Volume 3 Issue 2
June  2024
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Guanghui Cai, Zhendong Cao, Fankai Xie, Huaxian Jia, Wei Liu, Yaxian Wang, Feng Liu, Xinguo Ren, Sheng Meng, Miao Liu. Predicting structure-dependent Hubbard U parameters via machine learning[J]. Materials Futures, 2024, 3(2): 025601. doi: 10.1088/2752-5724/ad19e2
Citation: Guanghui Cai, Zhendong Cao, Fankai Xie, Huaxian Jia, Wei Liu, Yaxian Wang, Feng Liu, Xinguo Ren, Sheng Meng, Miao Liu. Predicting structure-dependent Hubbard U parameters via machine learning[J]. Materials Futures, 2024, 3(2): 025601. doi: 10.1088/2752-5724/ad19e2
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Predicting structure-dependent Hubbard U parameters via machine learning

© 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Songshan Lake Materials Laboratory
Materials Futures, Volume 3, Number 2
  • Received Date: 2023-11-02
  • Accepted Date: 2023-12-27
  • Rev Recd Date: 2023-12-21
  • Publish Date: 2024-01-24
doi: 10.1088/2752-5724/ad19e2
  • 1.

    Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

  • 2.

    School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

  • 3.

    Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, People’s Republic of China

  • 4.

    Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

  • 5.

    Tencent AI Lab, Tencent, Shenzhen 518057, People’s Republic of China

  • 6.

    Department of Materials Science and Engineering, University of Utah, Salt Lake City, UT 84112, United States of America

  • Data availability statement

    Data will be available upon request. The code for BO and ML in this work can be found at: https://github.com/zdcao121/ml4dftu

    G Cai and Z Cao contributed equally to this work.

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    Abstract
  • AbstractDFT + U is a widely used treatment in the density functional theory (DFT) to deal with correlated materials that contain open-shell elements, whereby the quantitative and sometimes even qualitative failures of local and semi-local approximations can be corrected without much computational overhead. However, finding appropriate U parameters for a given system and structure is non-trivial and computationally intensive, because the U value has generally a strong chemical and structural dependence. In this work, we address this issue by building a machine learning (ML) model that enables the prediction of material- and structure-specific U values at nearly no computational cost. Using Mn-O system as an example, the ML model is trained by calibrating DFT + U electronic structures with the hybrid functional results of more than 3000 structures. The model allows us to determine an accurate U value (MAE = 0.128 eV, R2 = 0.97) for any given Mn-O structure. Further analysis reveals that M-O bond lengths are key local structural properties in determining the U value. This approach of the ML U model is universally applicable, to significantly expand and solidify the use of the DFT + U method.
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    • Author contributions

    M L proposed and led this project. Z C and G C wrote the code. Z C performed the calculations and analyzed the results. X R and S M copiloted the project with important intellectual contributions. F X, H J, and W L provided assistance with the ML algorithm. Z C and M L wrote the manuscript. Y W, F L, X R, and S M reviewed and revised the manuscript. G C and Z C contributed equally to this work.

    Conflict of interest

    The authors declare no competing interests.

