Atomistic Modeling of Lithium Materials from Deep Learning Potential with Ab Initio Accuracy

Haidi Wang Tao Li Yufan Yao Xiaofeng Liu Weiduo Zhu Zhao Chen Zhongjun Li Wei Hu

Haidi Wang, Tao Li, Yufan Yao, Xiaofeng Liu, Weiduo Zhu, Zhao Chen, Zhongjun Li, Wei Hu. Atomistic Modeling of Lithium Materials from Deep Learning Potential with Ab Initio Accuracy[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2211173
Citation: Haidi Wang, Tao Li, Yufan Yao, Xiaofeng Liu, Weiduo Zhu, Zhao Chen, Zhongjun Li, Wei Hu. Atomistic Modeling of Lithium Materials from Deep Learning Potential with Ab Initio Accuracy[J]. Chinese Journal of Chemical Physics . doi: 10.1063/1674-0068/cjcp2211173

doi: 10.1063/1674-0068/cjcp2211173

Atomistic Modeling of Lithium Materials from Deep Learning Potential with Ab Initio Accuracy

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  • Figure  1.  Basic workflow of DP-GEN based on concurrent learning scheme.

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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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出版历程
  • 收稿日期:  2022-11-30
  • 录用日期:  2022-12-20
  • 网络出版日期:  2022-12-27

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