A scheme is developed for creating pseudopotentials for use in correlated-electron calculations. Pseudopotentials for the light elements H, Li, Be, B, C, N, O, and F, are reported, based on data from high-level quantum chemical calculations. Results obtained with these correlated electron pseudopotentials (CEPPs) are compared with data for atomic energy levels and the dissociation energies, molecular geometries and zero-point vibrational energies of small molecules obtained from coupled cluster single double triple (CCSD(T)) calculations with large basis sets. The CEPPs give better results in correlated-electron calculations than Hartree-Fock-based pseudopotentials available in the literature.
A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li--F, Sc--Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies they provide with all electron results, with all quantities evaluated using coupled cluster singles doubles and triples calculations. Errors inherent in the …
The consistency between the exchange-correlation functional used in pseudopotential construction and in the actual density functional theory calculation is essential for the accurate prediction of fundamental properties of materials. However, routine hybrid density functional calculations at present still rely on GGA pseudopotentials due to the lack of hybrid functional pseudopotentials. Here, we present a scheme for generating hybrid functional pseudopotentials, and we analyze the importance of pseudopotential density functional consistency for hybrid functionals. We benchmark our PBE0 pseudo…
We present a general method of constructing \textit{in-situ} pseodopotentials from first principles, all-electron, full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate. (ii) Replacing the oscillating part of the wavefunction (inside the muffin-tin spheres) of this state, with a smooth function. (iii) Representing the smooth wavefunction in a Fourier series, and (iv) inverting the Kohn-Sham equation, to extract the pseudopotential that pr…
Nowadays pseudopotential density-functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed pseudopotential tables that were built from all-electron atomic calculations using few popular semi-local exchange-correlation functionals, while pseudopotentials based on more modern functionals, like meta-GGA and hybrid functionals, or for many-body methods, such as $GW$, are often not available. Because of this, employing pseudopotentials created with inconsistent exchange-correlation functionals has become a common practice. O…
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills the same smoothness conditions imposed by the Troullier-Martins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials are represented by a polynomial of degree twenty-two. We compare our method to the Troullier-Martins approach in electronic structure calculations for diamond and iron in the bcc structure and find that the two methods perform equally …
Growth in computational resources has lead to the application of real space diffusion quantum Monte Carlo (DMC) to increasingly heavy elements. Although generally assumed to be small, we find that when using standard techniques the pseudopotential localization error can be large, on the order of an electron volt for an isolated cerium atom. We formally show that localization error can be reduced to zero with improvements to the Jastrow factor alone and we define a metric of Jastrow sensitivity that may be useful in the design of pseudopotentials. We employ an extrapolation scheme to extract th…
Structure factors obtained from diffraction experiments are one of the most important quantities for characterizing the electronic and structural properties of materials. Methods for calculating this quantity from plane-wave density functional theory (DFT) codes are typically prohibitively expensive to perform, requiring the electron density to be constructed and evaluated on dense real-space grids. Making use of the projector functions found in both the Vanderbilt ultrasoft pseudopotential and projector augmented wave methods, we implement an approach to calculate structure factors which avoi…
The implementation of ultrasoft pseudopotentials into time-dependent density-functional perturbation theory is detailed for both the Sternheimer approach and the Liouville-Lanczos (LL) method, and equations are presented in the scalar relativistic approximation for periodic solids with finite momentum transfer q. The LL method is applied to calculations of the electron energy loss (EEL) spectrum of face-centered cubic bulk Au both at vanishing and finite q. Our study reveals the richness of the physics underlying the various contributions to the density fluctuation in gold. In particular, our …
Core reconstruction in pseudopotential calculations
本文提出了一种从赝势计算中获得全电子结果的新方法。这是通过使用Inglesfield的嵌入势方法在原子核区域中进行局部计算来实现的[J.Phys. C { \bf 14}，3795（1981）]。在这种方法中，核心区域是\emph{reconstructed}，并且没有进行先前解决该问题所需的简化近似（例如电荷密度/电势的球形对称或冻结核心电子）。嵌入方法需要一个准确的实空间格林函数，并给出了一组数值本征态在构建这个引入的误差分析。结果提出了散装铝的全电子重建，电荷密度和态密度。
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 have implemented recently developed multiple-projector pseudopotentials into the planewave based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller planewave cut-offs while maintaining or improving transferability. This reduces the computational cost of pw-AFQMC, increasing its reach to larger and more complicated systems. We discuss the use of non-local pseudopotentials in the separable Kleinman-Bylander form, and the implementation in pw-AFQMC of the multiple-projector optimized norm-conserving pseudopotential ONCVPSP of Hamann. Th…
Understanding the quantum dynamics of spin defects and their coherence properties requires accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from first-principles calculations. We present a real-space approach based on density functional theory for the calculation of spin-Hamiltonian parameters, where only selected atoms are treated at the all-electron level, while the rest of the system is described with the pseudopotential approximation. Our approach permits calculations for systems containing more than 1000 at…
