the band gap and other electronic properties of the ternary compound In$_{1-x}$Ga$_{x}$N using a 64-atom supercell model.
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…
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…
The development of new exchange-correlation functionals within density functional theory means that increasingly accurate information is accessible at moderate computational cost. Recently, a newly developed self-consistent hybrid functional has been proposed [Skone \textit{et al.} Phys. Rev. B \textbf{89}, 195112 (2014)], which allows for a reliable and accurate calculation of material properties using a fully \textit{ab initio} procedure. Here, we apply this new functional to wurtzite ZnO, rutile SnO$_2$, and rocksalt MgO. We present calculated structural, electronic, and optical properties,…
Range separated hybrid density functionals are very successful in describing a wide range of molecular and solid state properties accurately. Range separated hybrid functionals are designed from spherically averaged or system averaged reversed engineered exchange hole. In the present attempt, we employ screened range separated hybrid functional scheme to the meta-GGA rung by using Tao-Mo semilocal exchange hole (or functional). The hybrid functional proposed here utilizes the spherically averaged density matrix expansion based exchange hole in range separation scheme. For slowly varying densit…
Finite-momentum dielectric function and excitonic effects from time-dependent density-functional theory with dielectrically screened hybrid functionals
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…
In first-principles calculations, hybrid functional is often used to improve accuracy from local exchange correlation functionals. A drawback is that evaluating the hybrid functional needs significantly more computing effort. When spin-orbit coupling (SOC) is taken into account, the non-collinear spin structure increases computing effort by at least eight times. As a result, hybrid functional calculations with SOC are intractable in most cases. In this paper, we present an approximate solution to this problem by developing an efficient method based on a mixed linear combination of atomic orbit…
Lattice thermal conductivity of Cu$_2$O was studied using ab initio density functional methods. The performance of generalized gradient approximation, GGA-PBE, and PBE0 exchange-correlation functionals was compared for various electronic and phonon-related properties. 3d transition metal oxides such as Cu$_2$O are known to be a challenging case for pure GGA functionals and in comparison to GGA-PBE the PBE0 hybrid functional clearly improves the description of both electronic and phonon-related properties. The most striking difference is found in the lattice thermal conductivity, where GGA unde…
The lattice constants of Strontium titanate perovskite has been studied using the Density functional theory formalism at the PBE and the HSE levels of theory. The study has been done in all the 3 existing phases; namely cubic, orthorhombic and tetragonal, however, experimental details are available only for the cubic phase so far.
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 …
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…
We show that a naive treatment of open-shell systems in hybrid density functional calculations ignoring the spin dependence causes significant errors due to a kind of self interaction that is not emerged in spin-dependent calculations. As numerical examples, we compare the results of the LDA, GGA, and PBE0 calculations on the ionization potential and electron affinity of C$_{60}$ molecule and the GGA and HSE calculations on the singly charged monovacancy in crystalline Si.
