Skip to content
naulon

No retraction, correction or concern found when last checked on Oct 18, 2026.

A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer

Tsz Wai Ko, Jonas A. Finkler, Stefan Goedecker and 1 more (opens in a new tab)

Nature Communications · 2021 · CC BY

doi:10.1038/s41467-020-20427-2 (opens in a new tab)

Abstract

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

Read at PubMed Central (opens in a new tab)

References 68

  1. 1.

    McCammon JA, Gelin BR, Karplus M. Dynamics of folded proteins. Nature. 1977;267:585-590.

    Not in our library10.1038/267585a0 (opens in a new tab)

  2. 2.

    Jorgensen WL, Ravimohan C. Monte Carlo simulation of differences in free energies of hydration. J. Chem. Phys. 1985;83:3050-3054.

    Not in our library10.1063/1.449208 (opens in a new tab)

  3. 3.

    Behler J. Perspective: machine learning potentials for atomistic simulations. J. Chem. Phys. 2016;145:170901.

    Not in our library10.1063/1.4966192 (opens in a new tab)

  4. 4.

    Botu V, Batra R, Chapman J, Ramprasad R. Machine learning force fields: construction, validation, and outlook. J. Phys. Chem. C. 2017;121:511-522.

    Not in our library10.1021/acs.jpcc.6b10908 (opens in a new tab)

  5. 5.

    Deringer VL, Caro MA, Csányi G. Machine learning interatomic potentials as emerging tools for materials science. Adv. Mater. 2019;31:1902765.

    Not in our library10.1002/adma.201902765 (opens in a new tab)

  6. 6.
  7. 7.

    Noé F, Tkatchenko A, Müller K-R, Clementi C. Machine learning for molecular simulation. Annu. Rev. Phys. Chem. 2020;71:361-390.

    Not in our library10.1146/annurev-physchem-042018-052331 (opens in a new tab)

  8. 8.

    Blank TB, Brown SD, Calhoun AW, Doren DJ. Neural network models of potential energy surfaces. J. Chem. Phys. 1995;103:4129-4137.

    Not in our library10.1063/1.469597 (opens in a new tab)

  9. 9.

    Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 2007;98:146401.

    Not in our library10.1103/physrevlett.98.146401 (opens in a new tab)

  10. 10.

    Schütt KT, Sauceda HE, Kindermans P-J, Tkatchenko A, Müller K-R. SchNet-A deep learning architecture for molecules and materials. J. Chem. Phys. 2018;148:241722.

    Not in our library10.1063/1.5019779 (opens in a new tab)

  11. 11.

    Unke OT, Meuwly M. PhysNet: a neural network for predicting energies, forces, dipole moments, and partial charges. J. Chem. Theory Comput. 2019;15:3678-3693.

    Not in our library10.1021/acs.jctc.9b00181 (opens in a new tab)

  12. 12.

    Smith JS, Isayev O, Roitberg AE. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 2017;8:3192-3203.

    Not in our library10.1039/c6sc05720a (opens in a new tab)

  13. 13.

    Bartók AP, Payne MC, Kondor R, Csányi G. Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 2010;104:136403.

    Not in our library10.1103/physrevlett.104.136403 (opens in a new tab)

  14. 14.

    Shapeev AV. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale Model. Simul. 2016;14:1153-1173.

    Not in our library10.1137/15m1054183 (opens in a new tab)

  15. 15.

    Thompson AP, Swiler LP, Trott CR, Foiles SM, Tucker GJ. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials. J. Chem. Phys. 2015;285:316-330.

    Not in our library

  16. 16.

    Drautz R. Atomic cluster expansion for accurate and transferable interatomic potentials. Phys. Rev. B. 2019;99:014104.

    Not in our library10.1103/physrevb.99.014104 (opens in a new tab)

  17. 17.

    Balabin RM, Lomakina EI. Support vector machine regression (LS-SVM)-an alternative to artificial neural networks (ANNs) for the analysis of quantum chemistry data? Phys. Chem. Chem. Phys. 2011;13:11710.

    Not in our library10.1039/c1cp00051a (opens in a new tab)

  18. 18.

    Behler J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations. Phys. Chem. Chem. Phys. 2011;13:17930-17955.

