Understanding the Effects of Electric Fields on Molecules through Gradient Path Curvature

External electric fields (EFs) have recently been shown to be capable of catalyzing reactions. However, the exact effect of EFs on the electron charge density, ρ(r), is not always intuitive and requires further investigation in order to design efficient EF catalysts. While previous work has used gradient bundle integration to quantify subtle changes to ρ(r) from external EFs, this method is numerically expensive. A less expensive method for quantifying the rearrangement of ρ(r) from external EFs is needed to build useful predictive models. We propose studying the curvature of gradient paths that bound gradient bundles. We found that the average curvature of individual gradient paths does not usually correlate with electron counts in specific gradient bundles. However, the average curvatures of gradient paths in atomic basins were found to primarily be determined by the electronegativity of bonded atoms, similar to previous studies on total curvatures of interatomic surfaces. We also found that the change of average curvatures over atomic basins correlated with average changes in atomic electron counts when applying an EF. This fundamental understanding of charge density rearrangement can be leveraged to build predictive models for reactivity based on gradient path curvatures.