Analysis of atomic-orbital basis sets from the projection of plane-wave results

TL;DR

This paper introduces a projection-based method to analyze and optimize atomic-orbital basis sets from plane-wave calculations, improving basis quality assessment and enabling efficient basis optimization for electronic structure calculations.

Contribution

The authors develop a spilling-based projection technique for evaluating and optimizing atomic basis sets, linking basis quality to energy errors and enabling targeted improvements.

Findings

Spilling correlates with mean square energy band errors.

Optimized bases improve band gap descriptions in semiconductors.

Finite-range orbitals perform comparably to infinite-range ones.

Abstract

The projection of the eigenfunctions obtained in standard plane-wave first-principle calculations is used for analyzing atomic-orbital basis sets. The "spilling" defining the error in such a projection allows the evaluation of the quality of an atomic-orbital basis set for a given system and its systematic variational optimization. The same projection allows obtaining the band structure and the Hamiltonian matrix elements in the previously optimized atomic basis. The spilling is shown to correlate with the mean square error in the energy bands, indicating that the basis optimization via spilling minimization is qualitatively equivalent to the energy-minimization scheme, but involves a much smaller computational effort. The spilling minimization also allows the optimization of bases for uses different than total-energy calculations, like the description of the band gap in semiconductors. The method is applied to the characterization of finite-range pseudo-atomic orbitals {[}O. F. Sankey and D. J. Niklewski, Phys. Rev. B {\bf 40}, 3979 (1989){]} in comparison to infinite-range pseudo-atomic and Slater-type orbitals. The bases are evaluated and optimized for several zincblende semiconductors and for aluminum. The quality of the finite-range orbitals is found to be perfectly comparable to the others with the advantage of a limited range of interacions. A simple scheme is proposed to expand the basis without increasing the range. It is found that a double-$z$ basis substantially improves the basis performance on diamond, whereas $d$-polarization is required for Si and Al for similar results. Finally, the projection allows the chemical analysis of the plane-wave results via population analysis on the previously optimized atomic basis.