On the impact of nuclear quantum effects on quantum chemical topology

It is well established that nuclear quantum effects (NQEs) can significantly impact the structure and reactivity of molecules containing light nuclei, yet their influence on real space chemical bonding descriptors remains largely unexplored. In this study, we present the first systematic analysis of how NQEs modify robust quantum chemical topology (QCT) indicators derived from the electronic density. Using nuclear-electronic orbital density functional theory (NEO-DFT), we treat selected protons quantum mechanically and analyze the resulting self-consistent electronic and protonic densities within the framework of the quantum theory of atoms in molecules. A diverse set of molecular systems spanning hydridic to protic hydrogen environments is investigated. We show that proton delocalization induces a characteristic, non-spherical depletion of the electronic density around the classical nuclear position, leading to systematic changes in atomic charges, bonded radii, delocalization indices, and bond critical point properties. Remarkably, the inclusion of NQEs restores chemically intuitive bond polarities in several cases where conventional Born-Oppenheimer DFT yields counterintuitive topological charges. Clear correlations are identified between protonic descriptors (size, displacement, and quadrupolar distortion) and electronic topological responses. These results demonstrate that NEO-DFT, combined with QCT analysis, provides a physically transparent and computationally efficient route to incorporate NQEs into real space bonding pictures, opening new perspectives for the interpretation of hydrogen bonding, proton transfer, and anharmonic effects in complex molecular systems.