Semilocal exchange-correlation functionals are the most accurate, realistic and widely used ones to describe the complex many-electron effects of two-dimensional quantum systems. Beyond local density approximation, the generalized gradient approximations(GGAs) are designed using reduced density gradient as main ingredient. An enhancement factor is constructed using the inhomogeneity parameter of GGAs by taking care of the low and high density behaviors of it. Thus, the exchange energy functional proposed by making use of the aforementioned enhancement factor, significantly reduces the error compare to the previously proposed gradient approximations. Another enhancement factor and corresponding energy functional is also constructed using the inhomogeneity parameter originally introduced by Becke [J. Chem. Phys. 109, 2092 (1998)]. Comprehensive testing and performance of both the functionals are demonstrated with respect to the exact exchange formalism by considering two-dimensional parabolically confined quantum dots with varying particle number and confinement strength as a test case.
The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate technique to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In…
An asymptotic corrected exchange hole potential analogous to Becke-Roussel [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)] is constructed by modeling the exchange hole using the generalized coordinate transformation based on density matrix expansion. The model potential is Laplacian free and the inhomogeneity present in the system is included in the momentum vector without affecting the uniform density limit. The parameters associated with the model exchange hole are fitted with the spherical atoms. The newly constructed potential along with Tran-Blaha modified Becke-Johnson (TBM…
We assess the performance of Tao-Mo semilocal exchange correlation (TM) functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using projector-augmented-wave method with the plane wave basis set in Vienna ab initio simulation package (VASP). The meta-GGA level semilocal functional TM is an all purpose exchange-correlation functional which performs accurately for the wide range of molecular and solid state properties. The exchange functional part of TM is designed from the density matrix expansion (DME) technique together with the slowly varying fourth order gradient expansion. The …
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…
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semiloca…
The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and NiO). This is done in the framework of the linearized augmented plane-wave method, which allows for a very accurate all-electron solution of electronic structure problems in solids. In order to assess the ability of the semilocal potentials to approximate the EXX-OEP, we considered the EXX total energy, electronic structure, electric-field gradient, and mag…
The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct ground state of MnO. The relative energy differences of zinc-blende (zb) …
The correct treatment of d electrons is of prime importance in order to predict the electronic properties of the prototype chalcopyrite semiconductors. The effect of d states is linked with the anion displacement parameter u, which in turn influences the bandgap of these systems. Semilocal exchange-correlation functionals which yield good structural properties of semiconductors and insulators often fail to predict reasonable u because of the underestimation of the bandgaps arising from the strong interplay between d electrons. In the present study, we show that the meta-generalized gradient ap…
Recently, Tao and Mo developed a new nonempirical semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density matrix expansion corrected to reproduce the fourth-order gradient expansion in the slowly varying limit, while the correlation part is based on the TPSS correlation model with a modification for the low-density limit. In the present work, the Tao-Mo functional is assessed by calculations on a variety of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 7 cohesive energies, and jellium surface exchange …
Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional $E_{\text{xc}}$ and/or potential $v_{\text{xc}}$. Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and …
A long range corrected range separated hybrid functional is developed based on the density matrix expansion (DME) based semilocal exchange hole with Lee-Yang-Parr (LYP) correlation. An extensive study involving the proposed range separated hybrid for thermodynamic as well as properties related to the fractional occupation number is compared with different BECKE88 family semilocal, hybrid and range separated hybrids. It has been observed that using Kohn-Sham kinetic energy dependent exchange hole several properties related to the fractional occupation number can be improved without hindering th…
In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015)]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In the present work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal appr…
Recently, Tao and Mo (TM) proposed an accurate all-purpose nonempirical meta-generalized gradient approximation (meta-GGA). The exchange part was derived from the density matrix approximation, while the correlation part is based on a modification of TPSS correlation in the low-density or strong-interaction limit. To further understand this density functional, we combine the TM exchange part with the original TPSS correlation and make a comprehensive assessment of this combination, which we call TMTPSS functional, on solids and solid surfaces. Our test includes 22 lattice constants and bulk mod…
The modern semilocal exchange potential is an accurate and efficient approximation to the exact exchange potential of density functional theory. We tried to combine it with the dynamical mean-field theory to derive a new first-principles many-body approach for studying correlated electronic materials. As a paradigm, this approach was employed to investigate the electronic structures and optical properties of strongly correlated ionic insulator YbS. Compared to the standard density functional theory plus dynamical mean-field theory which surprisingly failed to give an insulating solution, the n…
