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 interactionsfrom covalent via ionic bonding to dispersionthat
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.
Unraveling the atomistic and the electronic structure of solid–liquid interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technology. Density functional theory (DFT) calculations can, in principle, provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (LixMn2O4), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addition, a high-dimensional neural network for spin prediction is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale molecular dynamics. The simulations allow us to gain insights into a variety of properties, such as the dissociation of water molecules, proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces, including the manganese oxidation state distribution, Jahn–Teller distortions, and electron hopping.
Machine learning potentials have emerged as a powerful tool to extend the time and length scales of first-principles quality simulations. Still, most machine learning potentials cannot distinguish different electronic spin arrangements and thus are not applicable to materials in different magnetic states. Here we propose spin-dependent atom-centered symmetry functions as a type of descriptor taking the atomic spin degrees of freedom into account. When used as an input for a high-dimensional neural network potential (HDNNP), accurate potential energy surfaces of multicomponent systems can be constructed, describing multiple collinear magnetic states. We demonstrate the performance of these magnetic HDNNPs for the case of manganese oxide, MnO. The method predicts the magnetically distorted rhombohedral structure in excellent agreement with density functional theory and experiment. Its efficiency allows to determine the Néel temperature considering structural fluctuations, entropic effects, and defects. The method is general and is expected to be useful also for other types of systems such as oligonuclear transition metal complexes.
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