From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5

Abstract

The development of first-principles-quality reactive atomistic potentials for organic–inorganic hybrid materials is still a substantial challenge because of the very different physics of the atomic interactionsfrom covalent via ionic bonding to dispersionthat have to be described in an accurate and balanced way. In this work we used a prototypical metal–organic framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent atomic energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using density functional theory (DFT) reference calculations of small molecular fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of molecular fragments not included in the training set, is able to provide the equilibrium lattice constant of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the negative thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as atomic energies are not physical observables. The forces, which have RMSEs of about 94 meV/a 0 for the molecular fragments and 130 meV/a 0 for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for molecular dynamics simulations, provide a realistic estimate of the accuracy of atomistic potentials.

Identifying the Bottleneck for Heat Transport in Metal–Organic Frameworks

“…Employing the procedure described above, we obtained a thermal conductivity, , of (0.42 ± 0.04) W (mK) −1 at 300 K for MOF-5 with zinc (Zn)-based nodes when using the MOF-FF. As detailed in the Supporting Information, a similar value of (0.38 ± 0.03) W (mK) −1 is calculated employing a recently published (numerically much more demanding) neural network potential specifically developed for MOF-5, [23] corroborating the accuracy of the MOF-FF data. Both values are somewhat larger than the experimental result of 0.32 W (mK) −1 at 292 K. [9] This is not surprising, considering that in the simulations a perfect, defect-free structure is assumed, while the defects present in actual samples typically decrease .…”

Towards modeling spatiotemporal processes in metal–organic frameworks

“…MLPs can be used to calculate much more efficiently the PES with an accuracy matching the underlying QM data. The field of MLPs is in full expansion from the methodological side; however, to date there is only one paper where a MLP was generated for a MOFnamely, for MOF-5 [72]. The field of MLPs was initiated by Behler and Parrinello [73] with their seminal paper that proposed a neural-network methodology with atom-centered symmetry function (ACSF) descriptors to represent the chemical environment of the atoms.…”

Big-Data Science in Porous Materials: Materials Genomics and Machine Learning

“…The HDNNP which they trained in this way was able to correctly describe the negative thermal expansion and the phonon density of states. 286 …”