Graph Convolutional Neural Networks for (QM)ML/MM Molecular Dynamics Simulations

To accurately study chemical reactions in the condensed phase or within enzymes, both a quantum-mechanical description and sufficient configurational sampling is required to reach converged estimates. Here, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations play an important role, providing QM accuracy for the region of interest at a decreased computational cost. However, QM/MM simulations are still too expensive to study large systems on longer time scales. Recently, machine learning (ML) models have been proposed to replace the QM description. The main limitation of these models lies in the accurate description of long-range interactions present in condensed-phase systems. To overcome this issue, a recent workflow has been introduced combining a semi-empirical method (i.e. density functional tight binding (DFTB)) and a high-dimensional neural network potential (HDNNP) in a $\Delta$-learning scheme. This approach has been shown to be capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. One of the promising alternative approaches to efficiently take long-range effects into account is the development of graph convolutional neural networks (GCNN) for the prediction of the potential-energy surface. In this work, we investigate the use of GCNN models -- with and without a $\Delta$-learning scheme -- for (QM)ML/MM MD simulations. We show that the $\Delta$-learning approach using a GCNN and DFTB and as baseline achieves competitive performance on our benchmarking set of solutes and chemical reactions in water. The method is additionally validated by performing prospective (QM)ML/MM MD simulations of retinoic acid in water and S-adenoslymethioniat interacting with cytosine in water. The results indicate that the $\Delta$-learning GCNN model is a valuable alternative for (QM)ML/MM MD simulations of condensed-phase systems.