SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects

Abstract

Machine-learned force fields combine the accuracy of ab initio methods with the efficiency of conventional force fields. However, current machine-learned force fields typically ignore electronic degrees of freedom, such as the total charge or spin state, and assume chemical locality, which is problematic when molecules have inconsistent electronic states, or when nonlocal effects play a significant role. This work introduces SpookyNet, a deep neural network for constructing machine-learned force fields with explicit treatment of electronic degrees of freedom and nonlocality, modeled via self-attention in a transformer architecture. Chemically meaningful inductive biases and analytical corrections built into the network architecture allow it to properly model physical limits. SpookyNet improves upon the current state-of-the-art (or achieves similar performance) on popular quantum chemistry data sets. Notably, it is able to generalize across chemical and conformational space and can leverage the learned chemical insights, e.g. by predicting unknown spin states, thus helping to close a further important remaining gap for today’s machine learning models in quantum chemistry.

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References 112

1. 1.

   Warshel A. Molecular dynamics simulations of biological reactions. Acc. Chem. Res. 2002;35:385.

   Not in our library10.1021/ar010033z

2. 2.

   Karplus M, McCammon JA. Molecular dynamics simulations of biomolecules. Nat. Struct. Biol. 2002;9:646.

   Not in our library10.1038/nsb0902-646

3. 3.

   Dirac PAM. Quantum mechanics of many-electron systems. Proc. R. Soc. Lond. A. 1929;123:714.

   Not in our library

4. 4.

   Dykstra, C., Frenking, G., Kim, K., & Scuseria, G. (Eds.). Theory and applications of computational chemistry: the first forty years. (Elsevier 2005).

   Not in our library

5. 5.

   Unke OT, Koner D, Patra S, Käser S, Meuwly M. High-dimensional potential energy surfaces for molecular simulations: from empiricism to machine learning. Mach. Learn. Sci. Technol. 2020;1:013001.

   Not in our library

6. 6.

   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

7. 7.

   Rupp M, Tkatchenko A, Müller K-R, Von Lilienfeld OA. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 2012;108:058301.

   Not in our library10.1103/physrevlett.108.058301

8. 8.

   Bartók AP, et al. Machine learning unifies the modeling of materials and molecules. Sci. Adv. 2017;3:e1701816.

   Not in our library10.1126/sciadv.1701816

9. 9.

   Gastegger M, Schwiedrzik L, Bittermann M, Berzsenyi F, Marquetand P. wACSF—weighted atom-centered symmetry functions as descriptors in machine learning potentials. J. Chem. Phys. 2018;148:241709.

   Not in our library10.1063/1.5019667

10. 10.
    Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions · 2019

    No notice
11. 11.

    Unke OT, et al. Machine learning force fields. Chem. Rev. 2021;121:10142-10186.

    Not in our library10.1021/acs.chemrev.0c01111

12. 12.

    von Lilienfeld OA, Müller K-R, Tkatchenko A. Exploring chemical compound space with quantum-based machine learning. Nat. Rev. Chem. 2020;4:347.

    Not in our library10.1038/s41570-020-0189-9

13. 13.

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

    Not in our library10.1146/annurev-physchem-042018-052331

14. 14.
    Unsupervised Learning Methods for Molecular Simulation Data · 2021

    No notice
15. 15.

    Keith JA, et al. Combining machine learning and computational chemistry for predictive insights into chemical systems. Chem. Rev. 2021;121:9816-9872.

    Not in our library10.1021/acs.chemrev.1c00107

16. 16.

    Sauceda HE, Gastegger M, Chmiela S, Müller K-R, Tkatchenko A. Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields. J. Chem. Phys. 2020;153:124109.

    Not in our library10.1063/5.0023005

17. 17.

    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

18. 18.

    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

19. 19.

    McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 1943;5:115.

    Not in our library

20. 20.

    Unke OT, Meuwly M. Toolkit for the construction of reproducing kernel-based representations of data: application to multidimensional potential energy surfaces. J. Chem. Inf. Model. 2017;57:1923.

