Highly accurate experimental structure factors of silicon are available in the literature, and these provide the ideal test for any \emph{ab initio} method for the construction of the all-electron charge density. In a recent paper [J. R. Trail and D. M. Bird, Phys. Rev. B {\bf 60}, 7863 (1999)] a method has been developed for obtaining an accurate all-electron charge density from a first principles pseudopotential calculation by reconstructing the core region of an atom of choice. Here this method is applied to bulk silicon, and structure factors are derived and compared with experimental and Full-potential Linear Augmented Plane Wave results (FLAPW). We also compare with the result of assuming the core region is spherically symmetric, and with the result of constructing a charge density from the pseudo-valence density + frozen core electrons. Neither of these approximations provide accurate charge densities. The aspherical reconstruction is found to be as accurate as FLAPW results, and reproduces the residual error between the FLAPW and experimental results.
We present a method to make highly accurate pseudopotentials for use with orbital-free density functional theory (OF-DFT) with given exchange-correlation and kinetic energy functionals, which avoids the compounding of errors of Kohn-Sham DFT and OF-DFT. The pseudopotentials are fitted to reference (experimental or highly accurate quantum chemistry) values of interaction energies, geometries, and mechanical properties, using a genetic algorithm. This can enable routine large-scale ab initio simulations of many practically relevant materials. Pseudopotentials for Li, Na, and Mg resulting in accu…
Quantum Monte Carlo methods provide in principle an accurate treatment of the many-body problem of the ground and excited states of condensed systems. In practice, however, uncontrolled errors such as those arising from the fixed-node and pseudopotential approximations often limit the quality of results. We show that the accuracy of quantum Monte Carlo calculations is limited by using available pseudopotentials. In particular, it is necessary to include angular momentum channels in the pseudopotential for excited angular momentum states and to choose the local channel appropriately to obtain a…
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…
We present novel non-parametric representation math for local pseudopotentials (PP) based on Gaussian Process Regression (GPR). Local pseudopotentials are needed for materials simulations using Orbital-Free Density Functional Theory (OF-DFT) to reduce computational cost and to allow kinetic energy functional (KEF) application only to the valence density. Moreover, local PPs are important for the development of accurate KEFs for OF-DFT as they are only available for a limited number of elements. We optimize local PPs of tin (Sn) using GP regression to reproduce the experimental lattice constant…
A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {\bf 14}, 3795 (1981)]. In this method the core region is \emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an…
Quantum Monte Carlo and quantum chemistry techniques are used to investigate pseudopotential models of the lithium hydride (LiH) molecule. Interatomic potentials are calculated and tested by comparing with the experimental spectroscopic constants and well depth. Two recently-developed pseudopotentials are tested, and the effects of introducing a Li core polarization potential are investigated. The calculations are sufficiently accurate to isolate the errors from the pseudopotentials and core polarization potential. Core-valence correlation and core relaxation are found to be important in deter…
A recently published correlated electron pseudopotentials (CEPPs) method has been adapted for application to the 3d-transition metals, and to include relativistic effects. New CEPPs are reported for the atoms Sc$-$Fe, constructed from atomic quantum chemical calculations that include an accurate description of correlated electrons. Dissociation energies, molecular geometries, and zero-point vibrational energies of small molecules are compared with all electron results, with all quantities evaluated using coupled cluster singles doubles and triples (CCSD(T)) calculations. The CEPPs give better …
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…
Consistency between the exchange-correlation (xc) functional used during pseudopotential construction and planewave-based electronic structure calculations is important for an accurate and reliable description of the structure and properties of condensed-phase systems. In this work, we present a general scheme for constructing pseudopotentials with range-separated hybrid (RSH) xc functionals based on the solution of the all-electron radial integro-differential equation for a spherical atomic configuration. As proof-of-principle, we demonstrate pseudopotential construction with the PBE, PBE0, H…
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…
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…
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）
We derive an analytic connection between the screened self-consistent effective potential from density functional theory (DFT) and atomic effective pseudopotentials (AEPs). The motivation to derive AEPs is to address structures with thousands to hundred thousand atoms, as given in most nanostructures. The use of AEPs allows to bypass a self-consistent procedure and to address eigenstates around a certain region of the spectrum (e.g., around the band gap). The bulk AEP construction requires two simple DFT calculations of slightly deformed elongated cells. The ensuing AEPs are given on a fine re…
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…
Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotent…
Various many-body perturbation theory techniques for calculating electron behavior rely on {\it W}, the screened Coulomb interaction. Computing {\it W} requires complete knowledge of the dielectric response of the electronic system, and the fidelity of the calculated dielectric response limits the reliability of predicted electronic and structural properties. As a simplification, calculations often begin with the random-phase approximation (RPA). However, even RPA calculations are costly and scale poorly, typically as $N^4$ ($N$ representing the system size). A local approach has been shown to…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta functions weighted by appropriate factors. These factors are found from multipole expansion of atomic potentials in the crystal lattice, with considering effects such as screening. Fourier transform was then applied to describe the wave function in reciprocal space. Sampling can be uniform or non-uniform throughout space; however rate and interval optimization …
In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well-suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The la…
Ab initio calculations of the dynamical response of copper
基于{ \em ab initio}赝势计算，研究了局域$d$带在Cu动力学响应中的作用.在随机相位近似（RPA）和含时局域密度泛函近似（TDLDA）的密度响应函数进行评估。我们的研究结果表明，除了提供一个可极化的背景，降低了自由电子等离子体的频率，d-电子负责，在较高的能量和小的动量，在动力学结构因子的双峰结构。这些结果与实验测定的铜的光学响应是一致的。我们还分析了动力学散射截面对动量转移的依赖关系。
Density functionals with asymptotic corrections to the long-range potential provide entry-level methods for calculations on molecules that can sustain charge transfer, but similar applications in Materials Science are rare. We describe an implementation of the CAM-B3LYP range-separated functional within the Vienna Ab-initio Simulation Package (VASP) framework, together with its analytical functional derivatives. Results obtained for eight representative materials: aluminum, diamond, graphene, silicon, NaCl, MgO, 2D h-BN and 3D h-BN, indicate that CAM-B3LYP predictions embody mean-absolute devi…
We introduce a method to carry out zero-temperature calculations within density functional theory (DFT) but without relying on the Born-Oppenheimer (BO) approximation for the ionic motion. Our approach is based on the finite-temperature many-body path-integral formulation of quantum mechanics by taking the zero-temperature limit and treating the imaginary-time propagation of the electronic variables in the context of DFT. This goes beyond the familiar BO approximation and is limited from being an exact treatment of both electrons and ions only by the approximations involved in the DFT componen…