    Not in our library10.1039/c1cp21668f (opens in a new tab)

  19. 19.

    Handley CM, Popelier PL. Potential energy surfaces fitted by artificial neural networks. J. Phys. Chem. A. 2010;114:3371-3383.

    Not in our library10.1021/jp9105585 (opens in a new tab)

  20. 20.

    Prodan E, Kohn W. Nearsightedness of electronic matter. Proc. Natl. Acad. Sci. 2005;102:11635-11638.

    Not in our library10.1073/pnas.0505436102 (opens in a new tab)

  21. 21.

    Deng Z, Chen C, Li X-G, Ong SP. An electrostatic spectral neighbor analysis potential for lithium nitride. NPJ Comput. Mater. 2019;5:75.

    Not in our library10.1038/s41524-019-0212-1 (opens in a new tab)

  22. 22.

    Artrith N, Morawietz T, Behler J. High-dimensional neural-network potentials for multicomponent systems: applications to zinc oxide. Phys. Rev. B. 2011;83:153101.

    Not in our library10.1103/physrevb.83.153101 (opens in a new tab)

  23. 23.

    Morawietz T, Sharma V, Behler J. A neural network potential-energy surface for the water dimer based on environment-dependent atomic energies and charges. J. Chem. Phys. 2012;136:064103.

    Not in our library10.1063/1.3682557 (opens in a new tab)

  24. 24.

    Yao K, Herr JE, Toth DW, Mckintyre R, Parkhill J. The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics. Chem. Sci. 2018;9:2261-2269.

    Not in our library10.1039/c7sc04934j (opens in a new tab)

  25. 25.

    Bereau T, Andrienko D, Von Lilienfeld OA. Transferable atomic multipole machine learning models for small organic molecules. J. Chem. Theory Comput. 2015;11:3225-3233.

    Not in our library10.1021/acs.jctc.5b00301 (opens in a new tab)

  26. 26.

    Hoshino T, et al. First-principles calculations for vacancy formation energies in Cu and Al; non-local effect beyond the LSDA and lattice distortion. Comp. Mat. Sci. 1999;14:56.

    Not in our library10.1016/s0927-0256(98)00072-x (opens in a new tab)

  27. 27.

    Parsaeifard, B., Finkler, J. A. & Goedecker, S. Detecting non-local effects in the electronic structure of a simple covalent system with machine learning methods, arXiv:2008.11277 (2020).

    Not in our library

  28. 28.

    Rappe AK, Goddard WA. Charge equilibration for molecular dynamics simulations. J. Phys. Chem. 1991;95:3358.

    Not in our library10.1021/j100161a070 (opens in a new tab)

  29. 29.

    van Duin ACT, Dasgupta S, Lorant F, Goddard WA. ReaxFF: a reactive force field for hydrocarbons. J. Phys. Chem. A. 2001;105:9396-9409.

    Not in our library10.1021/jp004368u (opens in a new tab)

  30. 30.

    Zhou XW, Wadley HNG. A charge transfer ionic–embedded atom method potential for the O–Al–Ni–Co–Fe system. J. Phys.: Condens. Matter. 2005;17:3619.

    Not in our library

  31. 31.

    Gasteiger J, Marsili M. Iterative partial equalization of orbital electronegativity–a rapid access to atomic charges. Tetrahedron. 1980;36:3219-3228.

    Not in our library10.1016/0040-4020(80)80168-2 (opens in a new tab)

  32. 32.

    Ghasemi SA, Hofstetter A, Saha S, Goedecker S. Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network. Phys. Rev. B. 2015;92:045131.

    Not in our library10.1103/physrevb.92.045131 (opens in a new tab)

  33. 33.

    Faraji S, et al. High accuracy and transferability of a neural network potential through charge equilibration for calcium fluoride. Phys. Rev. B. 2017;95:104105.

    Not in our library10.1103/physrevb.95.104105 (opens in a new tab)

  34. 34.

    Amsler, M. et al. FLAME: a library of atomistic modeling environments. Comput. Phys. Commun.256, 107415 (2020)

    Not in our library

  35. 35.

    Hafizi R, Ghasemi SA, Hashemifar SJ, Akbarzadeh H. A neural-network potential through charge equilibration for WS2: From clusters to sheets. J. Chem. Phys. 2017;147:234306.

