Atomistic Modeling of Lithium Materials from Deep Learning Potential with Ab Initio Accuracy
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Abstract: Lithium has been paid great attention in recent years thanks to its significant applications for battery and lightweight alloy. Developing a potential model with high accuracy and efficiency is important for theoretical simulation of lithium materials. Here, we build a deep learning potential (DP) for elemental lithium based on a concurrent-learning scheme and DP representation of the density-functional theory (DFT) potential energy surface (PES), the DP model enables material simulations with close-to DFT accuracy but at much lower computational cost. The simulations show that basic parameters, equation of states, elasticity, defects and surface are consistent with the first principles results. More notably, the liquid radial distribution function (RDF) based on our DP model is found to match well with experiment data. Our results demonstrate that the developed DP model can be used for the simulation of lithium materials.
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Key words:
- Deep learning /
- Lithium /
- Density functional theory /
- Potential energy surface
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Figure 2. DP vs. DFT resut comparision. (a) Energy, (b) force in
$ x $ direction, (c) force in$ y $ direction, and (d) force in$ z $ direction for the training data and test data. The inset displays the energy or force error distributions.
Figure 3. Equation of states of 5 standard Li configurations (a) and 8 MP structures (b). Solid line and cross point denote DFT and DP results, respectively. The line stands for the DP data and the dot represents the DFT data. The inset displays local magnified image.
Figure 4. (a) Vacancy formation energy, the dash line shows the upper and lower limit with a shift of 0.1 eV/atom. (b) Interstitial formation energy, the dash line shows the upper and lower limit with a shift of 0.2 eV/atom. (c) Surface formation energy, the dash line shows the upper and lower limit with a shift of 0.04 J/m2. The calculated results include 5 standard Li configurations and 8 MP structures via DP, EAM, MEAM, and DFT simulation.
Figure 5. Comparison between the experimental and DP theoretical g(r) for liquid lithium at 470.15 K. The experimental data are labeled by black points and the theoretical ones is labeled by red line.
Table I. Training parameters (including the embedding neural network, fitting neural network, and training batch) and corresponding energy and force error (
$E_{\rm{training}}$ and$F_{\rm{training}}$ are training error of energy and force;$E_{\rm{test}}$ and$F_{\rm{test}}$ are test error of energy and force).Embedding net Fitting net Traing batch ($ \times10^6 $) $E_{\rm{training} }/{\rm{eV}}$ $F_{\rm{training} } /({\rm{eV} }/\text{Å})$ $E_{\rm{test} }/{\rm{eV} }$ $F_{\rm{test} }/({\rm{eV} }/\text{Å})$ 25×50×100 240×240×240 4 0.0023 0.0158 0.0024 0.0167 25×50×100 240×240×240 8 0.0027 0.0163 0.0022 0.0170 25×50×100 240×240×240 16 0.0020 0.0157 0.0023 0.0165 15×30×60 240×240×240 8 0.0022 0.0167 0.0028 0.0179 20×40×80 240×240×240 8 0.0034 0.0200 0.0039 0.0196 25×50×100 120×120×120 8 0.0028 0.0157 0.0028 0.0162 25×50×100 180×180×180 8 0.0019 0.0147 0.0021 0.0150 
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Table II. The average error of lattice parameters
