Localizing Electron Density Errors in Density Functional Theory

This work attempts to provide a clear picture on the relative quality of different Density Functional Approximations through the use of Quantum Chemical Topology on molecular electronic densities. In particular, two simple yet ever-important systems are studied, the N2 and CO molecules. Our results exemplify how real-space descriptors can clearly assess the calculated electronic density of a molecular system, avoiding unwanted error compensation present in simplified statistical metrics. Errors in ``well'' built functionals are shown to be concentrated in chemically meaningful regions of space, and hence they are predictable. Conversely, strongly parametrized functionals show isotropic errors that cannot be traced back to chemical transferable units. Moreover, we will show that energetic corrections are mapped back into improvements in the density in chemically meaningful regions. These results point at the relevance of real-space perspectives when parametrizing or assessing energy and density errors.