    Not in our library10.1021/acs.jcim.7b00090

21. 21.

    Chmiela S, et al. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 2017;3:e1603015.

    Not in our library10.1126/sciadv.1603015

22. 22.

    Chmiela S, Sauceda HE, Poltavsky I, Müller K-R, Tkatchenko A. sGDML: Constructing accurate and data efficient molecular force fields using machine learning. Computer Phys. Commun. 2019;240:38.

    Not in our library

23. 23.

    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.

    Not in our library10.1039/c6sc05720a

24. 24.

    Zhang L, Han J, Wang H, Car R, Weinan E. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 2018;120:143001.

    Not in our library10.1103/physrevlett.120.143001

25. 25.

    Unke OT, Meuwly M. A reactive, scalable, and transferable model for molecular energies from a neural network approach based on local information. J. Chem. Phys. 2018;148:241708.

    Not in our library10.1063/1.5017898

26. 26.

    Christensen AS, Bratholm LA, Faber FA, Anatole von Lilienfeld O. Anatole von Lilienfeld, O. FCHL revisited: faster and more accurate quantum machine learning. J. Chem. Phys. 2020;152:044107.

    Not in our library10.1063/1.5126701

27. 27.

    Vapnik, V. N. The Nature of Statistical Learning Theory. (Springer, 1995).

    Not in our library

28. 28.

    Cortes C, Vapnik V. Support-vector networks. Mach. Learn. 1995;20:273.

    Not in our library

29. 29.

    Müller K-R, Mika S, Ratsch G, Tsuda K, Schölkopf B. An introduction to kernel-based learning algorithms. IEEE Trans. Neural Netw. 2001;12:181.

    Not in our library10.1109/72.914517

30. 30.

    Schölkopf, B. & Smola, A. J. Learning with kernels: support vector machines, regularization, optimization, and beyond. (MIT press, 2002).

    Not in our library

31. 31.

    Braun ML, Buhmann JM, Müller K-R. On relevant dimensions in kernel feature spaces. J. Mach. Learn. Res. 2008;9:1875.

    Not in our library

32. 32.

    Hansen K, et al. Assessment and validation of machine learning methods for predicting molecular atomization energies. J. Chem. Theory Comput. 2013;9:3404.

    Not in our library10.1021/ct400195d

33. 33.
    Quantum-chemical insights from deep tensor neural networks · 2017

    No notice
34. 34.

    Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O. & Dahl, G. E. Neural message passing for quantum chemistry, in International Conference on Machine Learning, 1263–1272 https://proceedings.mlr.press/v70/gilmer17a.html (2017).

    Not in our library

35. 35.

    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

36. 36.

    Lubbers N, Smith JS, Barros K. Hierarchical modeling of molecular energies using a deep neural network. J. Chem. Phys. 2018;148:241715.

    Not in our library10.1063/1.5011181

37. 37.

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

    Not in our library10.1021/acs.jctc.9b00181

38. 38.

    Friesner RA. Ab initio quantum chemistry: methodology and applications. Proc. Natl Acad. Sci. USA. 2005;102:6648.

    Not in our library10.1073/pnas.0408036102

39. 39.

    Born, M. & Einstein, A. The Born-Einstein Letters 1916–1955 (Macmillan, 2005).

    Not in our library

40. 40.

    Noodleman L, Peng C, Case D, Mouesca J-M. Orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters. Coord. Chem. Rev. 1995;144:199.

    Not in our library

41. 41.

    Dreuw A, Weisman JL, Head-Gordon M. Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J. Chem. Phys. 2003;119:2943.

    Not in our library

42. 42.

    Duda L-C, et al. Resonant inelastic X-Ray scattering at the oxygen K resonance of NiO: nonlocal charge transfer and double-singlet excitations. Phys. Rev. Lett. 2006;96:067402.

    Not in our library10.1103/physrevlett.96.067402

43. 43.

