We present a formulation and implementation of the DFT+\textit{U} method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure calculations but also provides access to atomic forces and stresses, hence allowing for full structure relaxations of periodic systems. Furthermore, our implementation allows one to deal with non-collinear spin texture, with the spin-orbit coupling (SOC) effect treated self-consistently. The key aspect behind our implementation is a suitable definition of the correlated subspace when multiple atomic orbitals with the same angular momentum are used, and this is addressed via the "Mulliken charge projector" constructed in terms of the first (most localized) atomic orbital within the $d/f$ angular momentum channel. The important Hubbard $U$ and Hund $J$ parameters can be estimated from a screened Coulomb potential of the Yukawa type, with the screening parameter either chosen semi-empirically or determined from the Thomas-Fermi screening model. Benchmark calculations are performed for four late transition metal monoxide bulk systems, i.e., MnO, FeO, CoO, and NiO, and for the 5$d$-electron compounds IrO$_2$. For the former type of systems, we check the performance of our DFT+$U$ implementation for calculating band gaps, magnetic moments, electronic band structures, as well as forces and stresses; for the latter, the efficacy of our DFT+$U$+SOC implementation is assessed. Systematic comparisons with available experimental results, and especially with the results from other implementation schemes are carried out, which demonstrate the validity of our NAO-based DFT+$U$ formalism and implementation.
Pseudopotentials for Orbital-Free DFT: Capturing Nonlocality and Correcting Functional Approximants
Rutgers University（罗格斯大学）；University of Ibadan（伊巴丹大学）；Jilin University（吉林大学）；East African Institute for Fundamental Research (EAIFR), University of Rwanda（卢旺达大学东非基础研究院）；Lira University（利拉大学）
First-principles DFT study for the structural stability of Hydrogen passivated graphene (H-graphene) and atomic adsorption of oxygen on H-graphene with different schemes
Among the numerous 2D system that can be prepared via exfoliation, iron phosphorus trisulfide (FePS3) attracts a lot of attention recently due to its broad-range photoresponse, its unusual Ising-type magnetic order and possible applications in spintronic nano-devices. Despite various experimental and theoretical-computational reports, there are still uncertainties in identifying its magnetic ground state. In this paper, we investigate the structural and magnetic properties of single-layer FePS3 by using Density Functional Theory. Our findings show that orbital ordering leads to a variation in …
Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso
实现轨道自由能泛函的专业代码和耦合的专业与量子咖啡代码进行说明。这种结合使得无轨道DFT能够在相同的基础上（算法、恒温器、收敛参数等）驱动从头计算分子动力学模拟。对于Kohn-Sham（KS）DFT。所有实现的非相互作用自由能泛函都是单点的：局域密度近似（LDA;也称为有限T梯度-费米，ftTF），二阶梯度近似（SGA或有限T梯度校正TF），以及我们最近引入的有限T广义梯度近似（ftGGA）。通过无轨道方法消除KS轨道瓶颈使得在普通计算机上进行高T模拟成为可能，而对于KS分子动力学（MD）来说，在非常高性能的计算机系统上进行这些模拟将是昂贵的甚至是非常耗时的。报告了在2，000 K <= T <= 4，000，000 K的温度范围内对H进行的示例MD模拟，时间为小型集群（16-128个核心）甚至笔记本电脑。相对于KS驱动的计算，无轨道计算的速度在几倍到几百倍之间。
The unequal electronic occupation of localized orbitals (orbital polarization), and associated lowering of symmetry and degeneracy, play an important role in the properties of transition metal oxides. Here, we examine systematically the underlying origin of orbital polarization, taking as exemplar the 3$d$ manifold of Co$^{2+}$ in a variety of spin, orbital and structural phases in the double perovskite La$_2$CoTiO$_6$ and the (001) superlattice (LaCoO$_3$)$_1$+(LaTiO$_3$)$_1$ systems. Superlattices are of specific interest due to the large experimentally observed orbital polarization of their…
Orbital-free density functional theory (OF-DFT) runs at low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations. It is generally considered that OF-DFT strictly requires the use of local pseudopotentials, rather than orbital-dependent nonlocal pseudopotentials, for the calculation of electron-ion interaction energies, as no orbitals are available. This is unfortunate situation since the nonlocal pseudopotentials are known to give much better transferability and calculation accuracy than local ones. We report here t…
We study the dependence of kinetic energy densities (KED) on density-dependent variables that have been suggested in previous works on kinetic energy functionals (KEF) for orbital-free DFT (OF-DFT). We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KED for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature. This is achieved with weighted fitti…
While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AO) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participa…