$\delta_a $ ,$\delta_b $ ,$\delta_c $ , density$\delta_\rho $ and relative energy (${\delta_E} $ ) of different Li configurations calculated by DFT, DP, EAM, and MEAM.Model δa/% δb/% δc/% $\delta_\rho/\%$ ${\delta_E}/\%$ DFT 0.00 0.00 0.00 0.00 0.00 EAM 3.67 3.76 3.83 10.76 5930.97 MEAM 0.69 0.67 0.62 1.65 5485.61 DP 0.65 0.60 0.73 2.01 6.09
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Table III. The average error of Bulk modulus
$\delta_{B_{v}} $ , Shear modulus$\delta_{G_{v}} $ , Young’s modulus$\delta_{E_{v}} $ , and Poisson’s ratio$\delta_{\nu} $ calculated by the DFT, DP, EAM, and MEAM models.Model $\delta_{B_{v} }/\%$ $\delta_{G_{v}}/\%$ $\delta_{E_{v}}/\%$ $\delta_{\nu}/\%$ DFT 0.00 0.00 0.00 0.00 EAM 133.28 102.59 100.28 34.39 MEAM 10.86 45.23 40.51 32.59 DP 9.21 20.16 17.12 9.03
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[1] N. E. Prasad, A. Gokhale, and P. R. Rao, Sadhana 28, 209 (2003). doi: 10.1007/BF02717134 [2] N. E. Prasad, A. Gokhale, and R. Wanhill, Aluminumlithium Alloys: Processing, Properties, and Applications, Butterworth-Heinemann, (2013). [3] T. C. Chang, J. Y. Wang, C. L. Chu, and S. Lee, Mater. Lett. 60, 3272 (2006). doi: 10.1016/j.matlet.2006.03.052 [4] N. Nitta, F. Wu, J. T. Lee, and G. Yushin, Biochem. Pharmacol. 18, 252 (2015). doi: 10.1016/j.mattod.2014.10.040 [5] V. Santoro, D. D. DiJulio, and P. M. Bentley, J. Phys.: Conf. Ser. 746, 012012 (2016). doi: 10.1088/1742-6596/746/1/012012 [6] Y. C. Wang, J. Lv and Y. M. Ma, Comput. Phys. Commun. 183, 2063 (2012). doi: 10.1016/j.cpc.2012.05.008 [7] J. Lv, Y. Wang, L. Zhu, and Y. Ma, Phys. Rev. Lett. 106, 19 (2011). [8] S. A. Mack, S. M. Griffin, and J. B. Neaton, Proc. Natl. Acad. Sci. USA 116, 9197 (2019). doi: 10.1073/pnas.1821533116 [9] K. Shimizu, H. Ishikawa, D. Takao, T. Yagi, and K. Amaya, Nature 419, 597 (2002). doi: 10.1038/nature01098 [10] V. V. Struzhkin, M. I. Eremets, W. Gan, H. K. Mao, and R. J. Hemley, Science 298, 1213 (2002). doi: 10.1126/science.1078535 [11] T. Matsuoka and K. Shimizu, Nature 458, 186 (2009). doi: 10.1038/nature07827 [12] C. L. Guillaume, E. Gregoryanz, O. Degtyareva, M. I. McMahon, M. Hanfland, S. Evans, M. Guthrie, S. V. Sinogeikin, and H. Mao, Nat. Phys. 7, 211 (2011). doi: 10.1038/nphys1864 [13] G. J. Ackland, M. Dunuwille, M. Martinez-Canales, I. Loa, R. Zhang, S. Sinogeikin, W. Cai, and S. Deemyad, Science 356, 1254 (2017). doi: 10.1126/science.aal4886 [14] A. M. J. Schaeffer, W. B. Talmadge, S. R. Temple, and S. Deemyad, Phys. Rev. Lett. 109, 185702 (2012). doi: 10.1103/PhysRevLett.109.185702 [15] R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985). doi: 10.1103/PhysRevLett.55.2471 [16] S. Elatresh, S. Bonev, E. Gregoryanz, and N. Ashcroft, Phys. Rev. B 94, 104107 (2016). doi: 10.1103/PhysRevB.94.104107 [17] E. R. Hernández, A. Rodriguez-Prieto, A. Bergara, and D. Alfe, Phys. Rev. Lett. 104, 185701 (2010). doi: 10.1103/PhysRevLett.104.185701 [18] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). doi: 10.1103/PhysRev.140.A1133 [19] J. E. Jones, Proc. Math. Phys. Eng. Sci. 106, 463 (1924). [20] F. H. Stillinger and T. A. Weber, Phys. Rev. B 31, 5262 (1985). doi: 10.1103/PhysRevB.31.5262 [21] M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984). doi: 10.1103/PhysRevB.29.6443 [22] M. I. Baskes, Phys. Rev. B 46, 2727 (1992). doi: 10.1103/PhysRevB.46.2727 [23] J. R. Vella, F. H. Stillinger, A. Z. Panagiotopoulos, and