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arxiv: 2604.06927 · v1 · submitted 2026-04-08 · ❄️ cond-mat.str-el · physics.chem-ph· physics.comp-ph

Development of ab initio Hubbard parameter calculation schemes in the k-point sampling real-time TDDFT program in CP2K

Kota Hanasaki , Sandra Luber This is my paper

Pith reviewed 2026-05-10 17:53 UTC · model grok-4.3

classification ❄️ cond-mat.str-el physics.chem-phphysics.comp-ph
keywords Hubbard parameterslinear responsereal-time TDDFTenergy-dependentexchange-correlation effectsab initio calculationsstrongly correlated electronsk-point sampling
0
0 comments X

The pith

A new scheme computes energy-dependent Hubbard parameters that reflect exchange-correlation effects in real-time TDDFT.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper implements ab initio schemes for calculating Hubbard parameters inside a k-point sampling real-time time-dependent density functional theory program. It proposes extending the minimum-tracking linear-response method to produce energy-dependent parameters that include the exchange-correlation effects from the functional. This extension matters for modeling dynamical processes in strongly correlated electron systems more accurately than static parameters allow. The authors compare this approach to another linear-response scheme and find that each supports different dynamical applications despite similar performance on static properties.

Core claim

The authors have developed a new linear-response-based scheme for computing energy-dependent Hubbard parameters. This scheme extends the minimum-tracking linear-response method to incorporate the exchange-correlation effects included in the chosen functional. The implementation is done in the k-point sampling real-time TDDFT framework, enabling the parameters' use in time-dependent simulations. Discussion of its properties relative to an alternative scheme highlights distinct uses in dynamical contexts.

What carries the argument

The extended minimum-tracking linear-response method for energy-dependent Hubbard parameters, which tracks the minimum response to extract parameters sensitive to the exchange-correlation functional.

If this is right

  • Energy-dependent Hubbard parameters can now be used in real-time simulations to better capture dynamical correlation effects.
  • The new scheme produces parameters that reflect the exchange-correlation effects from the chosen functional.
  • Neither the new scheme nor the alternative shows clear superiority for static property calculations.
  • Each scheme has distinct applications in dynamical simulations based on its formulation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying the energy-dependent parameters could improve simulations of time-resolved phenomena such as photoexcitation in correlated materials.
  • Testing the scheme across different functionals would show how sensitive the parameters are to the choice of exchange-correlation approximation.
  • The approach provides a foundation for updating Hubbard parameters during real-time evolution of electronic states.

Load-bearing premise

That the extension of the minimum-tracking linear-response method to energy dependence accurately captures the exchange-correlation effects without introducing additional uncontrolled errors.

What would settle it

A calculation of the energy-dependent Hubbard parameters for a well-known material and direct comparison to values obtained from more advanced theoretical methods or from fitting to experimental data would confirm or refute the scheme's validity.

Figures

Figures reproduced from arXiv: 2604.06927 by Kota Hanasaki, Sandra Luber.

Figure 1
Figure 1. Figure 1: FIG. 1. Time-dependent Hubbard parameters in the strong-fie [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy-dependent Hubbard parameters for NiO and MnO [PITH_FULL_IMAGE:figures/full_fig_p025_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. PDOSs of ScN (a), TiO [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Energy-dependent Hubbard parameters for NiO and MnO [PITH_FULL_IMAGE:figures/full_fig_p032_4.png] view at source ↗
read the original abstract

We implemented ab initio Hubbard parameter calculation schemes in the k-point sampling real-time TDDFT (RT-TDDFT) program in CP2K. We propose a new linear-response-based calculation scheme for energy-dependent Hubbard parameters. Our scheme extends the minimum-tracking linear-response method proposed in [Moynihan et al., arXiv preprint arXiv:1704.08076(2017); E. B. Linscott et al., Phys. Rev. B 98, 235157 (2018)] to realize the calculation of energy-dependent Hubbard parameters that reflect the exchange-correlation (xc) effects included in the xc-functional. We discuss the properties of the minimum-tracking linear-response method in comparison to another promising scheme, ACBN0 [Agapito et al., Phys. Rev. X, 5, 011006 (2015)]. We show that, while neither clearly outperforms the other in the accuracy of static property calculations, each has a distinct dynamical application depending on its theoretical formulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript reports the implementation of ab initio Hubbard parameter calculation schemes inside the k-point sampling real-time TDDFT module of CP2K. It proposes and realizes a new linear-response scheme that extends the minimum-tracking method of Moynihan et al. and Linscott et al. to produce energy-dependent Hubbard parameters U(ω) that incorporate the exchange-correlation effects present in the chosen xc-functional. The work also compares the new scheme to ACBN0, concluding that the two approaches exhibit comparable accuracy for static properties but possess distinct advantages for dynamical applications.

