Implementation and application of a DFT$+U$$+V$ approach within the all-electron FLAPW method

TL;DR

The paper presents a first-principles implementation of the DFT$+U$+$V$ framework within the all-electron FLAPW formalism (FLEUR), with $U$ and $V$ determined via constrained RPA and projections based on MLWFs or muffin-tin functions. Benchmarking on graphene, Si, Ge, and NiO demonstrates improved band structures, gaps, and lattice properties relative to DFT, with closer agreement to GW and experiments, and reveals systematic differences arising from the projector choice. The work evidences that including intersite Coulomb terms $V$ captures charge-transfer and non-local correlation effects, particularly in covalent and charge-transfer insulators, while maintaining computational efficiency and interpretability. The approach provides a transferable, all-electron framework that spans Mott, charge-transfer, and covalent regimes, and points to future enhancements, such as self-consistent $U$/$V$ and energy-dependent interactions, as well as extensions to SOC and non-collinear magnetism.

Abstract

We present an implementation of the density-functional theory DFT$+U$$+V$ formalism within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method as implemented in the FLEUR code. The DFT$+U$$+V$ formalism extends DFT, supplemented by the onsite Coulomb interaction $U$, to address local correlation effects in localized states by incorporating intersite Coulomb interaction terms $V$. It holds promise for improving charge and bond disproportionation, charge and orbital ordering, charge density wave formation, charge transfer, and the intersite correlation resulting from hybridization between states of neighboring sites in a solid. $U$ and $V$ parameters are obtained from first principles using the constrained random-phase approximation (cRPA) employing two different atom basis representations to project the screened Coulomb interaction: the Wannier and the muffin-tin basis functions. We investigate in detail the impact of the $V$ term for typical covalently bonded materials like graphene, for bulk semiconductors such as silicon and germanium, and for charge-transfer insulators like NiO. Our results demonstrate an improvement in accuracy of specific properties across these systems, providing a framework for describing materials with different interaction regimes. We compare our DFT$+U$$+V$ results using our cRPA parameter sets with (i) previous DFT$+U$$+V$ calculation employing pseudopotential approximations, (ii) with experimental results and (iii) with our $GW$ results.

Figures (8)

• Figure 1: Band structure of graphene calculated using GGA (dashed black lines) and GGA+$U$$+V$, using both $u$- and $w$- cRPA parameters (red and green lines). The results are compared to the $GW$ band structure (blue dots).
• Figure 2: Band structure of graphene calculated using GGA (dashed black lines) and GGA+$U$$+V$(fit) (magenta lines). The results are compared with $GW$ (blue dots).
• Figure 3: Band structure of bulk Si calculated using GGA (dashed black lines) and GGA+$U$$+V$ using $u$- and $w$-cRPA parameters (red and green lines). The results are compared with the $GW$ band structure (blue dots).
• Figure 4: Band structure of bulk Si calculated using GGA and GGA+$U$$+V$ utilizing fit parameters. The results are compared to $GW$.
• Figure 5: Band structure of bulk Ge calculated using GGA and GGA+$U$$+V$ utilizing the fitted parameters. The results are compared to the $GW$ band structure.