On the Hirshfeld surface for copper(II) atoms in different coordination environments

Estimating electron density at the bond critical point through atomic Hirshfeld surfaces

Interatomic surfaces often carry information related to the electron distribution in a molecule or crystal, not only being a visual aid but also enabling quantitative analyses. Under certain conditions, atomic Hirshfeld surfaces present a high resemblance to the interatomic surfaces obtained through the quantum theory of atoms in molecules (QTAIM), with the advantage of being easily calculated, even for crystal structures determined at low resolutions (i.e. when a charge-density refinement is not performed). Here an empirical relation between the curvedness property of the Hirshfeld surfaces and the electron density at the bond critical point for certain types of covalent and coordination interactions involving carbon atoms has been obtained. The exponential function was tested to estimate the electron density in different crystalline systems, and the highest deviation from reference values obtained through QTAIM was just 16%. Additionally, fine details of this fit may be salient to the difference in electronegativity of the atoms involved in the bond.