Significance. If the implementation and benchmarks are sound, the contribution supplies a practical route to dynamical, xc-consistent Hubbard parameters inside an open-source RT-TDDFT code. This is useful for modeling time-dependent phenomena in correlated materials where static U values are insufficient. The explicit comparison of minimum-tracking and ACBN0 formulations clarifies their complementary regimes of applicability.

minor comments (3)
  1. The abstract states that the new scheme 'reflects the xc effects included in the xc-functional' but supplies no explicit formula or numerical illustration of how the minimum-tracking procedure transfers those effects into U(ω). Adding one short equation or a representative numerical example would strengthen the claim.
  2. Section describing the comparison to ACBN0 should explicitly list the materials, functionals, and observables used to conclude that 'neither clearly outperforms the other' for static properties; without these details the statement remains qualitative.
  3. The manuscript should clarify whether the energy-dependent U(ω) is obtained on-the-fly during the RT-TDDFT propagation or computed in a separate linear-response step, as this affects computational cost and reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance for dynamical applications in correlated materials, and recommendation for minor revision. The manuscript implements energy-dependent Hubbard parameters U(ω) via an extension of the minimum-tracking linear-response approach within CP2K's k-point RT-TDDFT, incorporating xc effects, and compares it to ACBN0 for static and dynamical regimes.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an implementation of Hubbard parameter schemes in k-point RT-TDDFT within CP2K, including a proposed extension of the minimum-tracking linear-response method (cited from Moynihan et al. and Linscott et al.) to energy-dependent U(ω) values. This extension is framed as a direct application of the existing formalism inside the TDDFT xc-functional, with comparisons to the independent ACBN0 method (Agapito et al.). No load-bearing self-citations appear, no parameters are fitted and then relabeled as predictions, and no derivation reduces by construction to the inputs; the central claims rest on the correctness of the cited prior formalisms and the code implementation rather than internal redefinitions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of linear-response theory within RT-TDDFT and on the assumption that the minimum-tracking procedure can be generalized to energy dependence while preserving xc effects. No new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Linear-response theory applies to the real-time TDDFT propagation in CP2K with k-point sampling.
    The new scheme is built directly on this established framework.
  • ad hoc to paper The xc-functional effects can be transferred into the Hubbard parameter via the minimum-tracking procedure without additional approximations.
    This is the key extension claimed in the abstract.

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Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages

  1. [1]

    The set of correlated orbitals, hereafte r labeled by symbol I, is characterized by the atomic species and the orbital angular momen tum ℓI (e.g., d-orbitals of Ni)

    The energy functional In DFT+U, the Coulomb interactions among selected sets of localized orbitals with strong correlation, hereafter referred to as correlated orbitals , are treated explicitly in the form of on-site interactions. The set of correlated orbitals, hereafte r labeled by symbol I, is characterized by the atomic species and the orbital angular...

    work page

  2. [2]

    Projection scheme The projected density matrix in Eq. (10) is given as ρ(I,A ) σ = P (I,A )ρσ P (I,A ) (11) 6 where the projection operator P (I,A ) in the coordinate representation is given as [32] P (I,A )(r, r′) = ∑ m,m ′∈ (I,A ) φ (I,A ) m (r) ( O− 1 (I,A ) ) mm′ φ (I,A ) ∗ m′ (r′) (12) with {φ (I,A ) m (r)} being a set of local orbitals representing ...

    work page

  3. [3]

    [25], we introduce the ‘renormalized’ occupation number

    ACBN0 Following Agapito et al. [25], we introduce the ‘renormalized’ occupation number. To make it consistent with our projection scheme Eq. (11), we use the following expression N (I)σ ψ λ kσ ≡ ∑ A Tr ( P (I,A )ρλ kσ P (I,A )) (15) where ρλ kσ is a part of the density matrix that consists only of a single KS orbital ψλ kσ as ρλ kσ (r, r′) ≡ ψλ k(r)θλ kψ ...

    work page

  4. [4]

