Simple implementation of complex functionals: scaled selfconsistency

TL;DR

This paper compares three approximate schemes for implementing complex density functionals using simpler, self-consistent approaches, demonstrating that scaled self-consistency methods are more accurate and versatile than traditional post-approaches.

Contribution

The paper introduces and rigorously analyzes a new local scaling approach for density functional implementation, expanding the toolkit for efficient complex functional calculations.

Findings

Scaled approaches outperform post-approaches in accuracy.

Scaled self-consistency improves eigenvalues and orbitals.

Method is effective across various systems and approximations.

Abstract

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of selfconsistent implementation of simpler functionals: (i) post-LDA evaluation of complex functionals at the LDA densities (or those of other simple functionals); (ii) application of a global scaling factor to the potential of the simple functional; and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully selfconsistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells and model Hamiltonians. Scaled approaches turn out to be, on average, better than post-approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled selfconsistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.