Abstract

In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard U parameters may be used to quantify and amend the self-interaction error (SIE) ascribed to selected subspaces. In order to enable the accurate, computationally convenient calculation of U by means of DFT algorithms that locate the ground-state without any diagonalisation, such as in linear-scaling DFT +U [1], a linear-response formulation for U is introduced here in terms of the fully-relaxed constrained ground-state density [2]. Expressing the total energy of self-consistent DFT +U in terms of a constrained search over ground-state densities and external DFT +U parameters that satisfy a self-consistency condition, the U parameters are relegated to the status of auxiliary variables. This enables the full comparability, conceptually and numerically, of approximately self-corrected DFT energies [3,4], such as when external parameters such as ionic positions are changed.

This ground-state tracking linear-response framework also addresses the open question of self-consistency over U in DFT +U. We show that the simplest self-consistency scheme is necessary and sufficient for DFT +U to correct the total energy for SIE under idealized one-electron conditions [3], and that the gap can also be simultaneously corrected if further generalisations are made [4]. For multi-electron systems such as transition-metal oxides (including closed-shell ones), we extend the framework to enable straightforward first-principles calculations of the Hund’s exchange parameter J, which we find to be critically important [5]. We also demonstrate successful first-principles U and J corrections for oxygen 2p orbitals.

[1] D. D. O’Regan, N. D. M. Hine, M. C. Payne, and A. A. Mostofi, Phys. Rev. B 85 , 085107 (2012).

[2] D. D. O’Regan and G. Teobaldi, Phys. Rev. B 94 , 035159 (2016).

[3] G. Moynihan, G. Teobaldi, and D. D. O’Regan, arXiv:1704.08076 (2017).

[4] G. Moynihan, G. Teobaldi, and D. D. O’Regan, Phys. Rev. B 94 , 220104® (2016).

[5] E. B. Linscott, D. J. Cole, M. C. Payne and D. D. O’Regan, Phys. Rev. B 98 , 235157 (2018).