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

W. Beida1,2,*, G. Bihlmayer1, C. Friedrich1, G. Michalicek1, D. Wortmann1, and S. Blügel1,2

  • *Contact author: w.beida@fz-juelich.de
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Phys. Rev. B 114, 045129 – Published 28 July, 2026

DOI: https://doi.org/10.1103/7sqg-q7kr

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 on-site 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) by 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 calculations employing pseudopotential approximations, (ii) experimental results, and (iii) our GW results.

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References (62)

  1. J. Hubbard, Electron correlations in narrow energy bands. II. The degenerate band case, Proc. R. Soc. London A 277, 237 (1964).
  2. A. B. Shick, A. I. Liechtenstein, and W. E. Pickett, Implementation of the LDA + U method using the full-potential linearized augmented plane-wave basis, Phys. Rev. B 60, 10763 (1999).
  3. V. L. Campo and M. Cococcioni, Extended DFT+U+V method with on-site and inter-site electronic interactions, J. Phys.: Condens. Matter 22, 055602 (2010).
  4. A. Subedi, O. E. Peil, and A. Georges, Low-energy description of the metal-insulator transition in the rare-earth nickelates, Phys. Rev. B 91, 075128 (2015).
  5. H. J. Xiang and M.-H. Whangbo, Charge order and the origin of giant magneto capacitance in LuFe2O4, Phys. Rev. Lett. 98, 246403 (2007).
  6. M. Freyss, B. Dorado, M. Bertolus, G. Jomard, E. Vathonne, P. Garcia, and B. Amadon, First-principles DFT+U study of radiation damage in UO2: F electron correlations and the local energy minima issue, Psi-k newsl 113, 35 (2012).
  7. B. Stahl and T. Bredow, Critical assessment of the DFT+ U approach for the prediction of vanadium dioxide properties, J. Comput. Chem. 41, 258 (2020).
  8. L. Haas, P. Mlkvik, N. A. Spaldin, and C. Ederer, Incorporating static intersite correlation effects in vanadium dioxide through DFT+V, Phys. Rev. Res. 6, 043177 (2024).
  9. T. O. Wehling, E. Sasioglu, C. Friedrich, A. I. Lichtenstein, M. I. Katsnelson, and S. Blügel, Strength of effective Coulomb interactions in graphene and graphite, Phys. Rev. Lett. 106, 236805 (2011).
  10. F. Haddadi, E. Linscott, I. Timrov, N. Marzari, and M. Gibertini, On-site and intersite Hubbard corrections in magnetic monolayers: The case of FePS3 and CrI3, Phys. Rev. Mater. 8, 014007 (2024).
  11. J. Huang, S.-H. Lee, Y.-W. Son, A. Supka, and S. Liu, First-principles study of two-dimensional ferroelectrics using self-consistent Hubbard parameters, Phys. Rev. B 102, 165157 (2020).
  12. M. Campetella, G. Marini, J. S. Zhou, and M. Calandra, Electron-phonon driven charge density wave in CuTe, Phys. Rev. B 108, 024304 (2023).
  13. G. Chen, M. Rösner, and J. L. Lado, Controlling magnetic frustration in 1T−TaS2 via Coulomb engineered long-range interactions, J. Phys.: Condens. Matter 34, 485805 (2022).
  14. J. Kim, K. W. Kim, B. Kim, C. J. Kang, D. Shin, S.-H. Lee, B.-C. Min, and N. Park, Exploitable magnetic anisotropy of the two-dimensional magnet CrI3, Nano Lett. 20, 929 (2020).
  15. N. Tancogne-Dejean and A. Rubio, Parameter-free hybridlike functional based on an extended Hubbard model: DFT+U+V, Phys. Rev. B 102, 155117 (2020).
  16. V. I. Anisimov, I. S. Elfimov, N. Hamada, and K. Terakura, Charge-ordered insulating state of Fe3O4 from first-principles electronic structure calculations, Phys. Rev. B 54, 4387 (1996).
  17. I. Timrov, F. Aquilante, M. Cococcioni, and N. Marzari, Accurate electronic properties and intercalation voltages of olivine-type Li-ion cathode materials from extended Hubbard functionals, PRX Energy 1, 033003 (2022).
