A Fragment-Based Construction of a Neural Network Potential for Metal-Organic Frameworks

Abstract

In recent years, many types of machine learning potentials (MLPs) have been developed, which are used to represent the high-dimensional potential-energy surface (PES) of a chemical system with similar accuracy as electronic structure methods. Commonly used MLPs rely on atomic energy contributions dependent on the local chemical environments. Frequently, in addition to the total energies, also atomic forces are used to construct the potentials, as these provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, the MLP training is based on smaller subsystems like molecular fragments or clusters, providing reliable reference forces. Additionally this procedure can substantially simplify the construction of the training sets. In this work, a well-defined method is proposed to determine structurally converged molecular fragments providing reliable training forces for high-dimensional neural network potentials (HDNNPs) based on the analysis of the Hessian. The Hessian permits the investigation of the atomic force dependency on the local environment and thus, the method serves as a locality test and allows to estimate the importance of long-range interactions. The procedure is illustrated for a series of simple, quasi-one-dimensional molecular model systems and the metal-organic frameworks IRMOF-1 (commonly known as MOF-5), -10 and-16 as examples for complex organic-inorganic hybrid materials. A fragment radius is dervied to construct size-converged molecular fragments as the foundation of a HDNNP data set. In the formalism of the HDNNP, the atomic force components depend on twice the cutoff radius compared to the atomic energy contributions. Because of this relation another set of size-reduced molecular fragment is derived to construct another HDNNP data set. Both data sets can be represented with similar accuracy. The validation of the resulting HDNNPs illustrates the equivalence of the predictions. Consequently, very efficient small molecular fragments are proposed for the construction of HDNNP data set.