    Cococcioni et al

    Linear response methods Linear response methods are based on the response of the syste m to an externally applied perturbation on the projected space. Cococcioni et al. [7] developed a scheme based on the density response χ and its Kohn-Sham correspondence χKS . Their theory has been success- fully applied to ab initio calculations of correlated systems [...

    work page

  5. [5]

    Comparison between methodologies The Hubbard parameters U and J are characterized as the screened Coulomb and ex- change interactions averaged over the orbitals in the projected s pace, respectively. In the linear response approaches, the screening is explicitly calculated fr om the linear response, while in ACBN0, the static correlation among KS orbitals...

    work page

  6. [6]

    We first rewrite 13 Eq

    Extension of linear response schemes The fact that cRPA is not a perfect tool for calculating U(ω ) motivates us to develop a possible alternative way to calculate U(ω ) using linear response theories. We first rewrite 13 Eq. (29a) as follows; U (I,A ) = 1 2 1 No ∑ m ⟨ φ (I,A ) m ⏐ ⏐ ⏐ ⏐ ⏐ ⏐ ∂ ( V Hxc ↑ +V Hxc ↓ ) ∂ ( N (I,A ) ↑ +N (I,A ) ↓ ) ⏐ ⏐ ⏐ ⏐ ⏐ ⏐ φ...

    work page

  7. [7]

    Hohenberg and W

    P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Ph ys. Rev. 136, B864 (1964)

    work page 1964

  8. [8]

    Kohn and L

    W. Kohn and L. J. Sham, Self-consistent equations includ ing exchange and correlation effects, Phys. Rev. 140, A1133 (1965)

    work page 1965

  9. [9]

    Runge and E

    E. Runge and E. K. U. Gross, Density-functional theory fo r time-dependent systems, Phys. Rev. Lett. 52, 997 (1984)

    work page 1984

  10. [10]

    J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981)

    work page 1981

  11. [11]

    Mori-Sanchez, A

    P. Mori-Sanchez, A. J. Cohen, and W. Yang, Many-electron self-interaction error in approxi- mate density functionals, The Journal of Chemical Physics 125, 201102 (2006)

    work page 2006

  12. [12]

    Mori-S´ anchez, A

    P. Mori-S´ anchez, A. J. Cohen, and W. Yang, Localization and delocalization errors in density functional theory and implications for band-gap predictio n, Physical review letters 100, 146401 (2008)

    work page 2008

  13. [13]

    Cococcioni and S

    M. Cococcioni and S. de Gironcoli, Linear response appro ach to the calculation of the effective interaction parameters in the LDA + U method, Phys. Rev. B 71, 035105 (2005)

    work page 2005

  14. [14]

    Moynihan, G

    G. Moynihan, G. Teobaldi, and D. D. O’Regan, A self-consi stent ground-state formulation of the first-principles hubbard U parameter validated on one-electron self-interaction err or, arXiv preprint arXiv:1704.08076 (2017)

    work page arXiv 2017

  15. [15]

    A. C. Burgess, E. Linscott, and D. D. O’Regan, DFT+ U -type functional derived to explicitly address the flat plane condition, Phys. Rev. B 107, L121115 (2023)

    work page 2023

  16. [16]

    V. I. Anisimov, J. Zaanen, and O. K. Andersen, Band theor y and mott insulators: Hubbard U instead of Stoner I, Phys. Rev. B 44, 943 (1991)

    work page 1991

  17. [17]

    S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphre ys, and A. P. Sutton, Electron- energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study, Phys. Rev. B 57, 1505 (1998)

    work page 1998

  18. [18]

    N. E. Kirchner-Hall, W. Zhao, Y. Xiong, I. Timrov, and I. Dabo, Extensive benchmarking of DFT+U calculations for predicting band gaps, Applied Sciences 11, 2395 (2021)

    work page 2021

  19. [19]

    G. C. Moore, M. K. Horton, E. Linscott, A. M. Ganose, M. Si ron, D. D. O’Regan, and K. A. Persson, High-throughput determination of hubbard U and hund J values for transition metal 33 oxides via the linear response formalism, Phys. Rev. Mater. 8, 014409 (2024)

    work page 2024

  20. [20]

    Adler, C.-J

    R. Adler, C.-J. Kang, C.-H. Yee, and G. Kotliar, Correla ted materials design: prospects and challenges, Reports on Progress in Physics 82, 012504 (2018)

    work page 2018

  21. [21]

