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.
Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional pseudopotential calculations are performed. To this end we compare band gaps obtained with norm-conserving pseudopotentials or the projector-augmented wave method with all-electron calculations for a large dataset of 473 solids. We focus in particular on density functionals that were designed specifically for band-gap calculations.
On average, the absolute error is about 0.1 eV, yielding absolute relative errors in the 5-10\% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent pseudopotential is rather harmless for most applications.
However, we find specific cases where absolute errors can be larger than 1 eV, or others where relative errors can amount to a large fraction of the band gap.
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…
Uncertainty of DFT calculated mechanical and structural properties of solids due to incompatibility of pseudopotentials and exchange-correlation functionals
The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the…
We develop an automated procedure to select the local potential of a separable pseudopotential that minimizes transferability errors for the isolated atom, and we show that this optimization leads to significant improvements in the accuracy of predicted solid-state properties. We present pseudopotentials for Y, In, and Sn. For these pseudopotentials, our method reduces solid-state errors by 88% on average, as measured by the $Δ$-factor test. These pseudopotentials are constructed in the Kleinman-Bylander form; however, our method is applicable to all separable pseudopotentials, such as ONCV ps…
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…
Local pseudopotential (LPP) is an important component of the orbital free density functional theory (OF-DFT), which is a promising large scale simulation method that can still maintain information of electron state in materials. Up to date, LPP is usually extracted from the solid state DFT calculations. It is unclear how to assess its transferability while applying to a much different chemical environment. Here we reveal a fundamental relation between the first principles norm-conserving PP (NCPP) and the LPP. Using the optimized effective potential method developed for exchange functional, we…
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…
Modeling high temperature (10's or 100's of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multi-site effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane wave basis sets. Here we explore the KKR Green's function method at these high temperature conditions. The method is all-electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations.…
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this compara…
The von Neumann stability analysis along with a Chapman-Enskog analysis is proposed for a single-relaxation-time lattice Boltzmann Method (LBM) for wave propagation in isotropic linear elastic solids, using a regular D2Q9 lattice. Different boundary conditions are considered: periodic, free surface, rigid interface. An original absorbing layer model is proposed to prevent spurious wave reflection at domain boundaries. The present method is assessed considering several test cases. First, a spatial Gaussian force modulated in time by a Ricker wavelet is used as a source. Comparisons are made wit…
Accelerating computational materials discovery with artificial intelligence and cloud high-performance computing: from large-scale screening to experimental validation
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming majority of pertinent methods is based on the assumption of a perfect model. Motivated by problems in solid mechanics which, as all problems in continuum thermodynamics, are described by conservation laws and phenomenological constitutive closures, we argue that in order to quantify model uncertainty in a physically meaningful manner, one should break open the …
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consist…
Constraint-aware functional cloning for stable and transferable machine-learned density functional theory
Catalan Institute of Nanoscience and Nanotechnology (ICN2)（加泰罗尼亚纳米科学与技术研究所）；Stony Brook University（石溪大学）；The New York Academy of Sciences（纽约科学院）；University of California, Irvine（加州大学尔湾分校）；Centro de Física de Materiales (CFM-MPC), CSIC-UPV/EHU（材料物理中心）
