arXiv subjects

Andrew C. Burgess

Publications and source records attributed to Andrew C. Burgess.

5 recordsLinked to original sources

arXiv2026

Validity of DFT+U band gaps in all its known functional forms

The Density Functional Theory plus Hubbard U (DFT+U) technique is one of the most widely used tools by condensed matter physicists and solid state chemists for the simulation of transition-metal and lanthanide bearing crystals, and increasingly of much more diverse chemistries... Since the earliest days, the gap in the DFT+U single-particle eigenspectrum has been associated with the fundamental band gap, and the method has typically found more success for spectra than for total-energy derived properties. There has been some doubt, however, as to the conceptual validity of this association. Here, extending findings from recent years regarding local, semi-local, and hybrid functionals within the generalized Kohn-Sham framework, we prove and numerically demonstrate that the DFT+U eigenspectrum gap is conceptually valid, in the specific sense that it matches its own fundamental gap calculated using total-energy differences. We emphasize that this does not imply its agreement with experimental values, and indeed our argument is independent of the Hubbard U parameter. The result holds for pristine periodic systems with converged k-point sampling but not, however, for defective ones, isolated systems, or systems in which added charges exhibit spontaneous localization. We show that bandgap validity for pristine solids holds in the presence of pseudopotentials and PAW potentials, when using hybrid functionals, and in DFT+U(+J) irrespective of the level of subspace projection onto the band-edge states. We survey every collinear-spin DFT+U-type functional known to have been published to date, within a unified notation... Returning to the related but different question of band-gap correction efficiency, we offer fresh analysis of DFT+U bandgap projection dependence, and each functional's effect on energies and gaps for the hydrogen lattice in the Mott-Hubbard limit.

cond-mat.str-el↗

arXiv2025

Accurate bandgaps of photovoltaic kesterites from first-principles DFT+U

Streamlined prediction of the electronic properties of photoactive materials warrants a Density Functional Theory (DFT) based approach that (i) yields reliable bandgaps, (ii) is free of empirically tuned parameters, and (iii) exhibits low computational overhead. Here we show that for Cu2ZnSnS4 and Cu2ZnGeS4 kesterite photovoltaic materials, all three of these demands are met by the DFT plus Hubbard U technique (DFT+U) with corrective parameters evaluated via minimum-tracking linear response. The predicted bandgaps are found to even marginally outperform those from the self-consistent GW approach. Key to this method's success is the application of Hubbard U corrections to all atomic subspaces that dominate the conduction and valence band edges, as opposed to the conventional approach of correcting 3d and 4f atomic states. Intriguingly, the inclusion of Hund's J corrections via the extended DFT+U+J functional significantly worsens these results. This under performance can be ameliorated through the use of the Burgess-Linscott-O'Regan (BLOR) flat-plane based Hubbard U plus Hund's J functional, with bandgap predictions in close agreement with the conventional DFT+U method. The DFT+U method is also used to predict defect-induced changes to the bandgap and associated formation energies, in 1,728-atom supercells.

cond-mat.mtrl-sci↗

arXiv2024

Flat-plane based double-counting free and parameter free many-body DFT+U

Burgess et al. have recently introduced the BLOR corrective exchange-correlation functional that is, by construction, the unique simplified rotationally-invariant DFT+U functional that enforces the flat-plane condition separately on each effective orbital of a localized subspace. Detached from the Hubbard model, functionals of this type are both double-counting correction free and, when optimized in situ using appropriate error quantifiers, effectively parameter free. In this work, the extension of the BLOR functional to address many-body errors (mBLOR) is derived. The mBLOR functional is built to enforce the flat-plane condition on the entire subspace, rather than on each orbital individually. In this way inter-orbital errors are corrected on the same footing as the single-particle ones. Focusing on exact test cases with strong inter-orbital interactions, the BLOR and mBLOR functionals were benchmarked against contemporary DFT+U functionals using the total energy extensivity condition on stretched homo-nuclear p-block dimers that represent various self-interaction and static-correlation error regimes. The BLOR functional outperformed all other DFT+$U$ functionals tested, which often act to increase total-energy errors, yet it still yielded large errors in some systems. mBLOR instead yielded low energy errors across all four strongly-correlated dimers, while being constructed using only semi-local approximation ingredients. As mBLOR would not otherwise introduce a band-gap correction in the manner that is a desirable feature of DFT+U, we developed a cost-free technique to reintroduce it automatically by moving the functional's unusual explicit derivative discontinuity into the potential. With this in place, mBLOR is the only known DFT$+U$ functional that opens the bandgap of stretched neutral homo-nuclear dimers without the aid of unphysical spin-symmetry breaking.

cond-mat.str-el↗

arXiv2024

The tilted-plane structure of the energy of finite quantum systems

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory (DFT). The magnetic analog of the DFT Koopmans' theorem is also derived. Moving to fractional electron count, the tilted plane condition is derived, lifting certain assumptions in previous works. This generalization of the flat plane condition characterizes the total energy surface of a finite system for all values of electron count N and magnetization M. This result is used in combination with tabulated spectroscopic data to show the flat plane-structure of the oxygen atom, among others. We find that derivative discontinuities with respect to electron count sometimes occur at non-integer values. A diverse set of tilted plane structures is shown to occur in d-orbital subspaces, depending on chemical coordination. General occupancy-based total-energy expressions are demonstrated thereby to be necessarily dependent on the symmetry-imposed degeneracies.

cond-mat.str-el↗

arXiv2023

The Convexity Condition of Density-Functional Theory

It has long been postulated that within density-functional theory (DFT) the total energy of a finite electronic system is convex with respect to electron count, so that 2 E_v[N_0] <= E_v[N_0 - 1] + E_v[N_0 + 1]. Using the infinite-separation-limit technique, this article proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof nonetheless confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham band-gap and the exchange-correlation derivative discontinuity of DFT.

physics.chem-ph↗