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Published January 15, 2017 | Published + Submitted
Journal Article Open

Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations


We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core subspace, spanned by the core eigenfunctions, and its complement, the valence subspace, and thereby enables an efficient computation of the Fermi-operator expansion by reducing the expansion to the valence-subspace projected Kohn-Sham Hamiltonian. The key ideas used in our approach are as follows: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate nonorthogonal localized functions spanning the Chebyshev-filtered subspace; (ii) compute the Kohn-Sham Hamiltonian projected onto the valence subspace; (iii) employ Fermi-operator expansion in terms of the valence-subspace projected Hamiltonian to compute the density matrix, electron density, and band energy. We demonstrate the accuracy and performance of the method on benchmark materials systems involving silicon nanoclusters up to 1330 electrons, a single gold atom, and a six-atom gold nanocluster. The benchmark studies on silicon nanoclusters revealed a staggering fivefold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of ∼10^(−4) Ha/atom with respect to reference calculations. Further, numerical investigations on gold suggest that spectrum splitting is indispensable to achieve meaningful accuracies, while employing Fermi-operator expansion.

Additional Information

© 2017 American Physical Society. (Received 25 August 2016; revised manuscript received 21 November 2016; published 5 January 2017) We gratefully acknowledge the support from the Air Force Office of Scientific Research under Grant No. FA9550-13-1-0113, and the support from the U.S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award No. W911NF-11-R-0001. V.G. also acknowledges the hospitality of the Division of Engineering and Applied Sciences at the California Institute of Technology while pursuing this work. We also acknowledge Advanced Research Computing at University of Michigan through the Flux computing platform, and Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575, for providing the computing resources.

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Submitted - 1608.07865.pdf

Published - PhysRevB.95.035111.pdf


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August 19, 2023
August 19, 2023