  18. The FLEUR project, https://www.flapw.de/
  19. D. Wortmann, G. Michalicek, N. Baadji, W. Beida, M. Betzinger, G. Bihlmayer, T. Bornhake, J. Bröder, T. Burnus, J. Enkovaara, et al., FLEUR, (Version MaX-R7.2) [Computer software], Zenodo, 2024, doi: 10.5281/zenodo.7576163.
  20. E. Bosoni, L. Beal, M. Bercx, P. Blaha, S. Blügel, J. Bröder, M. Callsen, S. Cottenier, A. Degomme, V. Dikan, et al., How to verify the precision of density-functional-theory implementations via reproducible and universal workflows, Nat. Rev. Phys. 6, 45 (2024).
  21. F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004).
  22. E. Şaşıoğlu, C. Friedrich, and S. Blügel, Effective Coulomb interaction in transition metals from constrained random-phase approximation, Phys. Rev. B 83, 121101(R) (2011).
  23. C. Friedrich, M. C. T. D. Müller, J. Kirchmair, R. Sakuma, E. Sasioglu, M. Niesert, and S. Blügel, Spex (Version 05.13.5) [Computer software], Zenodo, 2023, doi: 10.5281/zenodo.14017762.
  24. D. D. Koelling and G. O. Arbman, Use of energy derivative of the radial solution in an augmented plane wave method: Application to copper, J. Phys. F 5, 2041 (1975).
  25. E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O2 molecule, Phys. Rev. B 24, 864 (1981).
  26. L. A. Agapito, S. Curtarolo, and M. B. Nardelli, Reformulation of DFT+U as a pseudohybrid Hubbard density functional for accelerated materials discovery, Phys. Rev. X 5, 011006 (2015).
  27. K. Haule, C.-H. Yee, and K. Kim, Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5, Phys. Rev. B 81, 195107 (2010).
  28. A. G. Petukhov, I. I. Mazin, L. Chioncel, and A. I. Lichtenstein, Correlated metals and the LDA+ U method, Phys. Rev. B 67, 153106 (2003).
  29. F. Bultmark, F. Cricchio, O. Grånäs, and L. Nordström, Multipole decomposition of LDA+ U energy and its application to actinide compounds, Phys. Rev. B 80, 035121 (2009).
  30. F. Aryasetiawan, T. Miyake, and R. Sakuma, The constrained RPA method for calculating the Hubbard U from first-principles, in The LDA+DMFT Approach to Strongly Correlated Materials, edited by E. Pavarini, E. Koch, D. Vollhardt, and A. Lichtenstein, Modeling and Simulation Vol. 1 (Forschungszentrum, Jülich, 2011).
  31. N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
  32. A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
  33. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  34. F. Birch, Finite elastic strain of cubic crystals, Phys. Rev. 71, 809 (1947).
  35. C. Friedrich, S. Blügel, and A. Schindlmayr, Efficient implementation of the GW approximation within the all-electron FLAPW method, Phys. Rev. B 81, 125102 (2010).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/7sqg-q7kr for detailed cRPA-derived on-site and inter-site Coulomb interaction matrices, averaged Hubbard U and V parameters, and Hund's exchange values for graphene, bulk Si, Ge, and NiO in the u- and Wannier bases.
  37. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, Quasiparticle dynamics in graphene, Nat. Phys. 3, 36 (2007).
  38. Semiconductors on NSM, https://www.ioffe.ru/SVA/NSM/Semicond/.
  39. A. Jivani, H. Trivedi, P. Gajjar, and A. Jani, Some physical properties of Si(1−x)Gex solid solutions using pseudo-alloy atom model, Semicond. Phys. Quantum Electron. Optoelectron. 8, 14 (2005).
  40. L. D. Yuan, S. S. Li, and J. W. Luo, Direct bandgap emission from strain-doped germanium, Nat. Commun. 15, 618 (2024).
  41. A. Rohrbach, J. Hafner, and G. Kresse, Molecular adsorption on the surface of strongly correlated transition-metal oxides: A case study for CO/NiO (100), Phys. Rev. B 69, 075413 (2004).
