The Source Function and the Nature of the Chemical Bond

Of late, Bader and Gatti [1] showed that the electron density ρ at any point r within a molecule may be viewed as consisting of contributions from a local source (LS) operating at all other points r' . When the LS is integrated over regions Ω satisfying the QTAIM definition of an atom in a molecule, ρ(r) may be equated to a sum of atomic contributions SF(r;Ω), each of which is termed as the source function (SF) from the atom Ω to ρ(r). Such a decomposition enables one to view the properties of the density from a new perspective and establishes the source function (SF) as a potentially interesting tool to provide chemical insight [1,2]. For instance, application of the SF to hydrogen bonded systems has shown how this function is able to markedly distinguish hydrogen bonds of different strength [2]. The SF is a measure of the relative importance of an atom's or a group's contribution to the density at any point and the bond critical points (BCP) have been generally taken as the least biased choice for points representative of bonding interactions [1,2]. Analysis of LS(BCP, r'), along a bond path, introduces further detail [3]. The SF and a number of previous exemplar applications is reviewed. We then present new results [4] on the SF analysis for a set of saturated [M2(CO)x , M= Mn, Fe, Co, Ni, x = 10, 9, 8, 7] and unsaturated [Co2(CO)x, x= 8-5] binuclear 3d metal carbonyls, and for the M2(formamidinate)4 (M=Nb, Mo, Tc, Ru, Rh, and Pd) binuclear 4d metal complexes, using ab-initio electron densities. A description of the metalmetal bonding closely related to that provided by the localization/delocalization indices is afforded. The agreement persists even when the metal-metal bond bond is lacking and the internuclear metal-metal midpoint is taken as a reference point for evaluating the SF contributions. However, use of LS(BCP, r') along the bond path, unveils interesting differences as for how the charge density originates at the metalmetal midpoint when the system is metal-metal “bonded” or not. Most of the topological indices conventionally adopted to describe metal-metal bonds fail in reproducing the expected chemical trends for the set of investigated systems, with the adimensional |Vb|/Gb ratio and the ∇ 2 ρb value being particularly inadequate. One major advantage of the SF is that it is directly applicable to electron density distributions derived from experiment. Recent progresses [5] in deriving an ambiguity-free full population analysis from the SF are also mentioned.