Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons

TL;DR

This paper demonstrates the theoretical equivalence of charged and neutral density functional formulations in correcting many-body self-interaction errors for polarons, unifying different approaches and validating their consistent results across various materials.

Contribution

It establishes the formal equivalence between charged and neutral DFT approaches for polaron self-interaction correction, clarifying their relationship and applicability.

Findings

Charged and neutral formulations yield identical self-interaction corrected energies.

Methods produce consistent polaron properties across different materials.

Differences are due to structural and screening treatment, not fundamental formulation.

Abstract

The electron self-interaction problem in density functional theory affects the accurate modeling of polarons, particularly their localization and formation energy. Charged and neutral density functional formulations have been developed to address this issue, yet their relationship remains unclear. Here, we demonstrate their equivalence in treating the many-body self-interaction of the polaron state. In particular, we connect with each other piecewise-linear functionals based on adding an extra charge to the supercell, the pSIC approach derived from the energetics of the neutral defect with polaronic distortions in a supercell, and the unit-cell method for polarons based on electron-phonon couplings. We show that these approaches lead to the same formal expression of the self-interaction corrected energy, which is fully defined by the energetics of the neutral charge state of the charged polaronic structure. Residual differences between these methods solely arise from the achieved polaronic structure, which is affected by different treatments of electron-screening and finite-size effects. We apply these methods to a set of prototypical small hole and electron polarons, including the hole polaron in MgO, the hole polaron in $\beta$-Ga$_2$O$_3$, the $V_\text{k}$ center in NaI, the electron polaron in BiVO$_4$, and the electron polaron in TiO$_2$. We show that the ground-state properties of polarons obtained using charged and neutral density functional formulations are in excellent agreement.