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Communication: Singularity-free hybrid functional with a Gaussian-attenuating exact exchange in a plane-wave basis
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28.See supplementary material at http://dx.doi.org/10.1063/1.4811775 for details of the energy dependence and time cost of C and Al according to q and k grids using various functionals and bandgap results for the semiconductors and insulators using Gaussian basis set and plane waves with nk = 24/nq = 6 and nk = 8/(nq = 8, 4) grids of various functionals. [Supplementary Material]
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Figures

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FIG. 1.

Dependence of the total energy of Al (a) and C (b) calculated using several hybrid functionals on the number of points (along x-axis) used to sample the Fock exchange potential and on the size of the point grid used to represent the wave functions.

Image of FIG. 2.

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FIG. 2.

A comparison of bandgaps calculated using PBE, PBE0, HSE06, and Gau-PBE vs experimental bandgaps. The bandgaps using both Gaussian-type-orbital and plane waves are presented. In plane wave calculations, 24 × 24 × 24/6 × 6 × 6 is used. Only in ZnO and AlN, 8 × 8 × 8/8 × 8 × 8 is used.

Tables

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Table I.

Errors of semiconductor and insulator bandgaps of PBE, PBE0, HSE06, and Gau-PBE.

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/content/aip/journal/jcp/138/24/10.1063/1.4811775
2013-06-25
2014-04-19

Abstract

Integrable singularity in the exact exchange calculations in hybrid functionals is an old and well-known problem in plane-wave basis. Recently, we developed a hybrid functional named Gaussian-attenuating Perdew-Burke-Ernzerhof (Gau-PBE), which uses a Gaussian function as a modified Coulomb potential for the exact exchange. We found that the modified Coulomb potential of Gaussian function enables the exact exchange calculation in plane-wave basis to be singularity-free and, as a result, the Gau-PBE functional shows faster energy convergence on and grids for the exact exchange calculations. Also, a tight comparison (same and meshes) between Gau-PBE and two other hybrid functionals, i.e., PBE0 and HSE06, indicates Gau-PBE functional as the least computational time consuming. The Gau-PBE functional employed in conjunction with a plane wave basis provides bandgaps with higher accuracy than the PBE0 and HSE06 in agreement with bandgaps previously calculated using Gaussian-type-orbitals.

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Scitation: Communication: Singularity-free hybrid functional with a Gaussian-attenuating exact exchange in a plane-wave basis
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/24/10.1063/1.4811775
10.1063/1.4811775
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