    Not in our library10.1063/1.5003904 (opens in a new tab)

  36. 36.

    Faraji S, Ghasemi SA, Parsaeifard B, Goedecker S. Surface reconstructions and premelting of the (100) CaF2 surface. Phys. Chem. Chem. Phys. 2019;21:16270-16281.

    Not in our library10.1039/c9cp02213a (opens in a new tab)

  37. 37.

    Rasoulkhani R, et al. Energy landscape of ZnO clusters and low-density polymorphs. Phys. Rev. B. 2017;96:064108.

    Not in our library10.1103/physrevb.96.064108 (opens in a new tab)

  38. 38.

    Xie X, Persson KA, Small DW. Incorporating electronic information into machine learning potential energy surfaces via approaching the ground-state electronic energy as a function of atom-based electronic populations. J. Chem. Theory Comput. 2020;16:4256-4270.

    Not in our library10.1021/acs.jctc.0c00217 (opens in a new tab)

  39. 39.

    Zubatyuk, R., Smith, J., Nebgen, B.T., Tretiak, S. & Isayev, O. Teaching a neural network to attach and detach electrons from molecules, ChemRxiv 12725276.v1 (2020).

    Not in our library10.1038/s41467-021-24904-0 (opens in a new tab)

  40. 40.

    Hirshfeld FL. Bonded-atom fragments for describing molecular charge densities. Theor. Chim. Acta. 1977;44:129-138.

    Not in our library10.1007/bf00549096 (opens in a new tab)

  41. 41.

    Behler J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 2011;134:074106.

    Not in our library10.1063/1.3553717 (opens in a new tab)

  42. 42.

    Rappe AK, Goddard III WA. Charge equilibration for molecular dynamics simulations. J. Phys. Chem. 1991;95:3358-3363.

    Not in our library10.1021/j100161a070 (opens in a new tab)

  43. 43.

    Sifain AE, et al. Discovering a transferable charge assignment model using machine learning. J. Phys. Chem. Lett. 2018;9:4495-4501.

    Not in our library10.1021/acs.jpclett.8b01939 (opens in a new tab)

  44. 44.

    Ma Y, Lockwood GK, Garofalini SH. Development of a transferable variable charge potential for the study of energy conversion materials FeF2 and FeF3. J. Phys. Chem. C. 2011;115:24198-24205.

    Not in our library10.1021/jp207181s (opens in a new tab)

  45. 45.

    Fan Q, Pfeiffer GV. Theoretical study of linear Cn (n = 6–10) and HCnH (n = 2–10) molecules. Chem. Phys. Lett. 1989;162:472-478.

    Not in our library10.1016/0009-2614(89)87010-1 (opens in a new tab)

  46. 46.

    Horny` L, Petraco NDK, Schaefer HF. Odd carbon long linear chains HC2n+1H (n = 4–11): properties of the neutrals and radical anions. J. Am. Chem. Soc. 2002;124:14716-14720.

    Not in our library10.1021/ja0210190 (opens in a new tab)

  47. 47.

    Pan L, Rao BK, Gupta AK, Das GP, Ayyub P. H-substituted anionic carbon clusters CnH−(n ≤ 10): density functional studies and experimental observations. J. Chem. Phys. 2003;119:7705-7713.

    Not in our library10.1063/1.1609400 (opens in a new tab)

  48. 48.

    Duanmu K, et al. Geometries, binding energies, ionization potentials, and electron affinities of metal clusters: Mg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\,}_{n}^{0,\pm 1}$$\end{document}n0,±1, n= 1–7. J. Phys. Chem. C. 2016;120:13275-13286.

    Not in our library10.1021/acs.jpcc.6b03080 (opens in a new tab)

  49. 49.

    Goel N, Gautam S, Dharamvir K. Density functional studies of LiN and Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\,}_{N}^{+}$$\end{document}N+(N= 2–30) clusters: Structure, binding and charge distribution. Int. J. Quant. Chem. 2012;112:575-586.

    Not in our library10.1002/qua.23022 (opens in a new tab)

  50. 50.

    Fournier R. Trends in energies and geometric structures of neutral and charged aluminum clusters. J. Chem. Theory Comput. 2007;3:921-929.