    Capdevila-Cortada, Z

    M. Capdevila-Cortada, Z. /suppress Lodziana, and N. L´ opez, Per formance of DFT+ U ap- proaches in the study of catalytic materials, ACS Catalysis 6, 8370 (2016), https://doi.org/10.1021/acscatal.6b01907

    work page doi:10.1021/acscatal.6b01907 2016

  22. [22]

    Aykol and C

    M. Aykol and C. Wolverton, Local environment dependent GGA + U method for accurate thermochemistry of transition metal compounds, Phys. Rev. B 90, 115105 (2014)

    work page 2014

  23. [23]

    Aryasetiawan, M

    F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Bi ermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effe ctive models from electronic struc- ture calculations, Phys. Rev. B 70, 195104 (2004)

    work page 2004

  24. [24]

    Y. Wu, M. Caserta, T. Chiarotti, and N. Marzari, Electro nic structure and dynamical corre- lations in antiferromagnetic bifeo 3, arXiv preprint arXiv:2511.23181 (2025)

    work page arXiv 2025

  25. [25]

    Tancogne-Dejean, M

    N. Tancogne-Dejean, M. J. T. Oliveira, and A. Rubio, Sel f-consistent DFT + U method for real-space time-dependent density functional theory calc ulations, Phys. Rev. B 96, 245133 (2017)

    work page 2017

  26. [26]

    Beaulieu, S

    S. Beaulieu, S. Dong, N. Tancogne-Dejean, M. Dendzik, T . Pincelli, J. Mak- lar, R. P. Xian, M. A. Sentef, M. Wolf, A. Rubio, L. Rettig, and R. Ern- storfer, Ultrafast dynamical Lifshitz transition, Scienc e Advances 7, eabd9275 (2021), https://www.science.org/doi/pdf/10.1126/sciadv.abd9275

    work page doi:10.1126/sciadv.abd9275 2021

  27. [27]

    Cazali, A

    R. Cazali, A. Alic, M. Guer, C. J. Kaplan, F. Lepetit, O. T cherbakoff, S. Guizard, A. Rubio, N. Tancogne-Dejean, G. S. Chiuzb˘ aian, et al. , Correlations drive the attosecond response of strongly-correlated insulators, arXiv preprint arXiv:25 01.19238 (2025)

    work page 2025

  28. [28]

    Golez, E

    D. Golez, E. Paprotzki, P. Werner, and M. Eckstein, Meas uring the ultrafast screening of U in photo-excited charge-transfer insulators with time-re solved x-ray absorption spectroscopy, arXiv preprint arXiv:2409.06314 (2024)

    work page arXiv 2024

  29. [29]

    V. I. Anisimov and O. Gunnarsson, Density-functional c alculation of effective coulomb inter- actions in metals, Phys. Rev. B 43, 7570 (1991)

    work page 1991

  30. [30]

    E. B. Linscott, D. J. Cole, M. C. Payne, and D. D. O’Regan, Role of spin in the calculation of hubbard u and hund’s j parameters from first principles, Phys. Rev. B 98, 235157 (2018). 34

    work page 2018

  31. [31]

    L. A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli , Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated m aterials discovery, Phys. Rev. X 5, 011006 (2015)

    work page 2015

  32. [32]

    Honerkamp, H

    C. Honerkamp, H. Shinaoka, F. F. Assaad, and P. Werner, L imitations of constrained random phase approximation downfolding, Phys. Rev. B 98, 235151 (2018)

    work page 2018

  33. [33]

    Carta, I

    A. Carta, I. Timrov, S. Beck, and C. Ederer, Bridging con strained random-phase ap- proximation and linear response theory for computing hubba rd parameters, arXiv preprint arXiv:2505.03698 (2025)

    work page arXiv 2025

  34. [34]

    Tancogne-Dejean, M

    N. Tancogne-Dejean, M. A. Sentef, and A. Rubio, Ultrafa st transient absorption spectroscopy of the charge-transfer insulator NiO: Beyond the dynamical Franz-Keldysh effect, Phys. Rev. B 102, 115106 (2020)

    work page 2020

  35. [35]

    Hanasaki and S

    K. Hanasaki and S. Luber, Development of real-time TDDF T program with k-point sampling and DFT+ U in a gaussian and plane waves framework, Journal of Chemical Theory and Computation 21, 1879 (2025)

    work page 2025

  36. [36]

