A Multi-Resolution 3D-DenseNet for Chemical Shift Prediction in NMR Crystallography.

We have developed a deep learning algorithm for chemical shift prediction for atoms in molecular crystals that utilizes an atom-centered Gaussian density model for the 3D data representation of a molecule. We define multiple channels that describe different spatial resolutions for each atom type that utilizes cropping, pooling, and concatenation to create a multi-resolution 3D-DenseNet architecture (MR-3D-DenseNet). Because the training and testing time scale linearly with the number of samples, the MR-3D-DenseNet can exploit data augmentation that takes into account the property of rotational invariance of the chemical shifts, thereby also increasing the size of the training dataset by an order of magnitude without additional cost. We obtain very good agreement for 13C, 15N, and 17O chemical shifts when compared to ab initio quantum chemistry methods, with the highest accuracy found for 1H chemical shifts that is comparable to the error between the ab initio results and experimental measurements. Principal Component analysis (PCA) is used to both understand these greatly improved predictions for 1H , as well as indicating that chemical shift prediction for 13C, 15N, and 17O, which have far fewer training environments than the 1H atom type, will improve once more unique training samples are made available to exploit the deep network architecture.