Noncovalent Interactions in Density Functional Theory: All the Charge Density We Do Not See

Exact determination of the electronic density of molecules and materials would provide direct access to accurate bonded and nonbonded interatomic interactions via the Hellman-Feynman theorem. However, density-functional approximations (DFAs)─the workhorse methods for the electronic structure of atomistic systems─only provide approximate and sometimes unreliable electron densities. In this work, we demonstrate that long-range van der Waals (vdW) dispersion interactions can induce significant polarization in the electron density, with the magnitude of effect growing with system size. We evaluate vdW-induced density shifts using newly developed fully coupled and optimally tuned variant of many-body dispersion model (MBD@FCO), benchmarked against accurate coupled-cluster densities. Applied to supramolecular data sets (S12L and L7) and a prototype protein (Fip35-WW), our approach reveals that dispersion-driven polarization alters long-range electrostatic potentials by up to 4 kcal/mol and reshapes noncovalent interaction (NCI) isosurfaces, producing smooth and chemically interpretable interaction regions. These findings demonstrate that dispersion interactions leave a measurable imprint on the electron density, with implications for electrostatics, biomolecular modeling, and density-based chemical analysis. Our results bridge energy-based dispersion models and density-functional theory, paving the way toward dispersion-consistent DFAs and improved machine-learned models based on electron densities.