    Hanasaki, T

    K. Hanasaki, T. F. de Jong, K. Komarov, R. Kumar, M. Maliˇ s, J. Mattiat, L. I. Hernandez-Segura, L. Schreder, A. Sinyavskiy, and S. Luber , Exploring excited-state electronic structure, spectroscopy, and nonadiabatic dyn amics with cp2k’s multifaceted approach, The Journal of Physical Chemistry A 129, 7313 (2025), pMID: 40758753, https://doi.org/10.1021/...

    work page doi:10.1021/acs.jpca.5c02969 2025

  37. [37]

    D. D. O’Regan, M. C. Payne, and A. A. Mostofi, Subspace rep resentations in ab initio methods for strongly correlated systems, Phys. Rev. B 83, 245124 (2011)

    work page 2011

  38. [38]

    Z. Chai, R. Si, M. Chen, G. Teobaldi, D. D. O’Regan, and L. -M. Liu, Mini- mum tracking linear response hubbard and hund corrected den sity functional theory in cp2k, Journal of Chemical Theory and Computation 20, 8984 (2024), pMID: 39360658, https://doi.org/10.1021/acs.jctc.4c00964

    work page doi:10.1021/acs.jctc.4c00964 2024

  39. [39]

    Himmetoglu, A

    B. Himmetoglu, A. Floris, S. de Gironcoli, and M. Cococc ioni, Hubbard-corrected DFT energy functionals: The LDA+ U description of correlated systems, International Journal of Quantum Chemistry 114, 14 (2014), https://onlinelibrary.wiley.com/doi/pdf/1 0.1002/qua.24521

    work page 2014

  40. [40]

    Floris, S

    A. Floris, S. de Gironcoli, E. K. U. Gross, and M. Cococci oni, Vibrational properties of MnO and NiO from DFT + U -based density functional perturbation theory, Phys. Rev. B 84, 161102 35 (2011)

    work page 2011

  41. [41]

    H. J. Kulik, M. Cococcioni, D. A. Scherlis, and N. Marzar i, Density functional theory in transition-metal chemistry: A self-consistent hubbard U approach, Phys. Rev. Lett. 97, 103001 (2006)

    work page 2006

  42. [42]

    Goleˇ z, M

    D. Goleˇ z, M. Eckstein, and P. Werner, Multiband nonequ ilibrium GW + EDMFT formalism for correlated insulators, Phys. Rev. B 100, 235117 (2019)

    work page 2019

  43. [43]

    Vanzini and N

    M. Vanzini and N. Marzari, Towards a minimal descriptio n of dynamical correlation in metals, arXiv preprint arXiv:2309.12144 (2023)

    work page arXiv 2023

  44. [44]

    Leiria Campo and M

    V. Leiria Campo and M. Cococcioni, Extended DFT + U + V method with on-site and inter-site electronic interactions, Journal of Physics: C ondensed Matter 22, 055602 (2010)

    work page 2010

  45. [45]

    Nakamura, Y

    K. Nakamura, Y. Yoshimoto, Y. Nomura, T. Tadano, M. Kawa mura, T. Kosugi, K. Yoshimi, T. Misawa, and Y. Motoyama, RESPACK: An ab initio tool for der ivation of effective low- energy model of material, Computer Physics Communications 261, 107781 (2021)

    work page 2021

  46. [46]

    Miyake, F

    T. Miyake, F. Aryasetiawan, and M. Imada, Ab initio proc edure for constructing effective models of correlated materials with entangled band structu re, Phys. Rev. B 80, 155134 (2009)

    work page 2009

  47. [47]

    R. M. Martin, L. Reining, and D. M. Ceperley, Interacting electrons (Cambridge University Press, 2016)

    work page 2016

  48. [48]

    Yabana and G

    K. Yabana and G. F. Bertsch, Time-dependent local-dens ity approximation in real time, Phys. Rev. B 54, 4484 (1996)

    work page 1996

  49. [49]

    Timrov, N

    I. Timrov, N. Marzari, and M. Cococcioni, Hubbard param eters from density-functional per- turbation theory, Phys. Rev. B 98, 085127 (2018)

    work page 2018

  50. [50]

    Goedecker, M

    S. Goedecker, M. Teter, and J. Hutter, Separable dual-s pace gaussian pseudopotentials, Phys. Rev. B 54, 1703 (1996)

    work page 1996

  51. [51]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gr adient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  52. [52]

