High throughput screening of materials for technologically relevant areas, like identification of better catalysts, electronic materials, ceramics for high temperature applications and drug discovery, is an emerging topic of research. To facilitate this, density functional theory based (DFT) calculations are routinely used to calculate the electronic structure of a wide variety of materials. However, DFT calculations are expensive and the computing cost scales as the cube of the number of electrons present in the system. Thus, it is desirable to generate surrogate models that can mitigate these issues. To this end, we present a two step procedure to predict total energies of large three-dimensional systems (with periodic boundary conditions) with chemical accuracy (1kcal/mol) per atom using a small data set, meaning that such models can be trained on-the-fly. Our procedure is based on the idea of the Hohenberg-Kohn map proposed by Brockherde et al. (Nat. Commun, 8, 872 (2017)) and involves two training models: one, to predict the ground state charge density, $ρ(r)$, directly from the atomic structure, and another to predict the total energy from $ρ(r)$. To predict $ρ(r)$, we use many-body correlation descriptors to accurately describe the neighborhood of a grid point and to predict the total energy we use amplitudes of these many-body correlation descriptors. Utilizing the amplitudes of the many-body descriptors allows for uniquely identifying a structure while accounting for constraints, such as translational invariance; additionally, such a formulation is independent of the charge density grid.
Reply to Comment on "On the Original Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for Many-Electron Coulomb Systems" [Szczepanik, W; Dulak, M.; Wesolowski, T. A., Int. J. Quantum Chem. 106 (2006)]
结果表明，W. Szczepanik，M. Dulak和T. A. Wesolowski [Int. J. Quantum Chem.106（2006）]不能令人满意。
Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are discussed, highlighting the dual relationship between the ground-state energy and the universal density functional. Applications of the Lieb variation principle are reviewed, demonstrating how it may be utilized to calculate the Kohn-Sham potential of atoms and molecules, to study the exchange-correlation functional and the adiabatic connection by high-precis…
Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo（奥斯陆大学海勒拉斯量子分子科学中心化学系）；Department of Computer Science, Oslo Metropolitan University（奥斯陆城市大学计算机科学系）
This is a comprehensive review of the strong-interaction limit of density functional theory. It covers the derivation of the limiting strictly correlated electrons (SCE) functional from exact Hohenberg-Kohn DFT, basic aspects of SCE physics such as the nonlocal dependence of the SCE potential on the density, equivalent formulations and the mathematical interpretation as optimal transport with Coulomb cost, rigorous results (including exactly soluble cases), approximations, numerical methods, integration into Kohn-Sham DFT (KS SCE), and applications to molecular systems, an example being that K…
Differentiable but exact formulation of density-functional theory
密度泛函理论中的普适密度泛函$F$是一个复杂的、病态的密度函数，特别是$F$是不可微的，使得许多形式化的处理变得更加复杂。虽然$F$已经在凸分析方面被很好地表征为通过Hohenberg-Kohn和Lieb变分原理与基态能量$E$形成共轭对$(E,F)$，但是$F$仅在其域的小的（但是密集的）集合上是不可微的和次微的。在这篇文章中，我们应用凸分析的工具，Moreau-Yosida正则化，对任何$ε>0$，构造共轭泛函对$({}^ε\!E,{}^ε\!F)$，这些泛函对作为$ε\rightarrow 0^+$处处逐点收敛到$(E,F)$，并且使得${}^ε\!F$是（Fréchet）可微的。由于技术上的原因，我们将注意力限制在有限但大的盒子中的分子电子系统。值得注意的是，在Moreau-Yosida正则化中没有丢失任何信息：物理基态能量$E(v)$可以以简单的方式从正则化的基态能量${}^ε\!E(v)$精确地恢复。与原始$(E,F)$对有关的所有概念和结果在$({}^ε\! E, {}^ε\!F)$的结果中具有直接对应物。Moreau-Yosida正则化因此允许密度泛函理论的精确的、可微的公式化。特别地，利用${}^ε\!F$的可微性，给出了Kohn-Sham理论的严格公式，该公式不受标准Kohn-Sham理论中的非相互作用可表示性问题的影响。
