Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion plus Selected Inversion

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We describe how to apply the recently developed pole expansion plus selected inversion (PEpSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating charge density, total energy, Helmholtz free energy and atomic forces without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEpSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the ... continued below

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Lin, Lin; Chen, Mohan; Yang, Chao & He, Lixin February 10, 2012.

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We describe how to apply the recently developed pole expansion plus selected inversion (PEpSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating charge density, total energy, Helmholtz free energy and atomic forces without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEpSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEpSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEpSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEpSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes on a single processor. We also show that the use of PEpSI does not lead to loss of accuracy required in a practical DFT calculation.

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27

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  • Journal Name: Journal of Computational Physics

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  • Report No.: LBNL-5361E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 1076802
  • Archival Resource Key: ark:/67531/metadc831813

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  • February 10, 2012

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  • May 19, 2016, 9:45 a.m.

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  • Nov. 7, 2016, 8:14 p.m.

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Lin, Lin; Chen, Mohan; Yang, Chao & He, Lixin. Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion plus Selected Inversion, article, February 10, 2012; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc831813/: accessed August 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.