No Access Submitted: 28 April 2021 Accepted: 28 June 2021 Published Online: 15 July 2021
J. Chem. Phys. 155, 034106 (2021); https://doi.org/10.1063/5.0055341
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  • Keita Kobayashi
  • Yuki Nagai
  • Mitsuhiro Itakura
  • Motoyuki Shiga
Self-learning hybrid Monte Carlo (SLHMC) is a first-principles simulation that allows for exact ensemble generation on potential energy surfaces based on density functional theory. The statistical sampling can be accelerated with the assistance of smart trial moves by machine learning potentials. In the first report [Nagai et al., Phys. Rev. B 102, 041124(R) (2020)], the SLHMC approach was introduced for the simplest case of canonical sampling. We herein extend this idea to isothermal–isobaric ensembles to enable general applications for soft materials and liquids with large volume fluctuation. As a demonstration, the isothermal–isobaric SLHMC method was used to study the vibrational structure of liquid silica at temperatures close to the melting point, whereby the slow diffusive motion is beyond the time scale of first-principles molecular dynamics. It was found that the static structure factor thus computed from first-principles agrees quite well with the high-energy x-ray data.
M.S. acknowledges financial support from the JSPS KAKENHI (Grant Nos. 18H05519, 18K05208, and 21H01603) and the MEXT Program for Promoting Researches on the Supercomputer Fugaku (Fugaku Battery and Fuel Cell Project). Y.N. acknowledges financial support from the JSPS KAKENHI (Grant No. 20H05278). The calculations were performed on the supercomputing system HPE SGI8600 at the Japan Atomic Energy Agency. The crystal structures were drawn with VESTA.4343. K. Momma and F. Izumi, “VESTA: A three-dimensional visualization system for electronic and structural analysis,” J. Appl. Crystallogr. 41, 653–658 (2008). https://doi.org/10.1107/s0021889808012016
  1. 1. W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965). https://doi.org/10.1103/physrev.140.a1133, Google ScholarCrossref, ISI
  2. 2. Y. Nagai, M. Okumura, K. Kobayashi, and M. Shiga, “Self-learning hybrid Monte Carlo: A first-principles approach,” Phys. Rev. B 102, 041124(R) (2020). https://doi.org/10.1103/physrevb.102.041124, Google ScholarCrossref
  3. 3. S. Gottlieb, W. Liu, D. Toussaint, R. L. Renken, and R. L. Sugar, “Hybrid-molecular-dynamics algorithms for the numerical simulation of quantum chromodynamics,” Phys. Rev. D 35, 2531–2542 (1987). https://doi.org/10.1103/physrevd.35.2531, Google ScholarCrossref
  4. 4. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth, “Hybrid Monte Carlo,” Phys. Lett. B 195, 216–222 (1987). https://doi.org/10.1016/0370-2693(87)91197-x, Google ScholarCrossref
  5. 5. B. Mehlig, D. W. Heermann, and B. M. Forrest, “Hybrid Monte Carlo method for condensed-matter systems,” Phys. Rev. B 45, 679–685 (1992). https://doi.org/10.1103/physrevb.45.679, Google ScholarCrossref
  6. 6. W. Shinoda, M. Shiga, and M. Mikami, “Rapid estimation of elastic constants by molecular dynamics simulation under constant stress,” Phys. Rev. B 69, 134103 (2004). https://doi.org/10.1103/physrevb.69.134103, Google ScholarCrossref
  7. 7. A. Nakayama, T. Taketsugu, and M. Shiga, “Speed-up of ab initio hybrid Monte Carlo and ab initio path integral hybrid Monte Carlo simulations by using an auxiliary potential energy surface,” Chem. Lett. 38, 976–977 (2009). https://doi.org/10.1246/cl.2009.976, Google ScholarCrossref
  8. 8. J. Behler and M. Parrinello, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Phys. Rev. Lett. 98, 146401 (2007). https://doi.org/10.1103/physrevlett.98.146401, Google ScholarCrossref
