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To accurately study chemical reactions in the condensed phase or withinenzymes, both a quantum-mechanical description and sufficient configurationalsampling is required to reach converged estimates. Here, quantummechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations playan important role, providing QM accuracy for the region of interest at adecreased computational cost. However, QM/MM simulations are still tooexpensive to study large systems on longer time scales. Recently, machinelearning (ML) models have been proposed to replace the QM description. The mainlimitation of these models lies in the accurate description of long-rangeinteractions present in condensed-phase systems. To overcome this issue, arecent workflow has been introduced combining a semi-empirical method (i.e.density functional tight binding (DFTB)) and a high-dimensional neural networkpotential (HDNNP) in a $\Delta$-learning scheme. This approach has been shownto be capable of correctly incorporating long-range interactions within acutoff of 1.4 nm. One of the promising alternative approaches to efficientlytake long-range effects into account is the development of graph convolutionalneural networks (GCNN) for the prediction of the potential-energy surface. Inthis 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 achievescompetitive performance on our benchmarking set of solutes and chemicalreactions in water. The method is additionally validated by performingprospective (QM)ML/MM MD simulations of retinoic acid in water andS-adenoslymethioniat interacting with cytosine in water. The results indicatethat the $\Delta$-learning GCNN model is a valuable alternative for (QM)ML/MMMD simulations of condensed-phase systems.

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