Discrete discontinuous basis projection method for large-scale electronic structure calculations

Xu, Qimen; Suryanarayana, Phanish; Pask, John E.

doi:10.1063/1.5037794

Cited by 77 publications

(13 citation statements)

References 51 publications

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“…In recent years, there has been a significant increase in the efficiency of real-space methods due to a number of advances. Since early work in this area [20][21][22][23] , the degrees of freedom/atom required to obtain accurate ground state properties has been notably reduced by double-grid techniques 24 , ultrasoft pseudopotential formulations 25 , projector augmented wave methods 26 , high-order integration 27 , reformulation of nonlocal pseudopotential components 28,29 , and reduction of the eigenproblem by discontinuous projection 30 . Moreover, the need for effective preconditioners has been circumvented by substituting traditional iterative eigensolvers with the Chebyshev-polynomial filtered subspace iteration (CheFSI) 31 .…”

Section: Introductionmentioning

confidence: 99%

Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

2019

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We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established planewave and realspace codes. Using this implementation, we study the band structure and bending properties of X nanotubes and Xene sheets, respectively. Specifically, we first show that zigzag and armchair X nanotubes with radii in the range 1 to 5 nm are semiconducting, other than the armchair and zigzag type III carbon variants, for which we find a vanishingly small bandgap, indicative of metallic behavior. In particular, we find an inverse linear dependence of the bandgap with respect to the radius for all nanotubes, other than the armchair and zigzag type III carbon variants, for which we find an inverse quadratic dependence. Next, we exploit the connection between cyclic symmetry and uniform bending deformations to calculate the bending moduli of Xene sheets in both zigzag and armchair directions, while considering radii of curvature up to 5 nm. We find Kirchhoff-Love type bending behavior for all sheets, with graphene and stanene possessing the largest and smallest moduli, respectively. In addition, other than graphene, the sheets demonstrate significant anisotropy, with larger bending moduli along the armchair direction. Finally, we demonstrate that the proposed approach has very good parallel scaling and is highly efficient, enabling ab initio simulations of unprecedented size for systems with a high degree of cyclic symmetry. In particular, we show that even micron-sized nanotubes can be simulated with modest computational effort. Overall, the current work opens an avenue for the efficient ab-initio study of 1D nanostructures with large radii as well as 1D/2D nanostructures under uniform bending.

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Section: Introductionmentioning

confidence: 99%

Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

2019

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“…We note that the spectral quadrature step accounts for greater than 98 percent of the total time in each SCF iteration. The prefactor of spectral quadrature can be significantly reduced by incorporating reduced basis methods such as Discrete Discontinious Basis Projection ( [65]). Further, the number of SCF iterations to achieve a fixed target SCF error increases with system size in metallic systems due to charge sloshing [26].…”

Section: Convergence and Performancementioning

confidence: 99%

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

Ghosh

Bhattacharya

2022

Journal of Computational Physics

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“…The size of the real-space Hamiltonian would quickly make these approaches prohibitively expensive. One approach to address this would be to employ discrete discontinuous basis projection (DDBP) 102 to reduce Hamiltonian and orbital dimensions to a few tens per atom.…”

Section: Self-consistencymentioning

confidence: 99%

Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals

Diaz

Suryanarayana

et al. 2021

The Journal of Chemical Physics

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Most widely used density functional approximations suffer from self-interaction (SI) error, which can be corrected using the Perdew-Zunger (PZ) self-interaction correction (SIC). We implement the recently proposed size-extensive formulation of PZ-SIC using Fermi-Löwdin Orbitals (FLOs) in real space, which is amenable to systematic convergence and large-scale parallelization. We verify the new formulation within the generalized Slater scheme by computing atomization energies and ionization potentials of selected molecules and comparing to those obtained by existing FLOSIC implementations in Gaussian based codes. The results show good agreement between the two formulations, with new real-space results somewhat closer to experiment on average for the systems considered. We also obtain the ionization potentials and atomization energies by scaling down the Slater statistical average of SIC potentials. The results show that scaling down the average SIC potential improves both atomization energies and ionization potentials, bringing them closer to experiment. Finally, we verify the present formulation by calculating the barrier heights of chemical reactions in the BH6 dataset, where significant improvements are obtained relative to Gaussian based FLOSIC results.

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Discrete discontinuous basis projection method for large-scale electronic structure calculations

Cited by 77 publications

References 51 publications

Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

Symmetry-adapted real-space density functional theory for cylindrical geometries: Application to large group-IV nanotubes

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals

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