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 and the hole around the electron. It is also different in the way it interpolates between the rapidly varying iso-orbital density and the slowly varying density, which is determined by the wave vector analysis based on the exactly solvable infinite barrier model for jellium surface. Our numerical tests show that the exchange hole generated from this model mimics the conventional exact exchange hole quite well for atoms. Finally, as a simple application, we apply the hole model to construct a TPSS-based range-separation functional. Our tests show that this TPSS-based range-separation functional can substantially improve TPSS band gaps and barrier heights, without losing much accuracy of molecular atomization energies.
Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions
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…
Assessing The Band Gap Problem By Improving Upon The Semilocal Exchange Hole Potential
一种类似于Becke-Schlosel [A. D. Becke和M. R.通过使用基于密度矩阵展开的广义坐标变换对交换孔进行建模来构造[Escherssel，Phys.Rev.A39，3761（1989）]。模型势是拉普拉斯自由的，系统中存在的不均匀性被包括在动量矢量中，而不影响均匀密度极限。与模型交换孔相关的参数与球形原子拟合。新构造的势函数与Tran-Blaha修正的Becke-Johnson势函数（TBMBJ）[F. Tran和P. Blaha，Phys. Rev. Lett. 102，226401（2009）]电势相当精确地产生从半导体到绝缘体的各种材料的带隙。与TBMBJ和其他标准半局域交换泛函相比，带隙的结果得到了改善。
Correct and accurate polymorphic energy ordering of transition-metal monoxides obtained from semilocal and onsite-hybrid exchange-correlation approximations
Assessing the performance of the recent non-empirical semilocal density functionals on describing the lattice constants, bulk moduli and cohesive energies of alkali, alkaline-earth, and transition metals
在最近开发的元GGA（元广义梯度近似）半局域交换相关泛函的框架内，研究了碱金属、碱土金属和过渡金属的体性质（晶格常数、体模量和结合能）。为了建立元GGA泛函的适用性，广泛性和准确性，我们还把PBE（Perdew-Burke-Ernzerhof）和PBESol（PBE reparametrized for solids）泛函的结果。本论文的有趣的特点是，它测量最近开发的TM（陶-莫）和TMTPSS（TM交换与陶-Perdew-Staroverov-Scuseria（TPSS）相关）和SCAN（强约束和适当赋范）泛函描述上述属性的准确性。本系统的调查表明，TM是准确的，而在描述的晶格常数的内聚能和体积模量的准确性是偏向PBE和TPSS泛函。
Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids
泡利动能增强因子$α=(τ-τ^W)/τ^{unif}$是一个重要的密度成分，用于构造许多元广义梯度近似（meta-GGA）交换相关（XC）能量泛函，包括非常成功的强约束和适当赋范（SCAN）半局部泛函。最近还提出了另一种称为MGGAC的元GGA泛函[Phys. Rev. B 100，155140（2019）]，其仅取决于$α$成分，并基于Becke-Bessel方法与无尖氢交换空穴密度的推广。MGGAC泛函被证明是一个非常有用的和有竞争力的meta-GGA半局部泛函的固体和分子的电子结构性质。在成功引入$α$的基础上，我们提出了修正的MGGAC交换泛函的相关能，该泛函更精确、更稳健，尤其适用于均匀密度标度的高、低密度极限.目前XC功能，命名为修订MGGAC（rMGGAC），显示了令人印象深刻的改善固体的结构和能量性质相比，其以前的版本。此外，本构造的功能的评估表明是非常有用的固态物理在解决当前具有挑战性的固态问题。
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）
Improved electronic structure prediction of chalcopyrite semiconductors from a semilocal density functional based on Pauli kinetic energy enhancement factor
d电子的正确处理是至关重要的，以预测原型黄铜矿半导体的电子性质。d态的影响与阴离子位移参数u有关，这反过来又影响这些系统的带隙。半局域交换相关泛函产生良好的半导体和绝缘体的结构特性，往往无法预测合理的u，因为d电子之间的强相互作用所产生的带隙的低估。在本研究中，我们表明，从无尖氢密度（MGGAC）[Phys. Rev. B 100，155140（2019）]获得的亚广义梯度近似（meta-GGA）在理解黄铜矿电子性质的关键特征方面有所改进，其带隙与使用最先进的混合方法获得的带隙相当。此外，本评估还显示了泡利动能增强因子，$α=(τ-τ^W)/τ^{unif}$在描述黄铜矿中的d电子的重要性。本研究强烈表明，MGGAC功能内半局部近似可以是一个更好的和首选的选择，研究黄铜矿和其他固态系统，由于其优越的性能和显着低的计算成本。
RS-CIDER: A non-local machine learning model for approximating screened hybrid functionals
Center for Computational Science and Engineering, Massachusetts Institute of Technology（麻省理工学院计算科学与工程中心）；Department of Materials Science and Engineering, Massachusetts Institute of Technology（麻省理工学院材料科学与工程系）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Robert Bosch LLC Research and Technology Center, Watertown（罗伯特博世有限责任公司研究和技术中心）；Initiative for Computational Catalysis, Flatiron Institute（平顿研究所计算催化倡议）
Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors
Machine-learned exchange-correlation functionals for molecules, solids, and reactive surfaces
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）；Robert Bosch LLC Research and Technology Center（罗伯特博世有限责任公司研究与技术中心）；Initiative for Computational Catalysis, Flatiron Institute（计算催化倡议，平顿研究所）
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。
Efficient and improved prediction of the band offsets at semiconductor heterojunctions from meta-GGA density functionals
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）