    Bellec A, et al. Nonlocal activation of a bistable atom through a surface state charge-transfer process on Si(100)–(2 × 1):H. Phys. Rev. Lett. 2010;105:048302.

    Not in our library10.1103/physrevlett.105.048302

44. 44.

    Boström EV, Mikkelsen A, Verdozzi C, Perfetto E, Stefanucci G. Charge separation in donor–C60 complexes with real-time green functions: the importance of nonlocal correlations. Nano Lett. 2018;18:785.

    Not in our library10.1021/acs.nanolett.7b03995

45. 45.

    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 library

46. 46.

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

    Not in our library

47. 47.

    Wilmer CE, Kim KC, Snurr RQ. An extended charge equilibration method. J. Phys. Chem. Lett. 2012;3:2506.

    Not in our library10.1021/jz3008485

48. 48.

    Cheng Y-T, et al. A charge optimized many-body (comb) potential for titanium and titania. J. Phys. Condens. Matter. 2014;26:315007.

    Not in our library10.1088/0953-8984/26/31/315007

49. 49.
    A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer · 2021

    No notice
50. 50.

    Zubatyuk, R., Smith, J.S., Nebgen, B.T. et al. Teaching a neural network to attach and detach electrons from molecules. Nat. Commun.12, 4870 (2021).

    Not in our library10.1038/s41467-021-24904-0

51. 51.

    Zubatyuk R, Smith JS, Leszczynski J, Isayev O. Accurate and transferable multitask prediction of chemical properties with an atoms-in-molecules neural network. Sci. Adv. 2019;5:eaav6490.

    Not in our library10.1126/sciadv.aav6490

52. 52.

    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.

    Not in our library10.1021/acs.jctc.0c00217

53. 53.

    Qiao Z, Welborn M, Anandkumar A, Manby FR, Miller III TF. OrbNet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital features. J. Chem. Phys. 2020;153:124111.

    Not in our library10.1063/5.0021955

54. 54.

    Pfau D, Spencer JS, Matthews AG, Foulkes WMC. Ab initio solution of the many-electron Schrödinger equation with deep neural networks. Phys. Rev. Res. 2020;2:033429.

    Not in our library

55. 55.

    Hermann, J., Schätzle, Z. & Noé, F. Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 12, 891–897 (2020).

    Not in our library10.1038/s41557-020-0544-y

56. 56.

    Scherbela, M., Reisenhofer, R., Gerard, L., Marquetand, P. & Grohs, P. Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. arXiv preprint arXiv:2105.08351 (2021).

    Not in our library10.1038/s43588-022-00228-x

57. 57.

    Klicpera, J., Groß, J. & Günnemann, S. Directional message passing for molecular graphs. International Conference on Learning Representations (ICLR)https://openreview.net/forum?id=B1eWbxStPH (2020).

    Not in our library

58. 58.

    Bernstein S. Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités. Commun. Kharkov Math. Soc. 1912;13:1.

    Not in our library

59. 59.

    Thomas, N. et al. Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds. arXiv preprint arXiv:1802.08219 (2018).

    Not in our library

60. 60.

    Anderson, Brandon and Hy, Truong Son and Kondor, Risi, Cormorant: Covariant Molecular Neural Networks, Advances in Neural Information Processing Systems 32, https://papers.nips.cc/paper/2019/hash/03573b32b2746e6e8ca98b9123f2249b-Abstract.html (2019).

    Not in our library

61. 61.

    Schütt, K. T., Unke, O. T. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. Proceedings of the 38th International Conference on Machine Learning, 9377–9388 (2021).

    Not in our library

62. 62.
    E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials · 2022

    No notice
63. 63.

    Bartók AP, Kondor R, Csányi G. On representing chemical environments. Phys. Rev. B. 2013;87:184115.

    Not in our library

64. 64.

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

    Not in our library

65. 65.

    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.

    Not in our library10.1039/c7sc04934j

66. 66.

    Grisafi A, Ceriotti M. Incorporating long-range physics in atomic-scale machine learning. J. Chem. Phys. 2019;151:204105.

