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Getting the manifold right: The crucial role of orbital resolution in DFT+U for mixed d-f electron compounds

Kinga Warda, Eric Macke, Iurii Timrov, Lucio Colombi Ciacchi, Piotr M. Kowalski

TL;DR

The paper addresses how self-interaction errors in DFT complicate modeling of materials with partially filled $d$ and $f$ shells, notably actinide-containing AUO4 monouranates. It develops and tests orbital-resolved DFT$+U$ (OR-DFT$+U$) by defining targeted Hubbard manifolds for localized frontier orbitals, either via Wannier-based projectors (DFT$+U$(WF)) or selective orbital corrections (OR-DFT$+U$). The results show that careful disentanglement of localized and delocalized states yields accurate structural distortions and electronic descriptions across NiUO4, MnUO4, and CoUO4, with setup (3) offering the most consistent performance. The study underscores the importance of projector choice and manifold definition for reliable first-principles predictions in strongly covalent, mixed $d$/$f$ systems and points to practical routes for extending these methods to technologically relevant actinide solids.

Abstract

Accurately modeling compounds with partially filled $d$ and $f$ shells remains a hard challenge for density-functional theory, due to large self-interaction errors stemming from local or semi-local exchange-correlation functionals. Hubbard $U$ corrections can mitigate such errors, but are often detrimental to the description of hybridized states, leading to spurious force contributions and wrong lattice structures. Here, we show that careful disentanglement of localized and delocalized states leads to accurate predictions of electronic states and structural distortions in ternary monouranates (AUO$_4$, where A represents Mn, Co, or Ni), for which standard $U$ corrections generally fail. Crucial to achieving such accuracy is a minimization of the mismatch between the spatial extension of the projector functions and the true coordination geometry. This requires Wannier-like alternatives to atomic-orbital projector functions, or corrections of Hubbard manifolds exclusively comprised of the most localized A-$3d$, U-$5f$ and O-$2p$ orbitals. These findings open up the computational prediction of fundamental properties of actinide solids of critical technological importance.

Getting the manifold right: The crucial role of orbital resolution in DFT+U for mixed d-f electron compounds

TL;DR

The paper addresses how self-interaction errors in DFT complicate modeling of materials with partially filled and shells, notably actinide-containing AUO4 monouranates. It develops and tests orbital-resolved DFT (OR-DFT) by defining targeted Hubbard manifolds for localized frontier orbitals, either via Wannier-based projectors (DFT(WF)) or selective orbital corrections (OR-DFT). The results show that careful disentanglement of localized and delocalized states yields accurate structural distortions and electronic descriptions across NiUO4, MnUO4, and CoUO4, with setup (3) offering the most consistent performance. The study underscores the importance of projector choice and manifold definition for reliable first-principles predictions in strongly covalent, mixed / systems and points to practical routes for extending these methods to technologically relevant actinide solids.

Abstract

Accurately modeling compounds with partially filled and shells remains a hard challenge for density-functional theory, due to large self-interaction errors stemming from local or semi-local exchange-correlation functionals. Hubbard corrections can mitigate such errors, but are often detrimental to the description of hybridized states, leading to spurious force contributions and wrong lattice structures. Here, we show that careful disentanglement of localized and delocalized states leads to accurate predictions of electronic states and structural distortions in ternary monouranates (AUO, where A represents Mn, Co, or Ni), for which standard corrections generally fail. Crucial to achieving such accuracy is a minimization of the mismatch between the spatial extension of the projector functions and the true coordination geometry. This requires Wannier-like alternatives to atomic-orbital projector functions, or corrections of Hubbard manifolds exclusively comprised of the most localized A-, U- and O- orbitals. These findings open up the computational prediction of fundamental properties of actinide solids of critical technological importance.

Paper Structure

This paper contains 13 sections, 6 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Materials and methods
  3. Computational details
  4. Characterization of the structural distortions
  5. Results and discussion
  6. Response of the structure to variations in U
  7. Determination of orbital-resolved Hubbard manifolds
  8. Group-theoretical analysis of orbital splitting
  9. Analysis of the electronic occupations
  10. Evaluation of the Hubbard U parameters
  11. Structural distortions
  12. Projector mismatch as a source of spurious Hubbard forces
  13. Concluding remarks

Figures (6)

  • Figure 1: (a) Crystal structure of AUO4 in the orthorhombic Ibmm space group. Oxygen atoms O1 and O2 are shown in red and pink, respectively. (b) Schematic representation of the AO6 tilt angle $\theta$ around the b-axis, quantifying deviations from the idealized Cmmm symmetry. The UO6 octahedra is shown in cyan and the AO6 octahedra in purple. (c) The uranium off-centering $\delta_\mathrm{U}$ and axial oxygen off-centering $\delta_\mathrm{O}$, measured relative to the ideal $Cmmm$ atomic positions. The high-symmetry $Cmmm$ reference structure is indicated by dashed gray lines.
  • Figure 2: Impact of the Hubbard parameters (a) $U_{\mathrm{Ni\text{-}3}d}$ (at fixed $U_{\mathrm{U\text{-}5}f} = 2$ eV and $U_{\mathrm{O\text{-}2}p} = 1$ eV), (b) $U_{\mathrm{U\text{-}5}f}$ (at fixed $U_{\mathrm{Ni\text{-}3}d} = 4$ eV and $U_{\mathrm{O\text{-}2}p} = 1$ eV), and (c) $U_{\mathrm{O\text{-}2}p}$ (at fixed $U_{\mathrm{Ni\text{-}3}d} = 4$ eV and $U_{\mathrm{U\text{-}5}f} = 2$ eV fixed) on the cell volume and the magnitude of the oxygen distortion parameter in β-NiUO4. Solid lines serve as a guide for the eye.
  • Figure 3: Stacked projected density of states (PDOS) for (a) Ni-$3d$, (b) U-$5f$, and (c) O-$2p$ orbitals in β-NiUO4, obtained from trial DFT+$U$ calculations. Panels (d) and (e) show the integrated local density of states for the Ni-$3d$ energy intervals indicated by red and green shading in panel (a) at isovalues 0.0184 $e^-\cdot$Å$^{-3}$ and 0.0079 $e^-\cdot$Å$^{-3}$, respectively.
  • Figure 4: Molecular orbital (MO) diagram of an NiO6 octahedron in NiUO4 indicating the relative TM$-3d$ vs. O-$2p$ character of the MOs on the x-axis. The insets show the MOs corresponding to a few irreducible representations of interest. Data was generated by applying the linear combination of fragment orbitals method mullerFragment2024 implemented in LOBSTERmaintzLOBSTER2016 to the ground state of the trial DFT+$U$(OAO) setup.
  • Figure 5: Off-center displacements of uranium, $\delta_\mathrm{U}$, and O2 atoms, $\delta_\mathrm{O}$ (a,c,e), and octahedral tilt angle $\theta$ in (b,d,f) as obtained from bare PBEsol and DFT$+U$ calculations using differently defined Hubbard manifolds (see text and Table \ref{['tab:parameters']}). The DFT+U(WF) data points were taken from Ref. murphyTiltingDistortionRutileRelated2021.
  • ...and 1 more figures