    Not in our library10.1021/ct6003752 (opens in a new tab)

  51. 51.

    De S, et al. The effect of ionization on the global minima of small and medium sized silicon and magnesium clusters. J. Chem. Phys. 2011;134:124302.

    Not in our library10.1063/1.3569564 (opens in a new tab)

  52. 52.

    Haruta M, Daté M. Advances in the catalysis of Au nanoparticles. Appl. Catal. A. 2001;222:427-437.

    Not in our library10.1016/s0926-860x(01)00847-x (opens in a new tab)

  53. 53.

    Mammen N, Narasimhan S, de Gironcoli S. Tuning the morphology of gold clusters by substrate doping. J. Am. Chem. Soc. 2011;133:2801-2803.

    Not in our library10.1021/ja109663g (opens in a new tab)

  54. 54.

    Mammen N, Narasimhan S. Inducing wetting morphologies and increased reactivities of small Au clusters on doped oxide supports. J. Chem. Phys. 2018;149:174701.

    Not in our library10.1063/1.5053968 (opens in a new tab)

  55. 55.

    Shao X, et al. Tailoring the shape of metal Ad-particles by doping the oxide support. Angew. Chem. Int. Ed. 2011;50:11525-11527.

    Not in our library10.1002/anie.201105355 (opens in a new tab)

  56. 56.

    Artrith N, Hiller B, Behler J. Neural network potentials for metals and oxides-First applications to copper clusters at zinc oxide. Phys. Status Solidi B. 2013;250:1191-1203.

    Not in our library10.1002/pssb.201248370 (opens in a new tab)

  57. 57.

    Elias JS, et al. Elucidating the nature of the active phase in copper/ceria catalysts for CO oxidation. ACS Catal. 2016;6:1675-1679.

    Not in our library10.1021/acscatal.5b02666 (opens in a new tab)

  58. 58.

    Paleico ML, Behler J. Global optimization of copper clusters at the ZnO(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\bar{1}0$$\end{document}101¯0) surface using a DFT-based neural network potential and genetic algorithms. J. Chem. Phys. 2020;153:054704.

    Not in our library10.1063/5.0014876 (opens in a new tab)

  59. 59.

    Behler, J. RuNNer–A Program for Constructing High-dimensional Neural Network Potentials, Universität Göttingen 2020. (Universität Göttingen, 2020)

    Not in our library

  60. 60.

    Behler J. Constructing high-dimensional neural network potentials: A tutorial review. Int. J. Quant. Chem. 2015;115:1032-1050.

    Not in our library10.1002/qua.24890 (opens in a new tab)

  61. 61.

    Behler J. First principles neural network potentials for reactive simulations of large molecular and condensed systems. Angew. Chem. Int. Ed. 2017;56:12828-12840.

    Not in our library10.1002/anie.201703114 (opens in a new tab)

  62. 62.

    Blum V, et al. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 2009;180:2175-2196.

    Not in our library10.1016/j.cpc.2009.06.022 (opens in a new tab)

  63. 63.

    Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996;77:3865.

    Not in our library10.1103/physrevlett.77.3865 (opens in a new tab)

  64. 64.

    Barnett RN, Landman U. Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of (H2O)2. Phys. Rev. B. 1993;48:2081.

    Not in our library10.1103/physrevb.48.2081 (opens in a new tab)

  65. 65.

    Nosé S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984;81:511-519.

    Not in our library10.1063/1.447334 (opens in a new tab)

  66. 66.

    Stukowski A. Visualization and analysis of atomistic simulation data with OVITO - the Open Visualization Tool. Modell. Simul. Mater. Sci. Eng. 2010;18:015012.

    Not in our library10.1088/0965-0393/18/1/015012 (opens in a new tab)

  67. 67.

    Momma K, Izumi F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011;44:1272-1276.

    Not in our library10.1107/s0021889811038970 (opens in a new tab)

  68. 68.

Cited by papers we hold 7

Questions about this paper

We email you if it is retracted, withdrawn, corrected or flagged.

Reads

Read by people on this page

None yet.

Checked or read by AI through naulon

None yet.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.

Are you an author?

Is this your paper?

Claim it to add your note and be paid when agents cite it. Free.