  9. 9. A. P. Bartók, M. C. Payne, R. Kondor, and G. Csányi, “Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons,” Phys. Rev. Lett. 104, 136403 (2010). https://doi.org/10.1103/physrevlett.104.136403, Google ScholarCrossref, ISI
  10. 10. J. Behler, “Constructing high-dimensional neural network potentials: A tutorial review,” Int. J. Quantum Chem. 115, 1032–1050 (2015). https://doi.org/10.1002/qua.24890, Google ScholarCrossref, ISI
  11. 11. A. P. Bartók and G. Csányi, “Gaussian approximation potentials: A brief tutorial introduction,” Int. J. Quantum Chem. 115, 1051–1057 (2015). https://doi.org/10.1002/qua.24927, Google ScholarCrossref
  12. 12. J. Behler, “Perspective: Machine learning potentials for atomistic simulations,” J. Chem. Phys. 145, 170901 (2016). https://doi.org/10.1063/1.4966192, Google ScholarScitation, ISI
  13. 13. Q. Mei, C. J. Benmore, and J. K. R. Weber, “Structure of liquid SiO2: A measurement by high-energy x-ray diffraction,” Phys. Rev. Lett. 98, 057802 (2007). https://doi.org/10.1103/PhysRevLett.98.057802, Google ScholarCrossref
  14. 14. P. Vashishta, R. K. Kalia, J. P. Rino, and I. Ebbsjö, “Interaction potential for SiO2: A molecular-dynamics study of structural correlations,” Phys. Rev. B 41, 12197–12209 (1990). https://doi.org/10.1103/physrevb.41.12197, Google ScholarCrossref
  15. 15. W. Kob, “Computer simulations of supercooled liquids and glasses,” J. Phys.: Condens. Matter 11, R85–R115 (1999). https://doi.org/10.1088/0953-8984/11/10/003, Google ScholarCrossref
  16. 16. R. E. Ryltsev, N. M. Chtchelkatchev, and V. N. Ryzhov, “Superfragile glassy dynamics of a one-component system with isotropic potential: Competition of diffusion and frustration,” Phys. Rev. Lett. 110, 025701 (2013). https://doi.org/10.1103/physrevlett.110.025701, Google ScholarCrossref
  17. 17. J. Geske, B. Drossel, and M. Vogel, “Fragile-to-strong transition in liquid silica,” AIP Adv. 6, 035131 (2016). https://doi.org/10.1063/1.4945445, Google ScholarScitation, ISI
  18. 18. J. Sarnthein, A. Pasquarello, and R. Car, “Structural and electronic properties of liquid and amorphous SiO2: An ab initio molecular dynamics study,” Phys. Rev. Lett. 74, 4682–4685 (1995). https://doi.org/10.1103/physrevlett.74.4682, Google ScholarCrossref
  19. 19. J. Sarnthein, A. Pasquarello, and R. Car, “Model of vitreous SiO2 generated by an ab initio molecular-dynamics quench from the melt,” Phys. Rev. B 52, 12690–12695 (1995). https://doi.org/10.1103/physrevb.52.12690, Google ScholarCrossref
  20. 20. M. Kim, K. H. Khoo, and J. R. Chelikowsky, “Simulating liquid and amorphous silicon dioxide using real-space pseudopotentials,” Phys. Rev. B 86, 054104 (2012). https://doi.org/10.1103/physrevb.86.054104, Google ScholarCrossref
  21. 21. W. Li and Y. Ando, “Comparison of different machine learning models for the prediction of forces in copper and silicon dioxide,” Phys. Chem. Chem. Phys. 20, 30006–30020 (2018). https://doi.org/10.1039/c8cp04508a, Google ScholarCrossref
  22. 22. I. A. Balyakin, S. V. Rempel, R. E. Ryltsev, and A. A. Rempel, “Deep machine learning interatomic potential for liquid silica,” Phys. Rev. E 102, 052125 (2020). https://doi.org/10.1103/PhysRevE.102.052125, Google ScholarCrossref
  23. 23. N. Artrith and A. Urban, “An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2,” Comput. Mater. Sci. 114, 135–150 (2016). https://doi.org/10.1016/j.commatsci.2015.11.047, Google ScholarCrossref
  24. 24. A. M. Miksch, T. Morawietz, J. Kästner, A. Urban, and N. Artrith, “Strategies for the construction of machine-learning potentials for accurate and efficient atomic-scale simulations,” Mach. Learn.: Sci. Technol. (2021); arXiv:2101.10468 [cond-mat.mtrl-sci]. Google Scholar