The low energy band structure near the band gap determines the electrical performance of thermoelectric materials. Here, by using the hybrid-density functional theory (hybrid-DFT) calculations, we calculate the low energy band structure of Bi2Te3, Sb2Te3, Bi2Se3 and Sb2Se3 in tetradymite phase. We find that the band structure characteristics are very sensitive the selection of the exchange energy functional. The predictability of the band gaps and band degeneracies is not enhanced in hybrid-DFT calculations, as compared to DFT calculations. The poor prediction of low energy band structures is …
The repercussions of an inaccurate account of electronic states near the Fermi level EF by hybrid functionals in predicting several important metallic properties are investigated. The diffculties in- clude a vanishing or severely suppressed density of states (DOS) at EF, significantly widened valence bandwidth, greatly enhanced electron-phonon (el-ph) deformation potentials, and an overestimate of magnetic moment in transition metals. The erroneously enhanced el-ph coupling calculated by hybrid functionals may lead to a false prediction of lattice instability. The main culprit of the problem c…
Boltzmann transport calculations based on band structures generated with density functional theory (DFT) are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense ${\it k}$-point sampling of the Brillouin zone and are therefore typically limited to the generalized gradient approximation (GGA), whereas more accurate methods such as hybrid functionals would have been preferable. GGA variants, however, generally underestimate the band gap. While premature onset of minority carriers can be avoided with scissor corrections…
The shortcomings of semi-local and hybrid functionals: what we can learn from surface science studies
A study of the adsorption of CO on late 4d and $5d$ transition metal (111) surfaces (Ru, Rh, Pd, Ag, Os, Ir, and Pt) considering atop and hollow site adsorption is presented. The applied functionals include the gradient corrected PBE and BLYP functional, and the corresponding hybrid Hartree-Fock density functionals HSE and B3LYP. We find that PBE based hybrid functionals (specifically HSE) yield, with the exception of Pt, the correct site order on all considered metals, but they also considerably overestimate the adsorption energies compared to experiment. On the other hand, the semi-local BLY…
A self-consistent scheme for determining the optimal fraction of exact exchange for full-range hybrid functionals is presented and applied to the calculation of band gaps and dielectric constants of solids. The exchange-correlation functional is defined in a similar manner to the PBE0 functional, but the mixing parameter is set equal to the inverse macroscopic dielectric function and it is determined self-consistently by computing the optimal dielectric screening. We found excellent agreement with experiments for the properties of a broad class of systems, with band gaps ranging between 0.7 an…
Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)--- an accurate many body theory--- is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI$_3$, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approxi…
We apply a stochastic version of an optimally tuned range-separated hybrid functional to provide insight on the electronic properties of P- and B- doped Si nanocrystals of experimentally relevant sizes. We show that we can use the range-separation parameter for undoped systems to calculate accurate results for dopant activation energies. We apply this strategy for tuning functionals to study doped nanocrystals up to 2.5 nm in diameter at the hybrid functional level. In this confinement regime, the P- and B- dopants have large activation energies and have strongly localized states that lie deep…
In this work we investigate the electronic properties of mercaptocarboxylic acids with several carbon chain lengths adsorbed on ZnO-(10-10) surfaces via density functional theory calculations using semi-local and hybrid exchange-correlation functionals. Amongst the investigated structures, we identify the monodentate adsorption mode to be stable. Moreover, this mode introduces optically active states in the ZnO gap, is further confirmed by the calculation of the dielectric function at PBE0 and TD-PBE0 levels. One interesting finding is that adsorption mode and the dielectric properties of the …
Adsorption of small ligands on semiconductor surfaces is a possible route to modify these surfaces so that they can be used in biosensing and optoelectronic devices. In this work we perform density-functional theory calculations of electronic and optical properties of small ligands on GaN-(10$\bar1$0) surfaces. From the investigated anchor groups we show that thiol groups introduce states into the GaN band gap. However, these state are not optically active, at least for these perfect surfaces. This means that more realistic surfaces need to be considered to suggest how surface modification can…
The crystalline structure of ground-state orthorhombic SrRuO$_3$ is reproduced by applying hybrid density functional theory scheme to the functionals based on the revised generalized-gradient approximations for solid-state calculations. The amount of Hartree-Fock (HF) exchange energy is varied in the range of $5-20\%$ in order to systematically ascertain the optimum value of HF mixing which in turn ensures the best correspondence to the experimental measurements. Such investigation allows to expand the set of tools that could be used for the efficient theoretical modelling of, for example, onl…
