Large-Scale Calculations by Integrating the Fragmentation Approach With Neural Network Potentials
Rei Oshima
Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
Search for more papers by this authorMikito Fujinami
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan
Search for more papers by this authorYuya Nakajima
Central Technical Research Laboratory, ENEOS Corporation, Yokohama, Kanagawa, Japan
Search for more papers by this authorCorresponding Author
Hiromi Nakai
Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan
Correspondence:
Hiromi Nakai ([email protected])
Search for more papers by this authorRei Oshima
Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
Search for more papers by this authorMikito Fujinami
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan
Search for more papers by this authorYuya Nakajima
Central Technical Research Laboratory, ENEOS Corporation, Yokohama, Kanagawa, Japan
Search for more papers by this authorCorresponding Author
Hiromi Nakai
Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, Japan
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan
Correspondence:
Hiromi Nakai ([email protected])
Search for more papers by this authorFunding: This work was supported by the Ministry of Education, Culture, Sports, Science and Technology (JP24H01096) and the Japan Science and Technology Agency (JPMJSP2128).
ABSTRACT
A fragmentation method is introduced to enable large-scale molecular simulations using neural network potentials (NNPs). The method partitions a system into cube-shaped fragments and reconstructs the total energy using a many-body expansion formalism with a distance-based cut-off approximation. Validation with Au, NaCl, diamond, H2O, and graphite crystals demonstrated that including three-body interactions with 26 neighboring fragments reduces per-atom energy error to within 0.04 eV. This approach enables simulations of systems with up to 1 million atoms, surpassing conventional NNP limits. The scaling exponent for three-body calculations remains below 1.64, suggesting feasibility for even larger-scale applications.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
References
- 1T. B. Blank, S. D. Brown, A. W. Calhoun, and D. J. Doren, “Neural Network Models of Potential Energy Surfaces,” Journal of Chemical Physics 103 (1995): 4129–4137.
- 2D. F. R. Brown, M. N. Gibbs, and D. C. Clary, “Combiningab Initiocomputations, Neural Networks, and Diffusion Monte Carlo: An Efficient Method to Treat Weakly Bound Molecules,” Journal of Chemical Physics 105 (1996): 7597–7604.
- 3E. Tafeit, W. Estelberger, R. Horejsi, et al., “Neural Networks as a Tool for Compact Representation of Ab Initio Molecular Potential Energy Surfaces,” Journal of Molecular Graphics 14 (1996): 12–18.
- 4K. Tai No, B. Ha Chang, S. Yeon Kim, M. Shik Jhon, and H. A. Scheraga, “Description of the Potential Energy Surface of the Water Dimer With an Artificial Neural Network,” Chemical Physics Letters 271 (1997): 152–156.
10.1016/S0009-2614(97)00448-X Google Scholar
- 5F. V. Prudente and J. J. Soares Neto, “The Fitting of Potential Energy Surfaces Using Neural Networks. Application to the Study of the Photodissociation Processes,” Chemical Physics Letters 287 (1998): 585–589.
- 6S. Manzhos and T. Carrington, Jr., “A Random-Sampling High Dimensional Model Representation Neural Network for Building Potential Energy Surfaces,” Journal of Chemical Physics 125 (2006): 084109.
- 7S. Manzhos and T. Carrington, Jr., “Using Redundant Coordinates to Represent Potential Energy Surfaces With Lower-Dimensional Functions,” Journal of Chemical Physics 127 (2007): 014103.
- 8M. Malshe, R. Narulkar, L. M. Raff, et al., “Development of Generalized Potential-Energy Surfaces Using Many-Body Expansions, Neural Networks, and Moiety Energy Approximations,” Journal of Chemical Physics 130 (2009): 184102.
- 9J. Behler and M. Parrinello, “Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces,” Physical Review Letters 98 (2007): 146401.
- 10J. S. Smith, O. Isayev, and A. E. Roitberg, “ANI-1: An Extensible Neural Network Potential With DFT Accuracy at Force Field Computational Cost,” Chemical Science 8 (2017): 3192–3203.
- 11K. T. Schütt, H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko, and K.-R. Müller, “SchNet—A Deep Learning Architecture for Molecules and Materials,” Journal of Chemical Physics 148 (2018): 241722.
- 12N. Lubbers, J. S. Smith, and K. Barros, “Hierarchical Modeling of Molecular Energies Using a Deep Neural Network,” Journal of Chemical Physics 148 (2018): 241715.
- 13L. Zhang, J. Han, H. Wang, R. Car, and E. Weinan, “Deep Potential Molecular Dynamics: A Scalable Model With the Accuracy of Quantum Mechanics,” Physical Review Letters 120 (2018): 143001.
- 14O. T. Unke and M. Meuwly, “PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges,” Journal of Chemical Theory and Computation 15 (2019): 3678–3693.
- 15J. Gasteiger, J. Groß, and S. Günnemann, “Directional Message Passing for Molecular Graphs,” preprint, arXiv, April 5, 2022.
- 16K. T. Schütt, O. T. Unke, and M. Gastegger, “Equivariant Message Passing for the Prediction of Tensorial Properties and Molecular Spectra,” preprint, arXiv, June 7, 2021.
- 17S. Batzner, A. Musaelian, L. Sun, et al., “E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentias,” preprint, arXiv, December 16, 2021.
