Machine-learning based interatomic potential for studying of crystal structures properties

In the process of modeling multilayer semiconductor nanostructures, it is important to quickly obtain accurate values the characteristics of the structure under consideration. One of these characteristics is the value of the interaction energy of atoms within the structure. The energy value is also important for obtaining other quantities, such as bulk modulus of the structure, shear modulus etc. The paper considers a machine learning based method for obtaining the interaction energy of two atoms. A model built on the basis of the Gaussian Approximation Potential (GAP) is trained on a previously prepared sample and allows predicting the energy values of atom pairs for test data. The values of the coordinates of the interacting atoms, the distance between the atoms, the value of the lattice constant of the structure, an indication of the type of interacting atoms, and also the value describing the environment of the atoms were used as features. The coordinates of the atoms, the distance between the atoms, the lattice constant of the structure, an indication of the type of interacting atoms, the value describing the environment of the atoms were used as features. The computational experiment was carried out with structures of Si, Ge and C. There were estimated the rate of obtaining the energy of interacting atoms and the accuracy of the obtained value. The characteristics of speed and accuracy were compared with the characteristics that were achieved using the many-particle interatomic potential — the Tersoff potential.

1. Powell D. Elasticity, lattice dynamics and parameterization techniques for the Tersoff potential applied to elemental and type III—V semiconductors: Dis. (PhD). University of Sheffield, 2006, 259 p. URL: https://etheses.whiterose.ac.uk/15100/1/434519.pdf

2. Abgaryan K. K., Volodina O. V., Uvarov S. I. Mathematical modeling of point defect cluster formation in silicon based on molecular dynamic approach. Modern Electronic Materials, 2015, vol. 1, no. 3, pp. 82—87. DOI: 10.1016/j.moem.2016.03.001

3. Bartók-Pįrtay A. The Gaussian Approximation Potential: an interatomic potential derived from first principles quantum mechanics. Springer Science & Business Media, 2010. 107 p. DOI: 10.1007/978-3-642-14067-9

4. Kruglov I. A. Search for new compounds, study of their stability and properties using modern methods of computer design of materials: Diss. Cand. Sci. (Phys.-Math.). Moscow: Institute of High Pressure Physics. L.F. Vereshchagin RAS, 2018, 112 p. (In Russ.)

5. Gramacy R. B. Surrogates: Gaussian process modeling, design, and optimization for the applied sciences. Chapman and Hall/CRC, 2020, 559 p.

6. Vorontsov K. Mathematical Learning Methods on Precedents. Course of Lectures, 2006.

7. Rupp M., Tkatchenko A., Müller K.-R., von Lilienfeld O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett., 2012, vol. 108, no. 5, p. 058301. DOI: 10.1103/PhysRevLett.108.058301

8. Faber F., Lindmaa A., von Lilienfeld O. A., Armiento R. Crystal structure representations for machine learning models of formation energies. Int. J. Quantum Chem., 2015, vol. 115, no. 16, pp. 1094—1101. DOI: 10.1002/qua.24917

9. Bartók A. P., Csányi G. Gaussian approximation potentials: A brief tutorial introduction. Int. J. Quantum Chem., 2015, vol. 115, no. 16, pp. 1051—1057. DOI: 10.1002/qua.24927

10. Abgaryan K. K., Mutigullin I. V., Uvarov S. I., Uvarova O. V. Multiscale modeling of clusters of point defects in semiconductor structures. In: CEUR Workshop Proceedings, 2019, pp. 43—51. URL: http://ceur-ws.org/Vol-2426/paper7.pdf

11. Deringer V. L., Csányi G. Machine learning based interatomic potential for amorphous carbon. Phys. Rev. B, 2017, vol. 95, no. 9, p. 094203. DOI: 10.1103/PhysRevB.95.094203

12. Novikov I. S., Shapeev A. V. Improving accuracy of interatomic potentials: more physics or more data? A case study of silica. Materials Today Commun., 2019, vol. 18, pp. 74—80. DOI: 10.1016/j.mtcomm.2018.11.008

13. Wu S. Q., Ji M., Wang C. Z., Nguyen M. C., Zhao X., Umemoto K., Wentzcovitch R. M., Ho K. M. An adaptive genetic algorithm for crystal structure prediction. J. Phys.: Condens. Matter. 2014, vol. 26, no. 3, p. 035402. DOI: 10.1088/0953-8984/26/3/035402

14. Rupp M., Tkatchenko A., Müller K.-R., von Lilienfeld O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett., 2012, vol. 108, no. 5, p. 058301. DOI: 10.1103/PhysRevLett.108.058301

15. Coifman R. R., Kevrekidis I. G., Lafon S., Maggioni M., Nadler B. Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul., 2008, vol. 7, no. 2, pp. 842—864. DOI: 10.1137/070696325

16. Behler J., Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett., 2007, vol. 98, no. 14, p. 146401. DOI: 10.1103/PhysRevLett.98.146401

17. Hastie T., Tibshirani R., Friedman J. The elements of statistical learning: data mining, inference, and prediction. Springer Science & Business Media, 2009, 767 p. DOI: 10.1007/b94608