    Not in our library10.1063/1.5128375

67. 67.

    Bereau T, DiStasio Jr RA, Tkatchenko A, Von Lilienfeld OA. Non-covalent interactions across organic and biological subsets of chemical space: physics-based potentials parametrized from machine learning. J. Chem. Phys. 2018;148:241706.

    Not in our library10.1063/1.5009502

68. 68.

    Schwilk, M., Tahchieva, D. N. & von Lilienfeld, O. A. The QMspin data set: Several thousand carbene singlet and triplet state structures and vertical spin gaps computed at MRCISD+Q-F12/cc-pVDZ-F12 level of theory. Mater. Cloud Arch. 10.24435/materialscloud:2020.0051/v1 (2020a).

    Not in our library

69. 69.

    Schwilk, M., Tahchieva, D. N. & von Lilienfeld, O. A. Large yet bounded: Spin gap ranges in carbenes. arXiv preprint arXiv:2004.10600 (2020b).

    Not in our library

70. 70.
    A general-purpose machine-learning force field for bulk and nanostructured phosphorus · 2020

    Not checked
71. 71.

    Hoja J, et al. QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules. Sci. Data. 2021;8:43.

    Not in our library10.1038/s41597-021-00812-2

72. 72.

    Blum LC, Reymond J-L. 970 million druglike small molecules for virtual screening in the chemical universe database GDB-13. J. Am. Chem. Soc. 2009;131:8732.

    Not in our library10.1021/ja902302h

73. 73.

    Adamo C, Barone V. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 1999;110:6158.

    Not in our library

74. 74.

    Tkatchenko A, DiStasio Jr RA, Car R, Scheffler M. Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett. 2012;108:236402.

    Not in our library10.1103/physrevlett.108.236402

75. 75.

    Folmsbee D, Hutchison G. Assessing conformer energies using electronic structure and machine learning methods. Int. J. Quantum Chem. 2021;121:e26381.

    Not in our library

76. 76.

    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

77. 77.

    Tkatchenko A, Scheffler M. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 2009;102:073005.

    Not in our library10.1103/physrevlett.102.073005

78. 78.

    Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser, Lukasz and Polosukhin, Illia, Attention is All you Need, Advances in Neural Information Processing Systems 30, https://papers.nips.cc/paper/2017/hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html (2017).

    Not in our library

79. 79.

    Choromanski, K. et al. Rethinking attention with performers. International Conference on Learning Representations https://openreview.net/forum?id=Ua6zuk0WRH (2021).

    Not in our library

80. 80.

    Ziegler, J. F., Littmark, U. & Biersack, J. P. The Stopping and Range of Ions in Solids (Pergamon, 1985).

    Not in our library

81. 81.

    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 library

82. 82.

    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

83. 83.

    Morawietz T, Behler J. A density-functional theory-based neural network potential for water clusters including van der Waals corrections. J. Phys. Chem. A. 2013;117:7356.

    Not in our library10.1021/jp401225b

84. 84.

    Uteva E, Graham RS, Wilkinson RD, Wheatley RJ. Interpolation of intermolecular potentials using Gaussian processes. J. Chem. Phys. 2017;147:161706.

    Not in our library10.1063/1.4986489

85. 85.

    Samek, W., Montavon, G., Vedaldi, A., Hansen, L. K. & Müller, K.-R. In Explainable AI: Interpreting, Explaining and Visualizing Deep Learning, vol. 11700 (Springer Nature, 2019).

    Not in our library

86. 86.

    Samek W, Montavon G, Lapuschkin S, Anders CJ, Müller K-R. Explaining deep neural networks and beyond: a review of methods and applications. Proc. IEEE. 2021;109:247.

    Not in our library

87. 87.
    Unmasking Clever Hans predictors and assessing what machines really learn · 2019

    No notice
88. 88.

    Hendrycks, D. & Gimpel, K. Gaussian error linear units (GELUs). arXiv preprint arXiv:1606.08415 (2016).

