Research ArticleMATERIALS SCIENCE

Electronic structure at coarse-grained resolutions from supervised machine learning

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Science Advances  22 Mar 2019:
Vol. 5, no. 3, eaav1190
DOI: 10.1126/sciadv.aav1190
  • Fig. 1 Schematic of the ANN-ECG method used in this work.

    Schematic example shows a three-bead/monomer CG mapping for S3MT.

  • Fig. 2 Predictive accuracy of ANN-ECG versus TB Hamiltonian.

    Two-dimensional (2D) histogram plots of ANN-ECG performance applied to the (A) 300 and (B) 500 K/rigid datasets and the TB model (Eq. 1) applied to the (C) 300 and (D) 500 K/rigid datasets. Color bar denotes the probability distribution of predicted HOMO energy levels, and the inset shows the prediction in the interval of the highest-energy HOMO.

  • Fig. 3 ANN-ECG performance on rigid and flexible configurations.

    2D histograms of ANN-ECG performance with a (A) 300 K/flexible trained model applied to 300 K/flexible test set, (B) 500 K/flexible trained model applied to 500 K/flexible test set, (C) 300 K/flexible model applied to 300 K/rigid test set, and (D) 500 K/flexible model applied to 500 K/rigid test set. Color bar denotes the probability distribution of predicted values, and the inset shows the prediction in the interval of the highest-energy HOMO.

  • Fig. 4 ANN-ECG performance applied to a systematically reduced set of coarse-grained representations.

    (A) ANN-ECG fivefold cross-validated RMSE (green) and r2 (blue) of 300 K/flexible S3MT configurations as a function of CG resolution. (B) Visualizations of the CG mappings for S3MT occurring at all resolutions shown in (A). Resolution 8 in (A) corresponds to one CG bead per S3MT molecule and is not explicitly shown.

  • Fig. 5 ANN-ECG applied to the prediction of configurationally dependent dimer electronic structure.

    (A) Schematic of atomistic and coarse-grained representations of a S3MT dimer. (B) 2D histogram of ANN-ECG performance applied to the S3MT dimer six highest HOMO energy levels. (C) Schematic of dimer configurations taken from a classical MD simulation of the thiophene fluid, with both atomistic and CG representations shown. (D) 2D histogram of ANN-ECG performance applied to predict the hole self-exchange coupling between thiophene dimers at the CG resolution.

  • Table 1 RMSE and r2 results for all models and datasets in this study.
    MethodTrain/testValidationRMSE (meV)r2
    TB300 K/rigid54.7 ± 1.00.780 ± 0.001
    TB500 K/rigid66.7 ± 1.30.790 ± 0.001
    ANN300 K/rigid13.5 ± 0.50.989 ± 0.001
    ANN500 K/rigid19.7 ± 0.60.984 ± 0.001
    ANN300 K/flexible90.7 ± 0.60.573 ± 0.008
    ANN500 K/flexible121.7 ± 0.90.466 ± 0.009
    ANN300 K/rigid500 K/rigid29.3 ± 1.20.964 ± 0.003
    ANN500 K/rigid300 K/rigid12.4 ± 0.50.990 ± 0.007
    ANN300 K/flexible300 K/rigid61.4 ± 2.00.752 ± 0.016
    ANN500 K/flexible500 K/rigid82.7 ± 1.70.704 ± 0.010

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaav1190/DC1

    Fig. S1. Temperature transferability of the ANN-ECG model.

    Fig. S2. ANN-ECG performance versus training data aize for 500 K/rigid dataset.

    Fig. S3. Distribution of HOMO energy levels for 300 K/flexible and 300 K/rigid datasets.

    Fig. S4. Atomic numbering scheme used for each 3MT monomer.

    Fig. S5. Delta–machine learning fitting results for ANN-ECG using 300 K/rigid dataset.

    Fig. S6. Application of ANN-ECG to conjugated copolymer PTB7 and non-fullerene acceptor TPB.

    Fig. S7. ANN-ECG results for the HOMO-5→HOMO energy levels of S3MT using 300 K/rigid dataset computed at the BP86/6-31G* level of theory.

    Table S1. Hyperparameter optimization for ANN layers and neurons.

    Table S2. Hyperparameter optimization for number of training epochs.

    Table S3. Results using ANN-ECG and a systematic coarse-graining strategy.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Temperature transferability of the ANN-ECG model.
    • Fig. S2. ANN-ECG performance versus training data aize for 500 K/rigid dataset.
    • Fig. S3. Distribution of HOMO energy levels for 300 K/flexible and 300 K/rigid datasets.
    • Fig. S4. Atomic numbering scheme used for each 3MT monomer.
    • Fig. S5. Delta–machine learning fitting results for ANN-ECG using 300 K/rigid dataset.
    • Fig. S6. Application of ANN-ECG to conjugated copolymer PTB7 and non-fullerene acceptor TPB.
    • Fig. S7. ANN-ECG results for the HOMO-5→HOMO energy levels of S3MT using 300 K/rigid dataset computed at the BP86/6-31G* level of theory.
    • Table S1. Hyperparameter optimization for ANN layers and neurons.
    • Table S2. Hyperparameter optimization for number of training epochs.
    • Table S3. Results using ANN-ECG and a systematic coarse-graining strategy.

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