The positive definite Kohn-Sham kinetic energy(KS-KE) density plays crucial role in designing semilocal meta generalized gradient approximations(meta-GGAs) for low dimensional quantum systems. It has been rigorously shown that near nucleus and at the asymptotic region, the KE-KS differ from its von Weizsäcker(VW) counterpart as contributions from different orbitals (i.e., s and p orbitals) play important role. This has been explored using two dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients with different physical behaviors are also constructed and…
The bulk properties (lattice constants, bulk moduli, and cohesive energies) of alkali, alkaline-earth, and transition metals are studied within the framework of the recently developed meta-GGA (meta-Generalized Gradient Approximation) semilocal exchange-correlation functionals. To establish the applicability, broadness and accuracy of meta-GGA functionals we also put the results of PBE (Perdew-Burke-Ernzerhof) and PBEsol (PBE reparametrized for solids) functionals. The interesting feature of the present paper is that it measures the accuracy of the recently developed TM (Tao-Mo) and TMTPSS (TM…
Exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional, but also serves as a local ingredient in nonlocal range-separation density functional. However, due to the nonlocal nature, modelig the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The present model is distinct from previous models at small separation between an electron…
The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-GGA (meta-generalized gradient approximation) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of appropriate norms, including rare-gas atoms and nonbonded interactions. This SCAN (strongly constrained and appropriately normed) meta-GGA achieves remarkable accuracy for systems where…
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the non-locality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the image-like surface asymptotics of both the exchange-correlat…
The Pauli kinetic energy enhancement factor $α=(τ-τ^W)/τ^{unif}$ is an important density ingredient, used to construct many meta-generalized gradient approximations (meta-GGA) exchange-correlation (XC) energy functionals, including the very successful strongly constrained and appropriately normed (SCAN) semilocal functional. Another meta-GGA functional, known as MGGAC [Phys. Rev. B 100, 155140 (2019)], is also proposed in recent time depending only on the $α$ ingredient and based on the generalization of the Becke-Roussel approach with the cuspless hydrogen exchange hole density. The MGGAC fun…
It is highlighted recently that the Tao-Mo (TM) [Phys. Rev. Lett. 117, 073001 (2016)] semilocal exchange-correlation energy functional suffers from the order-of-limit problem, which affects the functional performance for phase transition pressures [J. Chem. Phys. 152, 244112 (2020)]. The root of the order-of-limit problem of the TM functional inherent within the interpolation function, which switches between the compact density and the slowly varying density. In this paper, we propose a different switch function that avoids the order-of-limit problem and interpolates correctly between the comp…
Quasi-two-dimensional (2D) systems, such as an electron gas confined in a quantum well, are important model systems for many-body theories. Earlier studies of the crossover from 3D to 2D in ground-state density-functional theory showed that local and semilocal exchange-correlation functionals which are based on the 3D electron gas are appropriate for wide quantum wells, but eventually break down as the 2D limit is approached. We now consider the dynamical case and study the performance of various linear-response exchange kernels in time-dependent density-functional theory. We compare approxima…
Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations
Helmholtz Institut Mainz（亥姆霍兹美因茨研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Institut für Physik, Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学物理研究所）
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。
The accuracy of effective masses predicted by density functional theory depends on the exchange-correlation functional employed, with nonlocal hybrid functionals giving more accurate results than semilocal functionals. In this article, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE), Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials for the calculation of effective masses with perturbation theory. We introduce the mstar60 dataset, which contains 60 effective masses derived from 18 semicond…
Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations and efficient and accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk band gaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performa…
Influence of Exchange-Correlation Functionals and Neural Network Architectures on Li$^+$-Ion Conductivity in Solid-State Electrolyte from Molecular Dynamics Simulations with Machine-Learning Force Fields
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）
We theoretically demonstrate that the ultrafast magnetic order dynamics in antiferromagnets is exchange-enhanced in comparison to their ferromagnetic counterparts. We provide an equation of motion for the magnetic order dynamics validated by computer simulations using atomistic spin dynamics methods. The exchange of angular momentum between sublattices speeds up the dynamics in antiferromagnets, a process absent in ferromagnets.
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…
A revised version of the semilocal exchange-correlation functional [Phys. Rev. Lett. 117, 073001 (2016)] (TM) is proposed by incorporating the modifications to its correlation content obtained from the full high-density second-order gradient expansion as proposed in the case of revised Tao-Perdew-Staroverov-Scuseria (revTPSS) [Phys. Rev. Lett. 103, 026403 (2009)] functional. The present construction improves the performance of TM functional over a wide range of quantum chemical and solid-state properties (thermochemistry and structural). More specifically, the cohesive energies, jellium surfac…
By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve drama…
