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 non-bonded interatomic interactions by virtue of the Hellman-Feynman theorem. However, density-functional approximations (DFA) -- the workhorse methods for the electronic structure of atomistic systems -- only provide approximate and sometimes unreliable electron densities. Here we show that long-range van der Waals (vdW) dispersion interactions can visibly modify the charge density, scale nontrivially with system size, and in some cases cause polarization of charge density that exceeds that of the underlying semi-local density functional. We use the fully-coupled Many-Body Dispersion model to compute the vdW charge density by an appropriate real-space projection of the collective fluctuations of optimally-tuned coupled harmonic oscillators that constitute the model. Our analysis highlights the potential unreliability of post-hoc methods for vdW dispersion interactions, has implications for detecting interacting regions in large (bio)molecules, and enables the construction of more accurate DFAs and machine-learned force fields based on the electron density.