    VandeVondele and J

    J. VandeVondele and J. Hutter, Gaussian basis sets for a ccurate calculations on molecular systems in gas and condensed phases, The Journal of Chemical Physics 127, 114105 (2007)

    work page 2007

  53. [53]

    H. J. Monkhorst and J. D. Pack, Special points for Brillo uin-zone integrations, Phys. Rev. B 13, 5188 (1976)

    work page 1976

  54. [54]

    H. A. Al-Brithen, A. R. Smith, and D. Gall, Surface and bu lk electronic structure of ScN(001) investigated by scanning tunneling microscopy/spectrosc opy and optical absorption spec- 36 troscopy, Phys. Rev. B 70, 045303 (2004)

    work page 2004

  55. [55]

    Tezuka, S

    Y. Tezuka, S. Shin, T. Ishii, T. Ejima, S. Suzuki, and S. S ato, Photoemission and bremsstrahlung isochromat spectroscopy studies of TiO 2 (rutile) and SrTiO 3, Journal of the Physical Society of Japan 63, 347 (1994)

    work page 1994

  56. [56]

    van Elp, R

    J. van Elp, R. H. Potze, H. Eskes, R. Berger, and G. A. Sawa tzky, Electronic structure of MnO, Phys. Rev. B 44, 1530 (1991)

    work page 1991

  57. [57]

    A. K. Cheetham and D. A. O. Hope, Magnetic ordering and ex change effects in the antiferro- magnetic solid solutions Mn xNi1−xO, Phys. Rev. B 27, 6964 (1983)

    work page 1983

  58. [58]

    G. A. Sawatzky and J. W. Allen, Magnitude and origin of th e band gap in NiO, Phys. Rev. Lett. 53, 2339 (1984)

    work page 1984

  59. [59]

    Ghijsen, L

    J. Ghijsen, L. H. Tjeng, J. van Elp, H. Eskes, J. Westerin k, G. A. Sawatzky, and M. T. Czyzyk, Electronic structure of Cu 2O and CuO, Phys. Rev. B 38, 11322 (1988)

    work page 1988

  60. [60]

    Marabelli, G

    F. Marabelli, G. B. Parravicini, and F. Salghetti-Drio li, Optical gap of CuO, Phys. Rev. B 52, 1433 (1995)

    work page 1995

  61. [61]

    J. B. Forsyth, P. J. Brown, and B. M. Wanklyn, Magnetism i n cupric oxide, Journal of Physics C: Solid State Physics 21, 2917 (1988)

    work page 1988

  62. [62]

    A. Mang, K. Reimann, and S. R¨ ubenacke, Band gaps, cryst al-field splitting, spin-orbit cou- pling, and exciton binding energies in ZnO under hydrostati c pressure, Solid State Commu- nications 94, 251 (1995)

    work page 1995

  63. [63]

    H. J. Kulik and N. Marzari, A self-consistent hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on b are FeO+, The Journal of Chemical Physics 129, 134314 (2008)

    work page 2008

  64. [64]

    Tancogne-Dejean, M

    N. Tancogne-Dejean, M. A. Sentef, and A. Rubio, Ultrafa st modification of hubbard U in a strongly correlated material: Ab initio high-harmonic gen eration in NiO, Phys. Rev. Lett. 121, 097402 (2018)

    work page 2018

  65. [65]

    G. F. Bertsch, J.-I. Iwata, A. Rubio, and K. Yabana, Real -space, real-time method for the dielectric function, Phys. Rev. B 62, 7998 (2000)

    work page 2000

  66. [66]

    J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G . E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expan sion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008). 37

    work page 2008

  67. [67]

    Trimarchi, Z

    G. Trimarchi, Z. Wang, and A. Zunger, Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the mott i nsulators MnO, FeO, CoO, and NiO, Phys. Rev. B 97, 035107 (2018)

    work page 2018

  68. [68]

    Kobayashi, Y

    S. Kobayashi, Y. Nohara, S. Yamamoto, and T. Fujiwara, G W approximation with LSDA+ U method and applications to NiO, MnO, and V 2O3, Phys. Rev. B 78, 155112 (2008)

    work page 2008

  69. [69]

    Y. Wang, S. Lany, J. Ghanbaja, Y. Fagot-Revurat, Y. P. Ch en, F. Soldera, D. Horwat, F. M¨ ucklich, and J. F. Pierson, Electronic structures of Cu 2O,Cu4O3, and CuO: A joint experimental and theoretical study, Phys. Rev. B 94, 245418 (2016). 38

    work page 2016