Auxiliary density functionals: a new class of methods for efficient, stable density functional theory calculations

TL;DR

This paper introduces auxiliary density functionals that improve the stability and efficiency of density functional theory calculations by dynamically mapping the Kohn-Sham system to an auxiliary system, reducing instabilities and scaling issues.

Contribution

The paper presents a novel class of auxiliary density functionals that enhance the stability and scalability of DFT calculations, including a bosonic auxiliary system example.

Findings

Eliminates instabilities in large system simulations

Provides good performance for bulk materials

Substantially improves scaling with system size

Abstract

A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density functional equation is solved implicitly for the density response, eliminating the instabilities that arise in conventional techniques for simulations of large, metallic or inhomogeneous systems. The auxiliary system is not required to be fermionic, and an example bosonic auxiliary density functional is presented which captures the key aspects of the fermionic Kohn-Sham behaviour. This bosonic auxiliary scheme is shown to provide good performance for a range of bulk materials, and a substantial improvement in the scaling of the calculation with system size for a variety of simulation systems.