Doping of Si using the scanning probe hydrogen depassivation lithography technique has been shown to enable placing and positioning small numbers of P atoms with nanometer accuracy. Several groups have now used this capability to build devices that exhibit desired quantum behavior determined by their atomistic details. What remains elusive, however, is the ability to control the precise number of atoms placed at a chosen site with 100% yield, thereby limiting the complexity and degree of perfection achievable. As an important step towards precise control of dopant number, we explore the adsorp…
Disordered elemental semiconductors, most notably a-C and a-Si, are ubiquitous in a myriad of different applications. These exploit their unique mechanical and electronic properties. In the past couple of decades, density functional theory (DFT) and other quantum mechanics-based computational simulation techniques have been successful at delivering a detailed understanding of the atomic and electronic structure of crystalline semiconductors. Unfortunately, the complex structure of disordered semiconductors sets the time and length scales required for DFT simulation of these materials out of re…
DFT-Assisted Investigation of the Electric Field and Charge Density Distribution of Pristine and Defective 2D WSe$_2$ by Differential Phase Contrast Imaging
Upscaling DFT-trained machine-learning interatomic potential toward Quantum Monte Carlo accuracy: Sulfur-vacancy migration in monolayer MoS$_2$ as a testbed
Institute of Informatics, Slovak Academy of Sciences（斯洛伐克科学院信息学研究所）；Faculty of Informatics and Information Technologies, Slovak University of Technology（斯洛伐克技术大学信息技术学院）；Computational Science Division, Argonne National Laboratory（阿贡国家实验室计算科学部）；Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）
Orbital-Free DFT-Assisted Machine-Learned Molecular Dynamics for Electric-Field-Driven Ionic Transport
The University of Tokyo（东京大学）；Quemix Inc.（Quemix公司）；Idemitsu Kosan Co., Ltd.（出光兴产株式会社）；National Institutes for Quantum Science and Technology (QST)（量子科学技术研究机构）
The self-consistent charge density functional tight-binding (DFTB) theory study of carbon adatoms using tuned Hubbard U parameters
Institute of Atomic and Molecular Physics, Jilin University（吉林大学原子与分子物理研究所）；Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy (Jilin University)（吉林大学应用原子分子光谱学吉林省重点实验室）
MinSurf: resolving the atomic-scale stability landscape of mineral surfaces
School of Transportation Science and Engineering, Harbin Institute of Technology（哈尔滨交通科学与工程学院）；Chongqing Research Institute of HIT（哈尔滨工业大学重庆研究院）；School of Science, Harbin Institute of Technology, Shenzhen（哈尔滨深圳科学技术学院）；National Engineering Laboratory for Reducing Emissions from Coal Combustion, Shandong University（山东大学煤炭燃烧减排国家工程实验室）；Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University（香港理工大学土木与环境工程系）；School of Highway, Chang’an University（长安大学公路学院）
We present the One-orbital Ensemble Self-Consistent Field (OE-SCF) method, an {alternative} orbital-free DFT solver that extends the applicability of DFT to system sizes beyond the nanoscale while retaining the accuracy required to be predictive. OE-SCF is an iterative solver where the (typically computationally expensive) Pauli potential is treated as an external potential and updated after each iteration. Because only up to a dozen iterations are needed to reach convergence, OE-SCF dramatically outperforms current orbital-free DFT solvers. Employing merely a single CPU, we carried out the la…
Fuzzy band structure of quantum dots by Bloch Orbital Expansion, unconventional insights into geometry-electronic structure relations
Ghent University（根特大学）；Basque Center for Materials, Applications, and Nanostructures（巴斯克材料、应用与纳米结构中心）；UPV/EHU Science Park（巴斯克理工大学/巴斯克大学科学园）；Ikerbasque Basque Foundation for Science（伊卡巴斯科巴斯克科学基金会）
Shell-correction and orbital-free density-functional methods for finite systems
基于密度泛函理论（DFT）的无轨道（OF）方法有望显著提高计算速度。在这一领域，精确的动能密度泛函的发展仍然是一个悬而未决的问题。在这一章中，我们回顾了最初应用于核物理的壳层校正方法（SCM，通常称为Strutinsky平均法）及其在DFT背景下的最新表述[Yannouleas和Landman，Phys. Rev. B 48，8376（1993）]。我们通过其早期的应用程序，凝聚态有限系统，包括金属簇，富勒烯，和金属纳米线的DFT-SCM方法。DFT-SCM结合了量子力学干涉效应，从而提供了一个改进相比，使用的F-DFT中的F-Fermi型动能密度泛函。
Density functional theory plus $U$ (DFT+$U$) is one of the most efficient first-principles methods to simulate the cold pressure properties of strongly-correlated materials. However, the applicability of DFT+$U$ at ultra-high pressure is not sufficiently studied, especially in the widely-used augmented schemes [such as projector augmented wave (PAW) and linearized augmented plane wave (LAPW)]. This work has systematically investigated the performance of DFT+$U$ in PAW and LAPW at the pressure up to several hundred GPa for the lanthanide metals, which is a typical strongly-correlated series. We…
