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Density calculation of Ionic Liquid [Hmim][PF6] via SLHMC method and QM7, QM9 database#

We create Neural Network Potential (NNP) of 1-hexyl-3-methylimidazolium hexafluorophosphate ([Hmim][PF6]), one of the ionic liquids, and performed the density calculation, using Self-Learning Hybrid Monte Carlo (SLHMC) method.

Create Neural Network Potential using SLHMC method#

We created NNP of 38 atoms system which packed each 1 unit of [Hmim]+ and [PF6]–.

  • NNP-MD was performed with NPT ensemble. First-principles MD for creation of initial NNP was done 200 steps, and NNP-MD was done 10 – 160 steps (2.5 – 40.0 fs) per SCF calculation.
  • Quantum ESPRESSO and Density Functional Theory using ultrasoft pseudo potentials was used for SCF calculation. The exchange-correlation functional was vdW-DF, the energy cut-off was 50 Ry, and k-point was sampled Γ-point only.
  • The structure of Neural Network was 30 nodes x 2 layer, using 50 Behler-type G2/G3 functions for symmetric functions. The symmetric function's cut-off was 5 Å. In addition, The atomic charges reproduced with third-generation HDNNP.
  • Using Intel Xeon Gold 6330 (2 CPUs, 56 cores), SLHMC calculation completed in 11 hours and 47 minutes. The total number of training data was 5000 finally.
  • The energy error converged to 2.1 meV/atom finally. The density of the ionic liquid wasn't fixed to one value, and the sufficient accuracy couldn't obtain by training with only 1 unit.
Energy error
Density of Ionic Liquid

QM7 and QM9 database application#

  • To improve the accuracy of NNP we made, the NNP was retrained with adding train data (about 8000 structures) previously prepared using QM7 and QM9 databases.

  • Using the retrained NNP, a NNP-MD calculation of 3 x 3 x 3 supercell (27 units) system were done. As a result, an accurate reproduction of the density was verified.

    • From this result, the viscosity coefficient and the diffusion coefficient can be calculated too. In addition, since the atomic charges are also output, it is efficient at analysis of electric properties such as the permittivity.
Supercell model
Density of ionic liquid
Density / (g/cm3)
Calculation 1.29
Experiment 1.29[1]
  • [1] Gardas, R. L., et al., (2007) J. Chem. Eng. Data 52(1), 80–88.

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