Transferability and interpretability of vibrational normalizing-flow coordinates

The choice of vibrational coordinates is crucial for the accuracy, efficiency, and interpretability of molecular vibrational dynamics and spectra calculations. We explore the recently proposed normalizing-flow vibrational coordinates, which are learned molecule-specific coordinate transformations optimized for a given basis set. Much like how spherical coordinates naturally simplify the hydrogen atom by embedding physical insight into the coordinate system, normalizing-flow coordinates offload complexity from the basis functions into the coordinate transformation itself. This shift not only improves basis-set convergence but also enhances the interpretability of vibrational motions. We provide an analysis of the utility, interpretation, and associated constraints of normalizing-flow vibrational coordinates. Moreover, we demonstrate that these coordinates can be generalized across different isotopologues and even structurally related molecules, achieved with minimal fine-tuning of selected output parameters.