    Not in our library

89. 89.

    Elfwing S, Uchibe E, Doya K. Sigmoid-weighted linear units for neural network function approximation in reinforcement learning. Neural Netw. 2018;107:3.

    Not in our library10.1016/j.neunet.2017.12.012

90. 90.

    Ramachandran, P., Zoph, B. & Le, Q. V. Searching for activation functions. arXiv preprint arXiv:1710.05941 (2017).

    Not in our library

91. 91.

    Nair, V. & Hinton, G. E. Rectified linear units improve restricted boltzmann machines. in ICML International Conference on Machine Learning (2010).

    Not in our library

92. 92.

    Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks, in Proc. thirteenth international conference on artificial intelligence and statistics, 249–256 (JMLR Workshop and Conference Proceedings, 2010).

    Not in our library

93. 93.

    Srivastava, R., Greff, K. & Schmidhuber, J. Highway networks. arXiv preprint arXiv:1505.00387 (2015).

    Not in our library

94. 94.

    He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition, in Proc. IEEE conference on computer vision and pattern recognition 770–778 (2016).

    Not in our library

95. 95.

    He, K., Zhang, X., Ren, S. & Sun, J. Identity mappings in deep residual networks. in European conference on computer vision, 630–645 (Springer, 2016).

    Not in our library

96. 96.

    Kowalski, G. J. In Information Retrieval Systems: Theory and Implementation, Vol. 1 (Springer, 2007).

    Not in our library

97. 97.

    Ewald PP. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. der Phys. 1921;369:253.

    Not in our library

98. 98.
    Machine learning molecular dynamics for the simulation of infrared spectra · 2017

    No notice
99. 99.

    Hermann J, DiStasio Jr RA, Tkatchenko A. First-principles models for van der Waals interactions in molecules and materials: concepts, theory, and applications. Chem. Rev. 2017;117:4714.

    Not in our library10.1021/acs.chemrev.6b00446

100. 100.

     Caldeweyher E, et al. A generally applicable atomic-charge dependent london dispersion correction. J. Chem. Phys. 2019;150:154122.

     Not in our library10.1063/1.5090222

101. 101.

     Reddi, S. J., Kale, S. & Kumar, S. On the convergence of Adam and beyond. International Conference on Learning Representations (2018).

     Not in our library

102. 102.

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

     Not in our library

103. 103.

     Kingma, D. P. & Ba, J. Adam: A method for stochastic optimization. International Conference for Learning Representations (2015).

     Not in our library

104. 104.

     Bannwarth C, Ehlert S, Grimme S. GFN2-xTB—an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. J. Chem. Theory Comput. 2019;15:1652.

     Not in our library10.1021/acs.jctc.8b01176

105. 105.

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

     Not in our library

106. 106.

     Ren X, et al. Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions. N. J. Phys. 2012;14:053020.

     Not in our library

107. 107.

     Pozdnyakov SN, et al. Incompleteness of atomic structure representations. Phys. Rev. Lett. 2020;125:166001.

     Not in our library10.1103/physrevlett.125.166001

108. 108.

     Unke, O. Singlet/triplet carbene and Ag\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{3}^{+}$$\end{document}3+/Ag\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{3}^{-}$$\end{document}3−data. 10.5281/zenodo.5115732 (2021).

     Not in our library

109. 109.

     Pozdnyakov, S., Willatt, M. & Ceriotti, M. Randomly-displaced methane configurations. Mater. Cloud Arch. 10.24435/materialscloud:qy-dp (2020a).

     Not in our library

110. 110.

     Hoja, J. et al. QM7-X: A comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules, (Version 1.0) [Data set]. Zenodo10.5281/zenodo.3905361 (2020).

     Not in our library10.1038/s41597-021-00812-2

111. 111.
     A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer · 2021

     No notice
112. 112.

     Paszke, A. et al. PyTorch: An imperative style, high-performance deep learning library. arXiv preprint arXiv:1912.01703 (2019).

     Not in our library

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