Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations
| Autor: | Kaushik Bhattacharya, Phani Motamarri, Vikram Gavini, Michael Ortiz |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
Density matrix Kohn–Sham equations FOS: Physical sciences 02 engineering and technology Eigenfunction Computational Physics (physics.comp-ph) 021001 nanoscience & nanotechnology 01 natural sciences Condensed Matter::Materials Science symbols.namesake Quantum mechanics 0103 physical sciences symbols Physics::Atomic and Molecular Clusters Density functional theory Degree of a polynomial 010306 general physics 0210 nano-technology Hamiltonian (quantum mechanics) Physics - Computational Physics Eigenvalues and eigenvectors Subspace topology |
| DOI: | 10.48550/arxiv.1608.07865 |
| Popis: | 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: (i) employ Chebyshev filtering to compute a subspace containing the occupied states followed by a localization procedure to generate non-orthogonal 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 nano-clusters up to 1330 electrons, a single gold atom and a six-atom gold nano-cluster. The benchmark studies on silicon nano-clusters revealed a staggering five-fold reduction in the Fermi-operator expansion polynomial degree by using the spectrum-splitting approach for accuracies in the ground-state energies of $\sim 10^{-4} Ha/atom$ 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. Comment: 12 pages, 5 figures |
| Databáze: | OpenAIRE |
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