  25. 25. M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010). Google Scholar
  26. 26. M. Shiga, PIMD: An open-source software for parallel molecular simulations, https://ccse.jaea.go.jp/software/PIMD/index.en.html. Google Scholar
  27. 27. S. Ruiz-Barragan, K. Ishimura, and M. Shiga, “On the hierarchical parallelization of ab initio simulations,” Chem. Phys. Lett. 646, 130–135 (2016). https://doi.org/10.1016/j.cplett.2016.01.017, Google ScholarCrossref
  28. 28. G. Kresse and J. Hafner, “Ab initio molecular dynamics for liquid metals,” Phys. Rev. B 47, 558–561 (1993). https://doi.org/10.1103/physrevb.47.558, Google ScholarCrossref, ISI
  29. 29. G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B 54, 11169–11186 (1996). https://doi.org/10.1103/physrevb.54.11169, Google ScholarCrossref, ISI
  30. 30. A. M. Cooper, J. Kästner, A. Urban, and N. Artrith, “Efficient training of ANN potentials by including atomic forces via Taylor expansion and application to water and a transition-metal oxide,” npj Comput. Mater. 6, 54 (2020). https://doi.org/10.1038/s41524-020-0323-8, Google ScholarCrossref
  31. 31. N. Artrith, A. Urban, and G. Ceder, “Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species,” Phys. Rev. B 96, 014112 (2017). https://doi.org/10.1103/physrevb.96.014112, Google ScholarCrossref
  32. 32. N. Artrith, , version 2.0.3, http://ann.atomistic.net/. Google Scholar
  33. 33. J. P. Perdew, “Accurate density functional for the energy: Real-space cutoff of the gradient expansion for the exchange hole,” Phys. Rev. Lett. 55, 1665–1668 (1985). https://doi.org/10.1103/physrevlett.55.1665, Google ScholarCrossref
  34. 34. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996). https://doi.org/10.1103/physrevlett.77.3865, Google ScholarCrossref, ISI
  35. 35. D. R. Lide, CRC Handbook of Chemistry and Physics, 88th ed. (CRC Press, 2007). Google Scholar
  36. 36. J. F. Bacon, A. A. Hasapis, and J. W. Wholley, Jr., “Viscosity and density of molten silica and high silica content glasses,” Phys. Chem. Glasses 1, 90–98 (1960). Google Scholar
  37. 37. I. A. Aksay, J. A. Pask, and R. F. Davis, “Densities of SiO2-Al2O3 melts,” J. Am. Ceram. Soc. 62, 332–336 (1979). https://doi.org/10.1111/j.1151-2916.1979.tb19071.x, Google ScholarCrossref
  38. 38. B. W. H. van Beest, G. J. Kramer, and R. A. van Santen, “Force fields for silicas and aluminophosphates based on ab initio calculations,” Phys. Rev. Lett. 64, 1955–1958 (1990). https://doi.org/10.1103/physrevlett.64.1955, Google ScholarCrossref
  39. 39. T. E. Faber and J. M. Ziman, “A theory of the electrical properties of liquid metals,” Philos. Mag. 11, 153–173 (1965). https://doi.org/10.1080/14786436508211931, Google ScholarCrossref
  40. 40. D. Waasmaier and A. Kirfel, “New analytical scattering actor functions for free atoms and ions,” Acta Crystallogr., Sect. A: Found. Crystallogr. 51, 416–431 (1995). https://doi.org/10.1107/s0108767394013292, Google ScholarCrossref
  41. 41. F. Wang and D. P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states,” Phys. Rev. Lett. 86, 2050–2053 (2001). https://doi.org/10.1103/physrevlett.86.2050, Google ScholarCrossref, ISI
  42. 42. A. Laio and M. Parrinello, “Escaping free-energy minima,” Proc. Natl. Acad. Sci. U. S. A. 99, 12562–12566 (2002). https://doi.org/10.1073/pnas.202427399, Google ScholarCrossref, ISI
  43. 43. K. Momma and F. Izumi, “VESTA: A three-dimensional visualization system for electronic and structural analysis,” J. Appl. Crystallogr. 41, 653–658 (2008). https://doi.org/10.1107/s0021889808012016, Google ScholarCrossref
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