The multipolar model bias on primary densities as revealed by the source function descriptor

The Source Function (SF), which enables one to equate the value of the electron density rho(r) at any point within a molecule to a sum of atomic contributions, is nowadays being employed by an increasing number of groups as a powerful tool to gain insight into the chemical bond. As the SF is defined in terms of the Laplacian of rho(r), L(r), one does not need to know the wavefunction to apply it and computation of the SF through the multipole model (MM) electron density obtained from X-ray structure factors appears to be straightforward. However, since the MM is known to bias the primary density8, and the more so its Laplacian L(r), the SF contributions should also be affected to some extent. The aim of the present work is to critically examine the results obtained by applying the SF to the MM electron density. Three test cases have been considered: exafluorocyclobutene, C4F6, carbon monoxyde, CO, and bis(pentacarbonylmanganese), Mn2(CO)10. The SF contributions at representative bond critical points (bcp's) have been evaluated from both the primary and the MM density, the latter having been computed from a set of theoretical structure factors for ideal crystals of non-interacting molecules. In the case of Mn2(CO)10, the SF contributions have been also compared to those obtained from a set of experimental structure factors9 to reconstruct the MM density (r). We show that the MM results are in general consistent with the theoretical ones, as they should be, with the SF being a quite interesting tool to provide chemical insight, whilst minimizing the MM bias on the primary density. Conversely, significant differences emerge for the SF contributions at the Mn–Mn bcp in Mn2(CO)10, where we demonstrate that the discrepancies between the theoretical and the experimental SF contributions arises from the MM inadequacies. The SF could be a valuable tool to check and improve the quality of the MM currently adopted in experimental studies of organometallic compounds.