We propose approximations which go beyond the local density approximation for the short-range exchange and correlation density functionals appearing in a multi-determinantal extension of the Kohn-Sham scheme. A first approximation consists in defining locally the range of the interaction in the correlation functional. Another approximation, more conventional, is based on a gradient expansion of the short-range exchange-correlation functional. Finally, we also test a short-range generalized-gradient approximation by extending the Perdew-Burke-Ernzerhof exchange-correlation functional to short-range interactions.
We develop relativistic short-range exchange energy functionals for four-component relativistic range-separated density-functional theory using a Dirac-Coulomb Hamiltonian in the no-pair approximation. We show how to improve the short-range local-density approximation exchange functional for large range-separation parameters by using the on-top exchange pair density as a new variable. We also develop a relativistic short-range generalized-gradient approximation exchange functional which further increases the accuracy for small range-separation parameters. Tests on the helium, beryllium, neon, …
Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to d…
A generalized exchange-correlation functional: the Neural-Networks approach
A Neural-Networks-based approach is proposed to construct a new type of exchange-correlation functional for density functional theory . It is applied to improve B3LYP functional by taking into account of high-order contributions to the exchange-correlation functional. The improved B3LYP functional is based on a neural network whose structure and synaptic weights are determined from 116 known experimental atomization energies, ionization potentials, proton affinities or total atomic energies which were used by Becke in his pioneer work on the hybrid functionals [J. Chem. Phys. ${\bf 98}$ , 5648…
In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals, and we discuss the main families of approximations for the exchange-correlation energy: semilocal approximations, single-determinant hybrid approximations, multideterminant hybrid approximations, dispersion-corrected approximations, as well as orbital-dependent exchange-correlation density functionals. The chapter aims at providing both a consistent bird's-eye…
Water on BN doped benzene: A hard test for exchange-correlation functionals and the impact of exact exchange on weak binding
密度泛函理论（DFT）对弱相互作用复合物的研究主要集中在范德华色散力的重要性上，而对交换作用的研究则少之又少。在这里，通过利用水和硼和氮掺杂的苯衍生物（1，2-氮杂硼）之间的微妙的结合，我们展示了如何精确的交换可以改变复杂的结合构象。基准值已经计算了三个方向的水单体的1，2-氮杂硼杂环从明确相关的量子化学方法，我们也使用扩散量子蒙特卡罗。对于一个流行的DFT交换相关泛函的主机，我们表明，缺乏确切的交换导致错误的最低能量方向的水对1，2-氮杂硼杂环。因此，我们建议，高比例的确切交换和相关的电子结构的改善可能需要掺杂表面上的物理吸附位点和复杂的有机分子的准确预测。同时，为了预测正确的绝对相互作用能，需要通过色散包含泛函来增强对交换的准确描述，并且某些非局部范德华泛函（optB 88-和optB 86 b-vdW）对于绝对相互作用能表现得非常好。通过与水在苯和环硼氮烷（B $_3$ N $_3$ H $_6$）上的比较，我们表明这些结果可能对水与掺杂石墨烯表面的相互作用具有影响，并提出了调节相互作用能的可能方式。
University of Oxford（牛津大学）；STFC Rutherford Appleton Laboratory（科学技术设施委员会卢瑟福·阿普尔顿实验室）
Improving the predictive capability of molecular properties in ab initio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum chemistry modelling remains severely limited by the scarcity and heterogeneity of appropriate experimental data. Here we show how training a neural network to replace the exchange-correlation functional within a fully-differentiable three-dimensional Kohn-Sham density functional theory (DFT) framework can greatly improve simulation accuracy. Using only eight ex…
Density-gradient-free variable in exchange-correlation functionals for detecting inhomogeneities in the electron density
提出了密度泛函理论中交换和关联泛函的另一种近似形式。该近似依赖于变量$u$，该变量能够在不使用$ρ$的衍生物的情况下检测电子密度$ρ$中的不均匀性。相反，$u$取决于轨道能量，轨道能量也可以用来测量系统与均匀电子气的区别。从Perdew，Burke和Ernzerhof（PBE）的功能开始[Phys. Rev. Lett. 77，3865（1996）]，构造了依赖于$u$的泛函。对固体的晶格常数、体积模量和内聚能的测试表明，这种$u$依赖的PBE样泛函平均与原始PBE或其固态版本PBESol一样准确。由于$u$比广义梯度近似（GGA）的泛函（如元GGA中使用的PBE和$α$）中使用的约化密度梯度$s$具有更大的非局域性，因此它肯定会对未来更精确的交换相关泛函的发展有用。
Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that, for non-empirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define a nov…
Van-der-Waals exchange-correlation functionals and their high pressure and warm dense matter applications
Helmholtz-Zentrum Dresden-Rossendorf e.V. (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心）；Michigan State University（密歇根州立大学）；University of Iowa（爱荷华大学）；Center for Advanced Systems Understanding (CASUS)（高级系统理解中心）
Density functional theory (DFT) is one of the primary approaches to get a solution to the many-body Schrodinger equation. The essential part of the DFT theory is the exchange-correlation (XC) functional, which can not be obtained in analytical form. Accordingly, the accuracy improvement of the DFT is mainly based on the development of XC functional approximations. Commonly, they are built upon analytic solutions in low- and high-density limits and result from quantum Monte Carlo or post-Hartree-Fock numerical calculations. However, there is no universal functional form to incorporate these dat…
Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a time-\textit{independent} extension of density-functional theory (DFT) which allows to compute excited-state energies via the derivatives of the ensemble energy with respect to the ensemble weights. Contrary to the time-dependent version of DFT (TD-DFT), double excitations can be easily computed within GOK-DFT. However, to take full advantage of this formalism, one must have access to a \textit{weight-dependent} exchange-correlation functional in order to model the infamous ensemble derivative contribution to the exc…
Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends monotonically upon N, and the N-> infinity limit is a bound for all N. These bounds have been shown to apply to the exact density functionals for the exchange- and exchange-correlation energies that must be approximated for an accurate and computationally efficient description of atoms, molecules, and solids. A tight bound on the exact exchange energy has been derived …