P. G. Debenedetti, J. Phys. Chem. B 119, 8960 (2015). doi: 10.1021/jp5077752 [24] Z. Cui, F. Gao, Z. Cui, and J. Qu, Model. Simul. Mat. Sci. Eng. 20, 015014 (2011). doi: https://iopscience.iop.org/article/10.1088/0965-0393/20/1/015014 [25] A. Nichol and G. J. Ackland, Phys. Rev. B 93, 1 (2016). [26] W. S Ko and J. Bae, Comput. Mater. Sci. 129, 202 (2017). doi: 10.1016/j.commatsci.2016.12.018 [27] J. Dorrell and L. B. Pártay, J. Phys. Chem. B 124, 6015 (2020). doi: 10.1021/acs.jpcb.0c03882 [28] L. Zhang, J. Han, H. Wang, R. Car, and W. E, Phys. Rev. Lett. 120, 143001 (2018). doi: 10.1103/PhysRevLett.120.143001 [29] J. Behler and M. Parrinello, Phys. Rev. Lett. 98, 146401 (2007). doi: 10.1103/PhysRevLett.98.146401 [30] A. P. Bartók, M. C. Payne, R. Kondor, and G. Csányi, Phys. Rev. Lett. 104, 136403 (2010). doi: 10.1103/PhysRevLett.104.136403 [31] A. P. Thompson, L. P. Swiler, C. R. Trott, S. M. Foiles, and G. J. Tucker, J. Comput. Phys. 285, 316 (2015). doi: 10.1016/j.jcp.2014.12.018 [32] A. V. Shapeev, Multiscale Model. Simul. 14, 1153 (2016). doi: 10.1137/15M1054183 [33] M. F. C. Andrade, H. Ko, L. Zhang, R. Car, and A. Selloni, Chem. Sci. 11, 2335 (2020). doi: 10.1039/C9SC05116C [34] L. Zhang, D Y. Lin, H. Wang, R. Car, and W. E, Phys. Rev. Mater. 3, 023804 (2019). doi: 10.1103/PhysRevMaterials.3.023804 [35] J. Zeng, L. Cao, M. Xu, T. Zhu, and J. Z. Zhang, Nat. Commun. 11, 1 (2020). doi: 10.1038/s41467-019-13993-7 [36] H. Wang, Y. Zhang, L. Zhang, and H. Wang, Front. Chem. 8, 589795 (2020). doi: 10.3389/fchem.2020.589795 [37] X. Wang, H. Wang, Q. Luo, and J. Yang, J. Chem. Phys. 157, 074304 (2022). doi: 10.1063/5.0100505 [38] Materials Project, https://www.materialsproject.org. [39] J. Behler, J. Chem. Phys 134, 074106 (2011). doi: 10.1063/1.3553717 [40] H. Wang, L. Zhang, J. Han, and W. E, Comput. Phys. Commun. 228, 178 (2018). doi: 10.1016/j.cpc.2018.03.016 [41] L. Zhang, J. Han, H. Wang, W. Saidi, R. Car, and W. E, NIPS'18 4441 (2018). doi: 10.48550/arXiv.1805.09003 [42] Y. Zhang, H. Wang, W. Chen, J. Zeng, L. Zhang, H. Wang, and W. E, Comput. Phys. Commun. 253, 107206 (2020). doi: 10.1016/j.cpc.2020.107206 [43] DP-data, https://github.com/deepmodeling/dpdata. [44] S. Plimpton, J. Comput. Phys. 117, 1 (1995). doi: 10.1006/jcph.1995.1039 [45] G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). doi: 10.1016/0927-0256(96)00008-0 [46] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). doi: 10.1103/PhysRevLett.77.3865 [47] J. D. Pack and H. J. Monkhorst, Phys. Rev. B 16, 1748 (1977). doi: 10.1103/PhysRevB.16.1748 [48] D. P. Kingma and J. Ba, in 3rd International Conference on Learning Representations, San Diego, CA, USA, May 7-9, 2015; Conference Track Proceedings, Y. Bengio and Y. LeCun Eds., (2015). [49] M. De Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Sluiter, C. K. Ande, S. Van Der Zwaag, J. J. Plata, C. Toher, S. Curtarolo, G. Ceder, K. A. Persson, and M. Asta, Sci. Data 2, 1 (2015). doi: 10.1038/sdata.2015.9 [50] S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson, and G. Ceder, Comput. Mater. Sci. 68, 314 (2013). doi: 10.1016/j.commatsci.2012.10.028 [51] D. Marx and M. Parrinello, J. Chem. Phys. 104, 4077 (1996). doi: 10.1063/1.471221 [52] P. S. Salmon, I. Petri, P. H. De Jong, P. Verkerk, H. E. Fischer, and W. S. Howells, J. Phys.: Condens. Matter 16, 195 (2004). doi: 10.1088/0953-8984/16/3/002 -
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