Bypassing the Kohn-Sham equations with machine learning

Abstract

Last year, at least 30,000 scientific papers used the Kohn–Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn–Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.

Full text

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

References 65

1. 1.

   Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965;140:A1133-A1138.

   Not in our library10.1103/physrev.140.a1133

2. 2.

   Pribram-Jones A, Gross DA, Burke K. DFT: a theory full of holes? Annu. Rev. Phys. Chem. 2015;66:283-304.

   Not in our library10.1146/annurev-physchem-040214-121420

3. 3.

   Perdew JP. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B. 1986;33:8822-8824.

   Not in our library10.1103/physrevb.33.8822

4. 4.

   Becke AD. Density functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993;98:5648-5652.

   Not in our library10.1063/1.464913

5. 5.

   National Science And Technology. Materials Genome Initiative for Global Competitiveness (General Books, 2011).

   Not in our library

6. 6.

   Jain A, et al. A high-throughput infrastructure for density functional theory calculations. Comput. Mater. Sci. 2011;50:2295-2310.

   Not in our library10.1016/j.commatsci.2011.02.023

7. 7.

   Pozun ZD, et al. Optimizing transition states via kernel-based machine learning. J. Chem. Phys. 2012;136:174101.

   Not in our library10.1063/1.4707167

8. 8.

   McGibbon RT, Pande VS. Learning kinetic distance metrics for Markov state models of protein conformational dynamics. J. Chem. Theory. Comput. 2013;9:2900-2906.

   Not in our library10.1021/ct400132h

9. 9.

   Fletcher TL, Davie SJ, Popelier PL. Prediction of intramolecular polarization of aromatic amino acids using kriging machine learning. J. Chem. Theory. Comput. 2014;10:3708-3719.

   Not in our library10.1021/ct500416k

10. 10.

    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

11. 11.

    Hautier G, Fischer CC, Jain A, Mueller T, Ceder G. Finding nature’s missing ternary oxide compounds using machine learning and density functional theory. Chem. Mater. 2010;22:3762-3767.

    Not in our library10.1021/cm100795d

12. 12.

    Hansen K, et al. Assessment and validation of machine learning methods for predicting molecular atomization energies. J. Chem. Theory Comput. 2013;9:3404-3419.

    Not in our library10.1021/ct400195d

13. 13.

    Schütt KT, et al. How to represent crystal structures for machine learning: towards fast prediction of electronic properties. Phys. Rev. B. 2014;89:205118.

    Not in our library10.1103/physrevb.89.205118

14. 14.

    Hansen K, et al. Machine learning predictions of molecular properties: accurate many-body potentials and nonlocality in chemical space. J. Phys. Chem. Lett. 2015;6:2326-2331.

    Not in our library10.1021/acs.jpclett.5b00831

15. 15.
    Quantum-chemical insights from deep tensor neural networks · 2017

    No notice
16. 16.

    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

17. 17.

    Seko A, Takahashi A, Tanaka I. Sparse representation for a potential energy surface. Phys. Rev. B. 2014;90:024101.

    Not in our library10.1103/physrevb.90.024101

18. 18.

    Li Z, Kermode JR, De Vita A. Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. Phys. Rev. Lett. 2015;114:096405.

    Not in our library10.1103/physrevlett.114.096405

19. 19.

    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

20. 20.

    Snyder JC, Rupp M, Hansen K, Müller K-R, Burke K. Finding density functionals with machine learning. Phys. Rev. Lett. 2012;108:253002.

    Not in our library10.1103/physrevlett.108.253002

21. 21.

    Snyder JC, et al. Orbital-free bond breaking via machine learning. J. Chem. Phys. 2013;139:224104.

    Not in our library10.1063/1.4834075

22. 22.

    Li L, et al. Understanding machine-learned density functionals. Int. J. Quantum Chem. 2016;116:819-833.

    Not in our library10.1002/qua.25040

23. 23.