    References(54)
  • [1]
    Perdew J P, Burke K, Ernzerhof M 1996 Generalized gradient approximation made simple Phys. Rev. Lett. 77 3865-8 doi: 10.1103/PhysRevLett.77.3865
    [2]
    Becke A D 1988 Density-functional exchange-energy approximation with correct asymptotic behavior Phys. Rev. A 38 3098-100 doi: 10.1103/PhysRevA.38.3098
    [3]
    Lee C, Yang W, Parr R G 1988 Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Phys. Rev. B 37 785-9 doi: 10.1103/PhysRevB.37.785
    [4]
    Anisimov V I, Zaanen J, Andersen O K 1991 Band theory and Mott insulators: Hubbard U instead of Stoner I Phys. Rev. B 44 943-54 doi: 10.1103/PhysRevB.44.943
    [5]
    Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study Phys. Rev. B 57 1505-9 doi: 10.1103/PhysRevB.57.1505
    [6]
    Han M J, Ozaki T, Yu J O 2006 (N) LDA + U electronic structure calculation method based on the nonorthogonal pseudoatomic orbital basis Phys. Rev. B 73 045110 doi: 10.1103/PhysRevB.73.045110
    [7]
    Wang L, Maxisch T, Ceder G 2006 Oxidation energies of transition metal oxides within the GGA + U framework Phys. Rev. B 73 195107 doi: 10.1103/PhysRevB.73.195107
    [8]
    Zhou F, Cococcioni M, Marianetti C A, Morgan D, Ceder G 2004 First-principles prediction of redox potentials in transition-metal compounds with LDA + U Phys. Rev. B 70 235121 doi: 10.1103/PhysRevB.70.235121
    [9]
    Cococcioni M, de Gironcoli S 2005 Linear response approach to the calculation of the effective interaction parameters in the LDA + U method Phys. Rev. B 71 035105 doi: 10.1103/PhysRevB.71.035105
    [10]
    Aryasetiawan F, Karlsson K, Jepsen O, Schönberger U 2006 Calculations of Hubbard U from first-principles Phys. Rev. B 74 125106 doi: 10.1103/PhysRevB.74.125106
    [11]
    Miyake T, Aryasetiawan F 2008 Screened Coulomb interaction in the maximally localized Wannier basis Phys. Rev. B 77 085122 doi: 10.1103/PhysRevB.77.085122
    [12]
    aolu E, Friedrich C, Blügel S 2011 Effective Coulomb interaction in transition metals from constrained random-phase approximation Phys. Rev. B 83 121101 doi: 10.1103/PhysRevB.83.121101
    [13]
    Yu M, Yang S, Wu C, Marom N 2020 Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization npj Comput. Mater. 6 180 doi: 10.1038/s41524-020-00446-9
    [14]
    Yu M, Moayedpour S, Yang S, Dardzinski D, Wu C, Pribiag V S, Marom N 2021 Dependence of the electronic structure of the EuS/InAs interface on the bonding configuration Phys. Rev. Mater. 5 064606 doi: 10.1103/PhysRevMaterials.5.064606
    [15]
    Yang S, Dardzinski D, Hwang A, Pikulin D I, Winkler G W, Marom N 2021 First-principles feasibility assessment of a topological insulator at the InAs/GaSb interface Phys. Rev. Mater. 5 084204 doi: 10.1103/PhysRevMaterials.5.084204
    [16]
    Popov M N, Spitaler J, Romaner L, Bedoya-Martínez N, Hammer R 2021 Bayesian optimization of Hubbard U’s for investigating InGaN superlattices Electron. Mater. 2 370-81 doi: 10.3390/electronicmat2030025
    [17]
    Lu D, Liu P 2014 Rationalization of the Hubbard U parameter in CeOx from first principles: unveiling the role of local structure in screening J. Chem. Phys. 140 084101 doi: 10.1063/1.4865831
    [18]
    Hsu H, Umemoto K, Cococcioni M, Wentzcovitch R 2009 First-principles study for low-spin LaCoO3 with a structurally consistent Hubbard U Phys. Rev. B 79 125124 doi: 10.1103/PhysRevB.79.125124
    [19]
    Tsuchiya T, Wentzcovitch R M, da Silva C R S, de Gironcoli S 2006 Spin transition in magnesiowüstite in Earth’s lower mantle Phys. Rev. Lett. 96 198501 doi: 10.1103/PhysRevLett.96.198501
    [20]
    Kulik H J, Marzari N 2011 Accurate potential energy surfaces with a DFT+U(R) approach J. Chem. Phys. 135 194105 doi: 10.1063/1.3660353
    [21]
    Heyd J, Scuseria G E, Ernzerhof M 2003 Hybrid functionals based on a screened Coulomb potential J. Chem. Phys. 118 8207-15 doi: 10.1063/1.1564060
    [22]
    Heyd J, Scuseria G E, Ernzerhof M 2006 Erratum: ‘Hybrid functionals based on a screened Coulomb potential’ [J. Chem. Phys. 118, 8207 (2003)] J. Chem. Phys. 124 219906 doi: 10.1063/1.2204597
    [23]
    Amit Y, Geman D 1997 Shape quantization and recognition with randomized trees Neural Comput. 9 1545-88 doi: 10.1162/neco.1997.9.7.1545
    [24]
    Ho T K 1998 The random subspace method for constructing decision forests IEEE Trans. Pattern Anal. Mach. Intell. 20 832-44 doi: 10.1109/34.709601
    [25]
    Kresse G, Furthmüller J 1996 Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B 54 11169-86 doi: 10.1103/PhysRevB.54.11169
    [26]
    Kresse G, Joubert D 1999 From ultrasoft pseudopotentials to the projector augmented-wave method Phys. Rev. B 59 1758-75 doi: 10.1103/PhysRevB.59.1758
    [27]
    Blöchl P E 1994 Projector augmented-wave method Phys. Rev. B 50 17953-79 doi: 10.1103/PhysRevB.50.17953
    [28]
    Tavadze P, Boucher R, Avendaño-Franco G, Kocan K X, Singh S, Dovale-Farelo V, Ibarra-Hernández W, Johnson M B, Mebane D S, Romero A H 2021 Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling npj Comput. Mater. 7 182 doi: 10.1038/s41524-021-00651-0
