GED-CRN Breaks the Data Barrier: High-Fidelity Electron Density Prediction Using Only 19 Training Molecules

Abstract

We present GED-CRN, a 3D convolutional residual network that achieves quantum-chemical accuracy (MAE =7.6×10⁻⁴ bohr⁻³) in predicting electron densities for AIE-active systems using only 19 training molecules—overcoming the data scarcity bottleneck via spatial cube sampling (2×2×2 bohr³) of pro-molecular densities and nuclear potentials. The model demonstrates 1500× faster computation than MP2 while preserving AIE-critical features (<0.1 Å vdW surface error), enabling high-throughput screening of π-conjugated materials with 50% lower error than conventional organic systems, as validated on QM9 and ASBase datasets. This few-shot learning paradigm bridges data-efficient quantum ML with functional luminescent material design.

Keywords

aggregation-induced emission / electron density / machine learning

References

[1] Y. Zhou, Y. Saad, M. L. Tiago, and J. R. Chelikowsky, “Self-Consistent-Field Calculations Using Chebyshev-Filtered Subspace Iteration,” Journal of Computational Physics 219 (2006): 172-184.

[2] T. Lv, Z. Zhong, Y. Liang, F. Li, J. Huang, and R. Zheng, “Deep Charge: Deep Learning Model of Electron Density From a One-Shot Density Functional Theory Calculation,” Physical Review B 108 (2023): 235159.

[3] V. Sahni, “The Hohenberg-Kohn Theorems and Kohn-Sham Density Functional Theory,” in Quantal Density Functional Theory (Springer Berlin Heidelberg, 2004), 99-123.

[4] S. C. Zhang, J. Zhu, Y. Zeng, H. Q. Mai, D. Wang, and X. Y. Zheng, “Interpretable Prediction of Aggregation-Induced Emission Molecules Based on Graph Neural Networks,” Chemical Communications 61 (2025): 8899-8902.

[5] Y. Zhao, K. Chen, B. Yu, et al., “Development of Organic Aggregation-Induced Emission Fluorescent Materials Based on Machine Learning Models and Experimental Validation,” Journal of Molecular Structure 1317 (2024): 139126.

[6] J. Mei, N. L. C. Leung, R. T. K. Kwok, J. W. Y. Lam, and B. Z. Tang, “Aggregation-Induced Emission: Together We Shine, United We Soar!,” Chemical Reviews 115 (2015): 11718-11940.

[7] Z. J. Baum, X. Yu, P. Y. Ayala, Y. Zhao, S. P. Watkins, and Q. Zhou, “Artificial Intelligence in Chemistry: Current Trends and Future Directions,” Journal of Chemical Information and Modeling 61 (2021): 3197-3212.

[8] Z. Fu, M. Wang, C. Huang, et al., “Flexible Antibacterial Degradable Bioelastomer Nanocomposites for Ultrasensitive Human-Machine Interaction Sensing Enabled by Machine Learning,” Aggregate 5 (2024): e522.

[9] D. Kamal, A. Chandrasekaran, R. Batra, and R. A. Ramprasad, “A Charge Density Prediction Model for Hydrocarbons Using Deep Neural Networks,” Machine Learning: Science and Technology 1 (2020): 025003.

[10] A. Grisafi, A. Fabrizio, B. Meyer, D. M. Wilkins, C. Corminboeuf, and M. Ceriotti, “Transferable Machine-Learning Model of the Electron Density,” ACS Central Science 5 (2019): 57-64.

[11] B. Cuevas-Zuviría and L. F. Pacios, “Analytical Model of Electron Density and Its Machine Learning Inference,” Journal of Chemical Information and Modeling 60 (2020): 3831-3842.

[12] K. T. Schütt, M. Gastegger, A. Tkatchenko, K. R. Müller, and R. J. Maurer, “Unifying Machine Learning and Quantum Chemistry With a Deep Neural Network for Molecular Wavefunctions,” Nature Communications 10 (2019): 5024.

[13] I. N. Levine, D. H. Busch, and H. Shull, Quantum Chemistry, vol. 6 (Pearson Prentice Hall, 2009).

[14] E. R. Johnson, S. Keinan, P. Mori-Sánchez, J. Contreras-García, A. J. Cohen, and W. Yang, “Revealing Noncovalent Interactions,” Journal of the American Chemical Society 132 (2010): 6498-6506.

[15] A. Krawczuk and P. Macchi, “Charge Density Analysis for Crystal Engineering,” Chemistry Central Journal 8 (2014): 68.

[16] J. H. Van Lenthe, R. Zwaans, H. J. J. Van Dam, and M. F. Guest, “Starting SCF Calculations by Superposition of Atomic Densities,” Journal of Computational Chemistry 27 (2006): 926-932.

[17] M. G. Medvedev, I. S. Bushmarinov, J. Sun, J. P. Perdew, and K. A. Lyssenko, “Density Functional Theory Is Straying From the Path Toward the Exact Functional,” Science 355 (2017): 49-52.

[18] PyO3/Maturin. PyO3; 2024, https://github.com/PyO3/maturin.

[19] A. Paszke, S. Gross, F. Massa, et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library (Curran Associates, Inc., 2019), 8024-8035.

[20] R. Ramakrishnan, P. O. Dral, M. Rupp, and O. A. von Lilienfeld, “Quantum Chemistry Structures and Properties of 134 Kilo Molecules,” Scientific Data 1 (2014): 140022.

[21] J. Gong, W. Gong, B. Wu, et al., “ASBase: The Universal Database for Aggregate Science,” Aggregate 4 (2023): e263.

[22] M. L. Connolly, “Computation of Molecular Volume,” Journal of the American Chemical society 107 (1985): 1118-1124.

[23] S. Lehtola, C. Steigemann, M. J. Oliveira, and M. A. Marques, “Recent Developments in Libxc—A Comprehensive Library of Functionals for Density Functional Theory,” SoftwareX 7 (2018): 1-5.

[24] Q. Sun, X. Zhang, S. Banerjee, et al., “Recent Developments in the PySCF Program Package,” The Journal of Chemical Physics 153 (2020): 024109.

[25] J. D. Thompson, C. J. Cramer, and D. G. Truhlar, “Parameterization of Charge Model 3 for AM1, PM3, BLYP, and B3LYP,” Journal of Computational Chemistry 24 (2003): 1291-1304.

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2025 The Author(s). Aggregate published by SCUT, AIEI, and John Wiley & Sons Australia, Ltd.