Spectral scheme for atomic structure calculations in density functional theory
Abstract
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number $Z = 1$ to $83$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.00534
- arXiv:
- arXiv:2406.00534
- Bibcode:
- 2024arXiv240600534B
- Keywords:
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- Physics - Computational Physics;
- Condensed Matter - Materials Science
- E-Print:
- 21 pages, 7 figures, 4 tables