Reaction enthalpies using the neural-network-based X1 approach: the important choice of input descriptors

Artificial neural networks represent a simple but efficient way to model and correct known errors existing between commonly used density functional computations and experimental data. The recently proposed X1 approach combines B3LYP energies with a neural-network correction. The latter receives input from a set of physical descriptors, which are primarily based on B3LYP energies. The method shows remarkable improvements for enthalpies of formation and bond energies, for molecules containing first and second row elements, in comparison to B3LYP. Here, reaction enthalpies of organic compounds containing H, C, N, and O are derived using the X1 method, as well as B3LYP, M05-2X, and G3. Despite the seemingly impressive results obtained with X1, our study reveals that underlying problems with B3LYP descriptions of medium and long-range correlation remain. Thus, X1, like B3LYP, breaks down when describing both linear and branched organic molecules. These deficiencies likely arise from the improper or insufficient selection of physical descriptors. To improve the B3LYP energies by means of a neural-network correction, we stress the importance of considering protobranching-dependent descriptors in the input layer of the neural network.