Spectral scheme for atomic structure calculations in density functional theory

TL;DR

This paper introduces a spectral computational scheme for atomic structure calculations within density functional theory, utilizing Chebyshev interpolation and differentiation to achieve high accuracy with fewer grid points.

Contribution

The authors develop a spectral method employing Chebyshev grids and differentiation matrices for efficient and accurate atomic calculations in density functional theory.

Findings

Achieves 1 microhartree accuracy with about 200 grid points.

Works effectively for atoms Z=1 to 83 with various exchange-correlation functionals.

Demonstrates high accuracy and efficiency in atomic DFT calculations.

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 $83$.