Interrogation and refinement of DFT+U+J energetics in magnetic systems

Abstract

With quantum computing just beyond the horizon, more emphasis than ever in history is placed on adaptable, efficient, yet accurate algorithms for routinely modeling properties of large-scale material systems. Among those electronic structure theories receiving the most scientific attention is density functional theory (DFT), which, despite its failures in the available computationally tractable local or semi-local approximative functionals, has undoubtedly accelerated the collective understanding of quantum many-body interactions and their precipitation of macroscopic phenomena.

Meanwhile, a surge in interest in technologically viable classes of materials with environmentally friendly applications—among them transition metal oxides, Prussian Blue analogues, and spin-crossover molecules—has impelled DFT practitioners and theorists to develop minimally invasive methods to manage DFT’s characteristic errors while preserving its first-principles status. Noticeably pronounced for the aforementioned strongly correlated systems are the self-interaction error (SIE, or more generally, the delocalization error) implicated in band-gap underestimation and energy-density non-linearity and quantified by the Hubbard U—and the static correlation error (SCE), associated with energy-magnetization curvature in degenerate and multi-valence systems.

The Hubbard family of corrective functionals (DFT+U+J) featuring in situ-calculated Hubbard U and Hund’s J parameters are called to rise to the challenge, spurring a return to first principles in search of innovative, efficient, and minimally parametrized ways to address SIE and SCE. The following dissertation describes a series of meticulously composed studies designed within the DFT+U+J framework to interrogate and rectify some of its remaining weaknesses and ambiguities.

We focus on obtaining state-of-the-art spin-based total energy differences in magnetic systems, metrics that DFT+U+J-type functionals have hitherto struggled to achieve. In one project, we calculate Heisenberg interatomic exchange-coupling parameters in terms of strict density-functional accessible total energy differences between magnetic configurations in nickel oxide and directly compare these parameters against other available theoretical values, such as those from costly hybrid functionals, and available experimental parameters (i.e., derived from magnon frequencies). Another project centers on spin-crossover adiabatic energy differences in a series of octahedrally coordinated iron II molecules. Generally, these studies resoundingly indicate that common Hubbard functionals with bespoke parametrization informed by the magnetic environment do not result in comparable total energies. Moreover, our results point toward misconstruction of the Hubbard functionals in incorporating magnetic considerations and a breakdown in either the two main linear response formalisms for determining the Hund's J or how the functionals incorporate this parameter.

Throughout these investigations are suggestions towards best practices in calculating the Hubbard U and Hund's J for non-ground-state magnetic orderings via linear response. Further projects takes this refinement to the next level by (i) automating linear response for the Abinit open-source electronic structure suite and (ii) identifying its dominant components, error analysis protocol, and logistics for practical implementation. Specifically, we lend a critical eye to the projector functions—the mechanisms that isolate the atomic subspaces destined for corrective treatment from the charge bath in which they are immersed. Our final project asserts that the projectors influence the magnitude of the Hubbard parameters in extremizable ways.

Without an accurate microscopic description of spin-based energetics and electronic structure properties, we are unlikely to design and/or discover new materials that optimize and tailor functionality while simultaneously minimizing, if not eliminating, impracticalities. Ultimately, this dissertation strives to contribute to the establishment of resilient techniques that go on to inform and facilitate automation of first-principles methods for high-throughput informatics. It represents a specialized but important cog in the machine we collectively build to accelerate materials discovery.