- 18D. Anstine, R. Zubatyuk, and O. Isayev, “AIMNet2: A Neural Network Potential to Meet Your Neutral, Charged, Organic, and Elemental-Organic Needs,” preprint, ChemRxiv, December 20, 2024.
- 19J. Zeng, L. Cao, M. Xu, T. Zhu, and J. Z. H. Zhang, “Complex Reaction Processes in Combustion Unraveled by Neural Network-Based Molecular Dynamics Simulation,” Nature Communications 11 (2020): 5713.
- 20V. Zaverkin, D. Holzmüller, R. Schuldt, and J. Kästner, “Predicting Properties of Periodic Systems From Cluster Data: A Case Study of Liquid Water,” Journal of Chemical Physics 156 (2022): 114103.
- 21C. Schran, F. Brieuc, and D. Marx, “Transferability of Machine Learning Potentials: Protonated Water Neural Network Potential Applied to the Protonated Water Hexamer,” Journal of Chemical Physics 154 (2021): 051101.
- 22S. Manzhos and T. Carrington, Jr., “Neural Network Potential Energy Surfaces for Small Molecules and Reactions,” Chemical Reviews 121 (2021): 10187–10217.
- 23D. W. Zhang and J. Z. H. Zhang, “Molecular Fractionation With Conjugate Caps for Full Quantum Mechanical Calculation of Protein–Molecule Interaction Energy,” Journal of Chemical Physics 119 (2003): 3599–3605.
- 24W. Li, S. Li, and Y. Jiang, “Generalized Energy-Based Fragmentation Approach for Computing the Ground-State Energies and Properties of Large Molecules,” Journal of Physical Chemistry A 111 (2007): 2193–2199.
- 25K. Kitaura, E. Ikeo, T. Asada, T. Nakano, and M. Uebayasi, “Fragment Molecular Orbital Method: An Approximate Computational Method for Large Molecules,” Chemical Physics Letters 313 (1999): 701–706.
- 26S. R. Gadre, R. N. Shirsat, and A. C. Limaye, “Molecular Tailoring Approach for Simulation of Electrostatic Properties,” Journal of Physical Chemistry 98 (1994): 9165–9169.
- 27V. Deev and M. A. Collins, “Approximate Ab Initio Energies by Systematic Molecular Fragmentation,” Journal of Chemical Physics 122 (2005): 154102.
- 28N. J. Mayhall and K. Raghavachari, “Molecules-In-Molecules: An Extrapolated Fragment-Based Approach for Accurate Calculations on Large Molecules and Materials,” Journal of Chemical Theory and Computation 7 (2011): 1336–1343.
- 29W. Yang, “Direct Calculation of Electron Density in Density-Functional Theory,” Physical Review Letters 66 (1991): 1438–1441.
- 30T. Akama, M. Kobayashi, and H. Nakai, “Implementation of Divide-and-Conquer Method Including Hartree-Fock Exchange Interaction,” Journal of Computational Chemistry 28 (2007): 2003–2012.
- 31P. D. Walker and P. G. Mezey, “Molecular Electron Density Lego Approach to Molecule Building,” Journal of the American Chemical Society 115 (1993): 12423–12430.
- 32A. Imamura, Y. Aoki, and K. Maekawa, “A Theoretical Synthesis of Polymers by Using Uniform Localization of Molecular Orbitals: Proposal of an Elongation Method,” Journal of Chemical Physics 95 (1991): 5419–5431.
- 33X. He and J. Z. H. Zhang, “A New Method for Direct Calculation of Total Energy of Protein,” Journal of Chemical Physics 122 (2005): 031103.
- 34D. Hankins, J. W. Moskowitz, and F. H. Stillinger, “Water Molecule Interactions,” Journal of Chemical Physics 53 (1970): 4544–4554.
- 35K. Yao, J. E. Herr, and J. Parkhill, “The Many-Body Expansion Combined With Neural Networks,” Journal of Chemical Physics 146 (2017): 014106.
- 36Z. Cheng, D. Zhao, J. Ma, W. Li, and S. Li, “An On-the-Fly Approach to Construct Generalized Energy-Based Fragmentation Machine Learning Force Fields of Complex Systems,” Journal of Chemical Theory and Computation 124 (2020): 5007–5014.
- 37S. Takamoto, C. Shinagawa, D. Motoki, et al., “Towards Universal Neural Network Potential for Material Discovery Applicable to Arbitrary Combination of 45 Elements,” Nature Communications 13 (2022): 2991.
- 38 Matlantis, “Software as a Service Style Material Discovery Tool,” https://matlantis.com/.
- 39J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters 77 (1996): 3865–3868.
- 40P. E. Blöchl, “Projector Augmented-Wave Method,” Physical Review B 50 (1994): 17953–17979.
- 41G. Kresse and D. Joubert, “From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method,” Physical Review B 59 (1999): 1758–1775.
- 42S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, “A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu,” Journal of Chemical Physics 132 (2010): 154104.
- 43S. Grimme, S. Ehrlich, and L. Goerigk, “Effect of the Damping Function in Dispersion Corrected Density Functional Theory,” Journal of Computational Chemistry 32 (2011): 1456–1465.
- 44A. Jain, S. P. Ong, G. Hautier, et al., “Commentary: The Materials Project: A Materials Genome Approach to Accelerating Materials Innovation,” APL Materials 1 (2013): 011002.
