Continuous Information Descriptors for Electron Localization: Relativistic Spatial Responses, Nonadditivity, and Chemical Bonding

-block spatial expansion. We reveal the intrinsic spatial nonadditivity of these logarithmic descriptors. Unlike scalar energies, the coupling between relativistic kinematics and exact exchange generates state-dependent spatial cross-terms driven by localized d/f electrons, necessitating fully coupled treatments for heavy elements. Extending to molecular architectures, we introduce the continuous Kullback-Leibler (KL) divergence against a promolecular reference to quantify the spatial information cost of chemical bonding. This geometric probe decouples the concentric spatial contraction of main-group covalent bonds from the anisotropic lobe-like expansion along transition metal coordination axes. These spatial divergence signatures offer three-dimensional diagnostic constraints for parametrizing next-generation heavy-element density functional approximations.