𝒱, however, is also a measure of total geometric Gaussian isosurface curvature within gradient bundles , and can deviate from the behavior of 𝒫 more so than 𝒯. In this case, note that on the carbon atoms, 𝒫 and 𝒯 each have four minimum CPs, one each above and below the molecular plane, and one each within the molecular plane on either side of the C=C bond. In 𝒱, however, there is an additional minimum CP on the "back" of the carbon atom at the H-C-H position on the sphere opposite the C=C bond path (indicated for 𝒫 at topleft of Figure ). This character is mirrored in the geometric descriptors (category C; bottom row) in the average gradient bundle curvature (𝜅̅ ) and average net gradient bundle curvature (𝜅̅ +,-) that also have "extra" minimum CPs in the same region on the C atoms; confirmation of the link between condensed volume and charge density geometric curvature. The average curvature-scaled gradient bundle torsion 7 (𝜅𝜏 OOO) shows immediately which gradient paths within an atomic basin will bend and curve primarily within the same plane. Here we see that gradient paths within the carbon atomic basins will have very low torsion if they are close to the molecular plane or the perpendicular plane-see the minimum CP representative gradient bundles in Figure -and that those at approximately 45° to both planes will achieve maximum torsion-see the saddle CP gradient bundle in the same figure. This is to be expected since both planes are symmetry planes and hence zero flux surfaces. The same general behavior is 7 𝜅̅ is computed as the gradient path integral of the angles between neighboring line segments along a discretized path, 𝜅̅ %&' is computed as the angle between the originating and terminal ends of a gradient path, and 𝜅𝜏 111 is computed as the gradient path integral of the of angles between planes defined by coincident pairs of line segments (three neighboring line segments, where the central segment is shared between the pairs) along the path, scaled at each line segment by the its value of path curvature. All three properties are computed for paths and then averaged over the gradient paths defining a particular gradient bundle to recover its values. also observed on the H atoms, in the molecular plane and the perpendicular plane containing a C-H bond axis. Investigations into the chemical significance of these pure geometric descriptors are ongoing, but preliminary results show that the distribution and redistribution of charge density curvature plays an important role in such fundamental chemical processes as carbonyl bond activation .