The Source Function

The electron density rho at any point r within a molecule may be viewed as consisting of contributions from a local source (LS) operating at all other points . When the LS is integrated over regions omega satisfying the QTAIM definition of an atom in a molecule, rho(r) may be equated to a sum of atomic contributions S(r;omega), each of which is termed as the source function (SF) from the atom omega to rho(r). Such a decomposition enables one to view the properties of rho from a new perspective and establishes the source function (SF) as an interesting tool to provide chemical insight. A number of paradigmatic SF applications to the study of chemical bonding will be discussed in this lecture. In particular, how the SF enables one to markedly distinguish hydrogen bonds of different strengths or to afford a description of the metal-metal (M-M) bonding, in d-block organometallic compounds, which is closely related to that provided by the localization and delocalization indices. This agreement holds true even when the M-M bond is lacking and the internuclear M-M midpoint is taken as a reference point. Use of the local form of the SF unveils interesting differences, according to whether the system is metal-metal "bonded" or not, in the relative contributions from the various molecular regions to the electron density at the M-M midpoint. Conversely, most of the topological indices conventionally adopted to describe M-M bonds seem to fail in reproducing the chemical trends observed in these compounds.