  42. A. Fujimori and F. Minami, Valence-band photoemission and optical absorption in Nickel compounds, Phys. Rev. B 30, 957 (1984).
  43. G. A. Sawatzky and J. W. Allen, Magnitude and origin of the band gap in NiO, Phys. Rev. Lett. 53, 2339 (1984).
  44. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 2004), Vol. 85.
  45. A. G. Gavriliuk, V. V. Struzhkin, A. G. Ivanova, V. B. Prakapenka, A. A. Mironovich, S. N. Aksenov, I. A. Troyan, and W. Morgenroth, The first-order structural transition in NiO at high pressure, Commun. Phys. 6, 23 (2023).
  46. E. Z. Kurmaev, R. G. Wilks, A. Moewes, L. D. Finkelstein, S. N. Shamin, and J. Kuneš, Oxygen x-ray emission and absorption spectra as a probe of the electronic structure of strongly correlated oxides, Phys. Rev. B 77, 165127 (2008).
  47. A. K. Cheetham and D. A. O. Hope, Magnetic ordering and exchange effects in the antiferromagnetic solid solutions MnxNi1−xO, Phys. Rev. B 27, 6964 (1983).
  48. R. Uno, Structure factors and temperature factors of NiO, J. Phys. Soc. Jpn. 18, 739 (1963).
  49. M. R. Thuler, R. L. Benbow, and Z. Hurych, Photoemission intensities at the 3p threshold resonance of NiO and Ni, Phys. Rev. B 27, 2082 (1983).
  50. J. van Elp, H. Eskes, P. Kuiper, and G. A. Sawatzky, Electronic structure of Li-doped NiO, Phys. Rev. B 45, 1612 (1992).
  51. X. Ren, I. Leonov, G. Keller, M. Kollar, I. Nekrasov, and D. Vollhardt, LDA+DMFT computation of the electronic spectrum of NiO, Phys. Rev. B 74, 195114 (2006).
  52. C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys. 110, 6158 (1999).
  53. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
  54. J. Heyd, G. E. Scuseria and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)], J. Chem. Phys. 124, 219906 (2006).
  55. W. Chen, G. Miceli, G.-M. Rignanese, and A. Pasquarello, Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators, Phys. Rev. Mater. 2, 073803 (2018).
  56. Z.-H. Cui, Y.-C. Wang, M.-Y. Zhang, X. Xu, and H. Jiang, Doubly screened hybrid functional: An accurate first-principles approach for both narrow-and wide-gap semiconductors, J. Phys. Chem. Lett. 9, 2338 (2018).
  57. P. Liu, C. Franchini, M. Marsman, and G. Kresse, Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO, J. Phys.: Condens. Matter 32, 015502 (2020).
  58. M. Redies, G. Michalicek, J. Bouaziz, C. Terboven, M. S. Müller, S. Blügel, and D. Wortmann, Fast all-electron hybrid functionals and their application to rare-earth iron garnets, Front. Mater. 9, 851458 (2022).
  59. I. Duchemin and F. Gygi, A scalable and accurate algorithm for the computation of Hartree–Fock exchange, Comput. Phys. Commun. 181, 855 (2010).
  60. R. Dovesi, K. Doll, M. Causà, M. Rérat, and P. D'Arco, The Hartree–Fock exchange for crystalline systems: The implementation with an (All-electron) Gaussian-type basis set and numerical evidence with reference to perovskites, J. Chem. Theory Comput. 22, 4767 (2026).
  61. Jülich Supercomputing Centre, JURECA: Data centric and booster modules implementing the modular supercomputing architecture at Jülich Supercomputing Centre, J. Large-Scale Res. Facil. 7, A182 (2021).
  62. W. Beida, G. Bihlmayer, C. Friedrich, G. Michalicek, D. Wortmann, and S. Blügel, Replication data for 'Implementation and application of a DFT+U+V approach within the all-electron FLAPW method’, Jülich data, 2026, https://doi.org/10.26165/JUELICH-DATA/WBIQAE.

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Phys. Rev. B 114, 045129– Published 28 July, 2026
  • Received 11 November 2025
  • Revised 8 April 2026
  • Accepted 1 July 2026
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