    [29]
    Liechtenstein A I, Anisimov V I, Zaanen J 1995 Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators Phys. Rev. B 52 R5467-70 doi: 10.1103/PhysRevB.52.R5467
    [30]
    Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, Reuter K, Scheffler M 2009 Ab initio molecular simulations with numeric atom-centered orbitals Comput. Phys. Commun. 180 2175-96 doi: 10.1016/j.cpc.2009.06.022
    [31]
    Ren X, Rinke P, Blum V, Wieferink J, Tkatchenko A, Sanfilippo A, Reuter K, Scheffler M 2012 Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions New J. Phys. 14 053020 doi: 10.1088/1367-2630/14/5/053020
    [32]
    Levchenko S V, Ren X, Wieferink J, Johanni R, Rinke P, Blum V, Scheffler M 2015 Hybrid functionals for large periodic systems in an all-electron, numeric atom-centered basis framework Comput. Phys. Commun. 192 60-69 doi: 10.1016/j.cpc.2015.02.021
    [33]
    Ong S P, Richards W D, Jain A, Hautier G, Kocher M, Cholia S, Gunter D, Chevrier V L, Persson K A, Ceder G 2013 Python materials genomics (pymatgen): a robust, open-source python library for materials analysis Comput. Mater. Sci. 68 314-9 doi: 10.1016/j.commatsci.2012.10.028
    [34]
    Fernando 2022 Bayesian optimization
    [35]
    Okazawa K, Tsuji Y, Kurino K, Yoshida M, Amamoto Y, Yoshizawa K 2022 Exploring the optimal alloy for nitrogen activation by combining Bayesian optimization with density functional theory calculations ACS Omega 7 45403-8 doi: 10.1021/acsomega.2c05988
    [36]
    scikit-learn/scikit-learn Scikit-learn: machine learning in Python (available at: https://github.com/scikit-learn/scikit-learn)
    [37]
    Liang Y, et al 2022 A universal model for accurately predicting the formation energy of inorganic compounds Sci. China Mater. 66 343-51 doi: 10.1007/s40843-022-2134-3
    [38]
    Ong S P, Wang L, Kang B, Ceder G 2008 Li−Fe−P−O 2 phase diagram from first principles calculations Chem. Mater. 20 1798-807 doi: 10.1021/cm702327g
    [39]
    Jain A, Hautier G, Ong S P, Moore C J, Fischer C C, Persson K A, Ceder G 2011 Formation enthalpies by mixing GGA and GGA + U calculations Phys. Rev. B 84 045115 doi: 10.1103/PhysRevB.84.045115
    [40]
    Liu M, Meng S 2022 Atomly.net materials database and its application in inorganic chemistry Sci. Sin.-Chim. 53 19-25 doi: 10.1360/SSC-2022-0167
    [41]
    Tomczak J M, Miyake T, Aryasetiawan F 2010 Realistic many-body models for manganese monoxide under pressure Phys. Rev. B 81 115116 doi: 10.1103/PhysRevB.81.115116
    [42]
    Ivashko O, et al 2019 Strain-engineering Mott-insulating La2CuO4 Nat. Commun. 10 786 doi: 10.1038/s41467-019-08664-6
    [43]
    Hedin L 1965 New method for calculating the one-particle Green’s function with application to the electron-gas problem Phys. Rev. 139 A796-823 doi: 10.1103/PhysRev.139.A796
    [44]
    Purvis G D, Bartlett R J 1982 A full coupledcluster singles and doubles model: the inclusion of disconnected triples J. Chem. Phys. 76 1910-8 doi: 10.1063/1.443164
    [45]
    Huhn W P, Blum V 2017 One-hundred-three compound band-structure benchmark of post-self-consistent spin-orbit coupling treatments in density functional theory Phys. Rev. Mater. 1 033803 doi: 10.1103/PhysRevMaterials.1.033803
    [46]
    Ye L-H, Luo N, Peng L-M, Weinert M, Freeman A J 2013 Dielectric constant of NiO and LDA + U Phys. Rev. B 87 075115 doi: 10.1103/PhysRevB.87.075115
    [47]
    Pask J E, Singh D J, Mazin I I, Hellberg C S, Kortus J 2001 Structural, electronic, and magnetic properties of MnO Phys. Rev. B 64 024403 doi: 10.1103/PhysRevB.64.024403
    [48]
    Deng H-X, Li J, Li S-S, Xia J-B, Walsh A, Wei S-H 2010 Origin of antiferromagnetism in CoO: a density functional theory study Appl. Phys. Lett. 96 162508 doi: 10.1063/1.3402772
    [49]
    Dufek P, Blaha P, Sliwko V, Schwarz K 1994 Generalized-gradient-approximation description of band splittings in transition-metal oxides and fluorides Phys. Rev. B 49 10170-5 doi: 10.1103/PhysRevB.49.10170
    [50]
    Jain A, et al 2013 Commentary: the materials project: a materials genome approach to accelerating materials innovation APL Mater. 1 011002 doi: 10.1063/1.4812323
    [51]
    Sit P H-L, Cococcioni M, Marzari N 2006 Realistic quantitative descriptions of electron transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics Phys. Rev. Lett. 97 028303 doi: 10.1103/PhysRevLett.97.028303
    [52]
    Sit P H-L, Cococcioni M, Marzari N 2007 Car-Parrinello molecular dynamics in the DFT+U formalism: structure and energetics of solvated ferrous and ferric ions J. Electroanal. Chem. 607 107-12 doi: 10.1016/j.jelechem.2007.01.008
    [53]
    Leiria Campo VJr, Cococcioni M 2010 Extended DFT + U + V method with on-site and inter-site electronic interactions J. Phys.: Condens. Matter 22 055602 doi: 10.1088/0953-8984/22/5/055602
    [54]
    Yu W, et al 2023 Active learning the high-dimensional transferable Hubbard U and V parameters in the DFT + U + V scheme J. Chem. Theory. Comput. 19 6425-33 doi: 10.1021/acs.jctc.2c01116
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