Large-scale all-electron density functional theory calculations using an enriched finite-element basis

Abstract

We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that are constructed from the solution of the Kohn-Sham (KS) problem for single atoms. We term these numerical basis functions as enrichment functions, and the resultant basis as the enriched finite element basis. The compact support for the enrichment functions is obtained by using smooth cutoff functions, which enhances the conditioning and maintains the locality of the enriched finite element basis. The integrals involved in the evaluation of the discrete KS Hamiltonian and overlap matrix in the enriched finite element basis are computed using an adaptive quadrature grid that is constructed based on the characteristics of enrichment functions. Further, we propose an efficient scheme to invert the overlap matrix by using a block-wise matrix inversion in conjunction with special reduced-order quadrature rules, which is required to transform the discrete Kohn-Sham problem to a standard eigenvalue problem. Finally, we solve the resulting standard eigenvalue problem, in each self-consistent field iteration, by using a Chebyshev polynomial based filtering technique to compute the relevant eigenspectrum. We demonstrate the accuracy, efficiency and parallel scalability of the proposed method on semiconducting and heavymetallic systems of various sizes, with the largest system containing 8694 electrons. We obtain accuracies in the ground-state energies that are ∼ 1 mHa with reference ground-state energies employing classical finite element as well as gaussian basis sets. Using the proposed formulation based on enriched finite element basis, for accuracies commensurate with chemical accuracy, we observe a staggering 50−300 fold reduction in the overall computational time when compared to classical finite element basis. Further, we find a significant outperformance by the enriched finite element basis when compared to the gaussian basis for the modest system sizes where we obtained convergence with gaussian basis. We also observe good parallel scalability of the numerical implementation up to 384 processors for a representative benchmark system comprising of 280-atom silicon nano-cluster.

Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate

“…Further, extending the Kohn-Sham studies, often conducted under the pseudopotential approximation, to all-electron Kohn-Sham DFT calculations will provide useful data to assess the accuracy of pseudopotentials in describing the dislocation cores, and this presents another worthwhile direction for future studies. We anticipate that the recent methodological developments towards large-scale real-space all-electron Kohn-Sham DFT calculations (Kanungo and Gavini, 2017;Motamarri et al, 2017) will be useful in these efforts. Material parameters of fcc Al computed using RS-OFDFT with Wang-Govind-Carter (WGC) kinetic energy functional (Wang et al, 1999), local density approximation (LDA) for the exchange-correlation energy (Perdew and Zunger, 1981), and Goodwin-Needs-Heine pseudopotential (Goodwin et al, 1990).…”

DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations

“…NV center in diamond) [115]. Implementation of enriched finite-element basis [38] in DFT-FE, which can enable large-scale efficient all-electron DFT calculations, is currently being pursued. Further, implementation of advanced exchange-correlation functionals (hybrid and dispersion corrected), advanced mixing schemes, spin-orbit coupling, and implementation of polarizability and dielectric calculations in DFT-FE are other efforts that are being pursued.…”

A machine learning approach for increased throughput of density functional theory substitutional alloy studies

“…Fax: 304-293-6689; Tel: 304-293-3256; E-mail: tdmusho@mail.wvu.edu wide range of material properties. The theory is able to reduce the many body Schrödinger equation to an effective single electron problem by relying on Hohenberg-Kohn theorem 12 and Kohn-Sham method 19 , thus making material property predictions computationally feasible 16 . The profound success of DFT for describing ground-state properties for vast classes of materials such as semiconductors, insulators, half metals, semimetals, transition metals, etc., at the nanostructure scale makes it one of the most used method for modern electronic structure analyses 3 .…”

“…The orthorhombic unit cell is made up of 24 O atoms 8 transition metal atoms (Bi) and 4 Mo atoms making a total of 36 atoms in a unit cell. La, and Yb are subbed into the 8 metal atom positions (Bi) (atom position numbers 3,16,17,18,19,20,21,22). These is the initial state of all DFT calculated structures and thus the numbers that correspond to each atom are the same for any configuration.…”