Figure 1.

Coordinate-free methods leverage deep learning to compute QC properties. (A) Many deep-learning-based QC calculation methods require coordinates from experiment or computational optimization, which can be time-consuming to obtain. Coordinate-free methods operate directly on structural formulas without the need for coordinates. (B) Many graph-based deep learning methods describe atoms by aggregating features from other atoms in their local environment. Atoms may also exchange information with global variables, as in message passing neural networks (MPNN-G). (C) Wave deep learning architecture describes atoms based only on their ancestors as defined by a breadth-first search. Information is propagated in Waves, forward and backward across a molecule. (D) Wave achieves better than chemical accuracy when predicting total energy on QM9, a standard benchmark dataset. This result is comparable to the published, coordinate-based methods. CF: Coordinate-free 3D: 3D coordinates used as input features, *value from published results.^19,38