Development of a Neural Network Potential for Metal-Organic Frameworks
Final Report Abstract
Metal-organic frameworks (MOFs) are an interesting class of hybrid organic-inorganic compounds. As porous crystalline materials they have found use in a wide range of applications, from gas storage to catalysis. However, investigating rather complex MOFs in computer simulations is severely hampered by the lack of reliable atomistic potentials enabling large-scale simulations with first-principles accuracy. To overcome this problem, in this project we have explored the applicability of efficient high-dimensional neural network potentials (HDNNPs), an important class of machine-learning potentials capable of representing potential energy surfaces with first principles quality, to a series of prototypical MOFs based on zinc-oxo clusters and several different organic linker molecules. The computationally most demanding step in the parameterization of HDNNPs is the generation of large training sets using density functional theory (DFT) calculations. In order to reduce the computational effort, an interesting approach is to replace large MOF bulk crystals, which often contain hundreds of atoms, by smaller molecular fragments centered at the different atomic sites containing the relevant information about the local atomic environments. In this project, we have shown that by using sufficiently large fragments reliable HDNNPs for crystalline MOFs can be generated. These HDNNPs reduce the computational effort in molecular dynamics simulations by several orders of magnitude while they essentially maintain the accuracy of the underlying electronic structure calculations. A key step in this approach has been the determination of the required fragment size, which on the one hand should be as small as possible to minimize the computational costs, but on the other hand needs to be large enough to include accurate information about the atomic interactions with their environments. To solve this problem, in this project we have developed a non-empirical systematic approach based on the Hessian, which contains all information about the dependence of the atomic forces on the positions of all other atoms in the system. Making use of the norm of the Hessian submatrices representing the specific interactions between the atoms, a rigorous procedure has been derived to determine the fragment size needed to compute converged DFT forces providing bulk-like values in the centers of the fragments. Moreover, in a second step, which is based on the analytic relation between the total potential energy and the atomic forces in HDNNPs, we have derived a strategy that allows to further drastically reduce the fragment size such that it becomes possible to construct accurate HDNNPs for bulk MOFs relying on molecular fragments, which are by themselves even too small to provide bulk-like forces for the central atoms. This is possible because the atomic environments defining the atomic energies, which in turn contain all relevant information for computing the forces, are smaller than the system size required to obtain structurally converged bulk-like forces in DFT. This systematic strategy, which relies on I) the DFT-based determination of the physical interaction range between the atoms, and II) the subsequent derivation of the required cutoff for the atomic environments in HDNNPs, has been tested and validated by constructing HDNNPs for a series of MOFs. The procedure is general and represents a blueprint for the efficient construction of machine learning potentials for all types of systems based on molecular fragments.
Publications
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From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5. Journal of Chemical Theory and Computation, 15(6), 3793-3809.
Eckhoff, Marco & Behler, Jörg
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Four Generations of High-Dimensional Neural Network Potentials. Chemical Reviews, 121(16), 10037-10072.
Behler, Jörg
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A Hessian-based assessment of atomic forces for training machine learning interatomic potentials. The Journal of Chemical Physics, 156(11).
Herbold, Marius & Behler, Jörg
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Roadmap on Machine learning in electronic structure. Electronic Structure, 4(2), 023004.
Kulik, H J; Hammerschmidt, T; Schmidt, J; Botti, S; Marques, M A L; Boley, M; Scheffler, M; Todorović, M; Rinke, P; Oses, C; Smolyanyuk, A; Curtarolo, S; Tkatchenko, A; Bartók, A P; Manzhos, S; Ihara, M; Carrington, T; Behler, J; Isayev, O; ... & Ghiringhelli, L M
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Machine learning transferable atomic forces for large systems from underconverged molecular fragments. Physical Chemistry Chemical Physics, 25(18), 12979-12989.
Herbold, Marius & Behler, Jörg