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without them, as illustrated by a calculation on Harmonium. In the regime when the model system approaches the Coulomb system, they allow the calculation of ground states, excited states, and properties, without making use of the Hohenberg-Kohn theorem. A…
By-passing the Kohn-Sham equations with machine learning
Technische Universität Berlin（柏林工业大学）；Max-Planck-Institut für Mikrostrukturphysik（马克斯·普朗克微结构物理研究所）；New York University（纽约大学）；University of California, Irvine（加州大学欧文分校）；Courant Institute of Mathematical Science, New York University（纽约大学库朗数学科学研究所）；NYU-ECNU Center for Computational Chemistry at NYU Shanghai（纽约大学上海纽约大学-华东师范大学计算化学中心）；Korea University（高丽大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
The basic idea of Frozen-Density Embedding Theory (FDET) is the constrained minimisation of the Hohenberg-Kohn density functional $E^{HK}[ρ]$ performed using the auxiliary functional $E_{v_{AB}}^{FDET}[Ψ_A,ρ_B]$, where $Ψ_A$ is the embedded $N_A$-electron wave-function and $ρ_B(\vec{\mathrm{r}})$ a non-negative function in real space integrating to a given number of electrons $N_B$. This choice of independent variables in the total energy functional $E_{v_{AB}}^{FDET}[Ψ_A,ρ_B]$ makes it possible to treat the corresponding two components of the total density using different methods in multi-lev…
Locality of correlation in density functional theory
Hohenberg-Kohn密度泛函很久以前就被证明在非相对论性半经典（或大$Z$）极限下对所有物质都可以简化为Hohenberg-Kohn密度泛函，也就是说，动能变成局域的。在此限制下，Exchange也成为本地的。原子相关能的数值数据支持这样的猜想，即相关性也是如此，但与原子的相关性要小得多。我们说明了如何扩大周围的大粒子数是等同于当地的密度近似和密度泛函近似的强相关性。分析高度精确的原子相关能，我们表明，相关能趋于$-A_c Z ln Z + B_c Z$的$Z$趋于无穷大，其中$Z$是原子序数，$A_c$是已知的，我们估计$B_c$约为37毫哈特树。局部密度近似精确地产生了$A_c$，但是对于$B_c$是一个非常不正确的值，这表明局部近似与单独的相关性不太相关。这个极限是密度泛函近似的非经验构造的基准。我们推测，除了原子，在大$Z$极限的局部密度近似的主要校正一般采取这种形式，但与$B_c$的TF密度的系统的功能。讨论了近似密度泛函的构造的影响。
Machine learning of electronic structure and atomistic properties from the external potential
Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Université Marie et Louis Pasteur, CNRS, LmB (UMR 6623)（玛丽·路易·巴斯德大学，法国国家科学研究中心，LmB（联合研究单位6623））
A new density functional method for electronic structure calculation of atoms and molecules
本章关注的是最近发展的一种新的DFT方法，用于精确、可靠地预测多电子系统。背景，需要这样一个计划，遇到的主要困难，以及他们的潜在补救措施进行了讨论，在一定程度上。在非相对论性Hohenberg-Kohn-Sham（HKS）DFT范围内，利用LCAO-MO原理，数值求解了相应的KS本征值问题。与通常使用的原子中心网格（ACG）不同，这里我们采用三维笛卡尔坐标网格（CCG）来直接在网格上构建原子中心局域基组，电子密度以及所有的两体势。Hartree势是通过傅立叶卷积技术通过分解在短期和长期的相互作用。我们提出的方案的可行性和可行性证明了一系列的化学系统，首先与均匀的，局部密度近似XC泛函，其次是非本地的，梯度和拉普拉斯相关的泛函。详细的，系统的分析所获得的结果相关的量子化学，作出，\emph{for the first time}，使用CCG，这清楚地说明了这种替代方法的意义，在本上下文中。如组分能量、总能量、电离能、势能曲线、原子化能等，的赝势计算，以及与文献数据进行彻底的比较，只要有可能。最后对该方法的发展前景进行了展望。总之，我们提出了一种新的基于CCG的\emph{variational} DFT方法，用于精确、可靠地计算原子和分子。
Enhancing molecular dynamics with equivariant machine-learned densities
BIFOLD and Machine Learning Group, Technische Universität Berlin（BIFOLD与机器学习组，柏林技术大学）；Department of Chemistry, New York University（纽约大学化学系）；Department of Artificial Intelligence, Korea University（韩国大学人工智能系）；Max-Planck-Institut für Informatik（马克斯·普朗克研究所（信息学））；Department of Physics and Astronomy, University of California, Irvine（加州大学 Irvine 分校物理与天文学系）；Department of Chemistry, University of California, Irvine（加州大学 Irvine 分校化学系）；Courant Institute of Mathematical Sciences, New York University（纽约大学数学科学学院）；NYU-ECNU Center for Computational Chemistry at NYU Shanghai（纽约大学上海计算化学中心）