Anatase and brookite are robust materials with enhanced photocatalytic properties. In this study, we used density functional theory (DFT) with a hybrid functional and the Hubbard on-site potential methods to determine electron and hole polaron geometries for anatase and brookite and their energetics. Localized electron and hole polarons were predicted not to form in anatase using DFT with hybrid functionals. In contrast, brookite formed both electron and hole polarons. The brookite electron-polaronic solution exhibits coexisting localized and delocalized states, with hole polarons mainly dispe…
We investigate band gaps, equilibrium structures, and phase stabilities of several bulk polymorphs of wide-gap oxide semiconductors ZnO, TiO2,ZrO2, and WO3. We are particularly concerned with assessing the performance of hybrid functionals built with the fraction of Hartree-Fock exact exchange obtained from the computed electronic dielectric constant of the material. We provide comparison with more standard density-functional theory and GW methods. We finally analyze the chemical reduction of TiO2 into Ti2O3, involving a change in oxide stoichiometry. We show that the dielectric-dependent hybr…
First-principles simulations of electronic properties of hybrid inorganic/organic interfaces are challenging, as common density-functional theory (DFT) approximations target specific material classes like bulk semiconductors or gas-phase molecules. Taking as a prototypical example anthracene physisorbed on monolayer MoS$_2$, we assess the ability of different \textit{ab initio} schemes to describe the electronic structure using semi-local and hybrid DFT. For the latter, an unconstrained three-parameter range-separation scheme is employed. Comparisons against many-body perturbation theory resul…
A combined approach of first-principles density-functional calculations and the systematic cluster-expansion scheme is presented. The dipole, quadrupole, and Coulomb matrix elements obtained from ab initio calculations are used as an input to the microscopic many-body theory of the excitonic optical response. To demonstrate the hybrid approach for a nontrivial semiconductor system, the near-bandgap excitonic optical absorption of rutile TiO2 is computed. Comparison with experiments yields strong evidence that the observed near-bandgap features are due to a dipole-forbidden but quadrupole-allow…
We derive first- and second-order piezoelectric coefficients for the zinc-blende III-V semiconductors, {Al,Ga,In}-{N,P,As,Sb}. The results are obtained within the Heyd-Scuseria-Ernzerhof hybrid-functional approach in the framework of density functional theory and the Berry-phase theory of electric polarization. To achieve a meaningful interpretation of the results, we build an intuitive phenomenological model based on the description of internal strain and the dynamics of the electronic charge centers. We discuss in detail first- and second-order internal strain effects, together with strain-i…
Hybrid functionals' non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a know drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact excha…
Roles of oxygen vacancies on ferromagnetism in Ni doped In2O3: A hybrid functional study
采用基于杂化泛函理论的第一性原理计算研究了氧空位对Ni掺杂In $_2$ O $_3$电子和磁性的影响.结果表明，Ni掺杂的In $_2$ O $_3$体系具有铁磁半导体特性。然而，氧空位的存在下，在相邻的Ni对之间的反铁磁耦合的氧空位桥接。反铁磁耦合被认为是由于强烈的Ni 3d-O 2 p杂化的超交换的主导作用。因此，氧空位在Ni：In $_2$ O $_3$多晶样品的较低饱和磁化强度中起关键作用，如在实验中观察到的。
Band gap tuning and dielectric properties of small organic ligands adsorbed on tin monolayers (stanene) have been investigated using first-principles calculations. Charge density analysis using density-functional theory shows that the ligands are chemisorbed on stanene and some of the groups can open a band gap in the originally metallic statene. Furthermore many-body GW calculations demonstrate that the dielectric properties of bare and ligand adsorbed stanene have a large anisotropy. Our findings of a finite gap opens a path for rational theoretical design of functionalized two-dimensional s…
Hybrid-functional calculations with plane-wave basis sets: The effect of the singularity correction on total energies, energy eigenvalues, and defect energy levels
Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding - when not out of reach - if high quality basis sets are used. We present a highly efficient multiple GPU implementation of the exact exchange operator which allows hybrid functional density-functional theory calculations with systematic basis sets without additional approximations for up to a thousand atoms. This method is implemented in a portable real-space-based algorithm, released as an open-source package. With such a framewo…
We investigate the long-standing problem of the hole localization at the Al impurity in quartz SiO$_2$, using a relatively recent DFT hybrid-functional method in which the exchange fraction is obtained \emph{ab initio}, based on an analogy with the static many-body COHSEX approximation to the electron self-energy. As the amount of the admixed exact exchange in hybrid functionals has been shown to be determinant for properly capturing the hole localization, this problem constitutes a prototypical benchmark for the accuracy of the method, allowing one to assess to what extent self-interaction ef…