    Li L, Baker TE, White SR, Burke K. Pure density functional for strong correlation and the thermodynamic limit from machine learning. Phys. Rev. B. 2016;94:245129.

    Not in our library10.1103/physrevb.94.245129

24. 24.

    Yao K, Parkhill J. Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks. J. Chem. Theory Comput. 2016;12:1139-1147.

    Not in our library10.1021/acs.jctc.5b01011

25. 25.

    Giannozzi P, et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter. 2009;21:395502.

    Not in our library10.1088/0953-8984/21/39/395502

26. 26.

    Snyder, J. C., Mika, S., Burke, K. & Müller, K.-R. in Empirical Inference (eds Schölkopf, B., Luo, Z. & Vovk, V.) 245–259 (Springer, 2013).

    Not in our library

27. 27.

    Snyder JC, Rupp M, Müller K-R, Burke K. Nonlinear gradient denoising: finding accurate extrema from inaccurate functional derivatives. Int. J. Quantum. Chem. 2015;115:1102-1114.

    Not in our library10.1002/qua.24937

28. 28.

    Ribeiro RF, Lee D, Cangi A, Elliott P, Burke K. Corrections to Thomas-Fermi densities at turning points and beyond. Phys. Rev. Lett. 2015;114:050401.

    Not in our library10.1103/physrevlett.114.050401

29. 29.

    Müller K-R, Mika S, Rätsch G, Tsuda K, Schölkopf B. An introduction to kernel-based learning algorithms. IEEE Trans. Neural. Netw. 2001;12:181-201.

    Not in our library10.1109/72.914517

30. 30.

    Kim M-C, Sim E, Burke K. Understanding and reducing errors in density functional calculations. Phys. Rev. Lett. 2013;111:073003.

    Not in our library10.1103/physrevlett.111.073003

31. 31.

    Kim M-C, Sim E, Burke K. Ions in solution: density corrected density functional theory (DC-DFT). J. Chem. Phys. 2014;140:18A528.

    Not in our library10.1063/1.4869189

32. 32.

    Kim M-C, Park H, Son S, Sim E, Burke K. Improved DFT potential energy surfaces via improved densities. J. Phys. Chem. Lett. 2015;6:3802-3807.

    Not in our library10.1021/acs.jpclett.5b01724

33. 33.

    Dreizler, R. M. & Gross, E. K. U. Density Functional Theory: an Approach to the Quantum Many-Body Problem (Springer-Verlag, 1990).

    Not in our library

34. 34.

    Schölkopf B, et al. Input space versus feature space in kernel-based methods. IEEE Trans. Neural Netw. 1999;10:1000-1017.

    Not in our library10.1109/72.788641

35. 35.

    Schölkopf B, Smola A, Müller K-R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 1998;10:1299-1319.

    Not in our library10.1162/089976698300017467

36. 36.

    Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996;77:3865-3868.

    Not in our library10.1103/physrevlett.77.3865

37. 37.

    Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B. 1999;59:1758-1775.

    Not in our library10.1103/physrevb.59.1758

38. 38.

    Blöchl PE. Projector augmented-wave method. Phys. Rev. B. 1994;50:17953-17979.

    Not in our library10.1103/physrevb.50.17953

39. 39.

    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

40. 40.

    Powell MJD. An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 1964;7:155-162.

    Not in our library10.1093/comjnl/7.2.155

Cited by papers we hold 8

• Gaussian Process Regression for Materials and Molecules · 2021
  No notice
• A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer · 2021
  No notice
• Generalization properties of neural network approximations to frustrated magnet ground states · 2020
  Not checked
• Quantum chemical accuracy from density functional approximations via machine learning · 2020
  No notice
• Exact exchange-correlation potentials from ground-state electron densities · 2019
  Not checked
• Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions · 2019
  No notice
• Data‐Driven Materials Science: Status, Challenges, and Perspectives · 2019
  Corrected
• Towards exact molecular dynamics simulations with machine-learned force fields · 2018
  No notice

Reads

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.