Localizing electron density errors in density functional theory.

The accuracy of different density functional approximations is assessed through the use of quantum chemical topology on molecular electron densities. In particular, three simple yet ever-important systems are studied: N2, CO and ethane. Our results exemplify how real-space descriptors can help understand the sources of errors in density functional theory, 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 chemically 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 relating energy and density errors.