Internal energies, enthalpies, phonon dispersion curves, and superconductivity of atomic metallic hydrogen are calculated. The (standard) use pseudopotentials in density-functional theory are compared with full (Coulomb)-potential all-electron linear muffin-tin orbital calculations. Quantitatively similar results are found as far as internal energies are concerned. Larger differences are found for phase-transition pressures; significant enough to affect the phase diagram. Electron--phonon spectral functions $α^2 F(ω)$ also show significant differences. Against expectation, the estimated superc…
Accurate structure factors from pseudopotential methods
硅的高精度实验结构因子在文献中是可用的，并且这些为用于构建全电子电荷密度的任何\emph{ab initio}方法提供了理想的测试。在最近的一篇论文中[J. R. Trail和D. M. Bird，Phys. Rev. B { \bf 60}，7863（1999）]已经开发了一种方法，用于通过重建所选原子的核心区域，从第一原理赝势计算获得精确的全电子电荷密度。在这里，这种方法被应用到体硅，结构因子推导和比较实验和全电位线性增强平面波结果（FLAPW）。我们还比较了假设芯区是球对称的结果，并与由赝价密度+冻结芯电子构造电荷密度的结果。这些近似值都不能提供准确的电荷密度。非球面重建被认为是准确的FLAPW的结果，并再现FLAPW和实验结果之间的残余误差。
Norm-conserving pseudopotentials are used by a significant number of electronic-structure packages, but the practical differences among codes in the handling of the associated data hinder their interoperability and make it difficult to compare their results. At the same time, existing formats lack provenance data, which makes it difficult to track and document computational workflows. To address these problems, we first propose a file format (PSML) that maps the basic concepts of the norm-conserving pseudopotential domain in a flexible form and supports the inclusion of provenance information …
Despite the enormous success and popularity of density-functional theory, systematic verification and validation studies are still limited in number and scope. Here, we propose a protocol to test publicly available pseudopotential libraries, based on several independent criteria including verification against all-electron equations of state and plane-wave convergence tests for phonon frequencies, band structure, cohesive energy and pressure. Adopting these criteria we obtain curated pseudopotential libraries (named SSSP or standard solid-state pseudopotential libraries), that we target for hig…
The electron-phonon interaction contribution to the electronic energies is included in density functional total energy calculations with ab initio pseudopotentials via the Allen formalism [Phys. Rev. B 18, 5217 (1978)] to obtain temperature dependent electronic structure of diamond and silicon. This method allows us to obtain the thermally-averaged ab initio electronic structure in a straightforward and computationally inexpensive way. Our investigations on the finite temperature electronic structure of diamond and silicon lead to a new criterion, temperature transferability, which is required…
The modified Becke-Johnson exchange potential combined with local-density approximation correlation (mBJLDA) has recently attracted interest because it provides highly improved band gaps at a very low computational cost. In this work we performed an extensive investigation of the performance of the mBJLDA potential employing a norm-conserving pseudopotential plane-waves approach (mBJLDA@PP), as implemented in the abinit code, using a test set of 83 solids representing a wide range of semiconductors and insulators. Our results confirm the conclusion of our previous study that the number of elec…
Recently, we developed a new method for generating effective core potentials (ECPs) using valence energy isospectrality with explicitly correlated all-electron (AE) excitations and norm-conservation criteria. We apply this methodology to the 3$^{rd}$-row main group elements, creating new correlation consistent effective core potentials (ccECPs) and also derive additional ECPs to complete the ccECP table for H-Kr. For K and Ca, we develop Ne-core ECPs and for the $4p$ main group elements, we construct [Ar]$3d^{10}$-core potentials. Scalar relativistic effects are included in their construction.…
We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z=1) to mercury (Z=80), with the exception of the 4f elements (57 <= Z <= 70). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be cho…
First-principles calculations in crystalline structures are often performed with a planewave basis set. To make the number of basis functions tractable two approximations are usually introduced: core electrons are frozen and the diverging Coulomb potential near the nucleus is replaced by a smoother expression. The norm-conserving pseudopotential was the first successful method to apply these approximations in a fully ab initio way. Later on, more efficient and more exact approaches were developed based on the ultrasoft and the projector augmented wave formalisms. These formalisms are however m…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the system is described as a truly semi-infinite solid with a surface region coupled to an electron reservoir, thereby overcoming several fundamental drawbacks of the traditional slab approach. The versatility of the method is demonstrated with several applications to surface physics and chemistry problems that are inherently difficult to address properly with the sl…
$G^0W^0$ implementation based on the pseudopotential and numerical-atomic-orbital basis-set framework: Algorithms and benchmarks
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；The NOMAD Laboratory at the FHI of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所NOMAD实验室）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；CAS Key Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息重点实验室）
Minimizing propagated density errors of atomic core-electron for simultaneously accurate bandgaps and lattice constants in closed-shell Copper semiconductors
Key Lab of advanced optoelectronic quantum architecture and measurement (MOE), and School of Interdisciplinary Science, Beijing Institute of Technology（北京理工大学光电量子架构与测量教育部重点实验室，交叉科学学院）；Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute（伦斯勒理工学院物理、应用物理和天文学系）
