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Calculations with high accuracy for atomic and inter-atomic properties, such as nuclear magnetic resonance (NMR) spectroscopy and bond dissociation energies (BDEs) are valuable for pharmaceutical molecule structural analysis, drug exploration, and screening. It is important that these calculations should include relativistic effects, which are computationally expensive to treat. Non-relativistic calculations are less expensive but their results are less accurate. In this study, we present a computational framework for predicting atomic and inter-atomic properties by using machine-learning in a non-relativistic but accurate and computationally inexpensive framework. The accurate atomic and inter-atomic properties are obtained with a low dimensional deep neural network (DNN) embedded in a fragment-based graph convolutional neural network (F-GCN). The F-GCN acts as an atomic fingerprint generator that converts the atomistic local environments into data for the DNN, which improves the learning ability, resulting in accurate results as compared to experiments. Using this framework, the 13C/1H NMR chemical shifts of Nevirapine and phenol O–H BDEs are predicted to be in good agreement with experimental measurement.