Revealing electron delocalization through the Source Function

The Source Function (SF) [1,2] enables one to view chemical bonding and other chemical paradigms under a new perspective and using only information from the electron density observable, rho, and its derivatives. Being completely independent from the tools used to get rho, the SF represents a very useful descriptor, able in many cases to bridge the gap between the rich information one gains from an ab-initio wavefunction of an ideal system and that, quite often more limited, but referred to a real system, obtained from an experimental rho derived from X-ray diffraction data. The potential uses of the SF are, however, yet not fully explored. In this lecture we discuss our recent work where the question of whether the SF is or is not capable to reveal electron delocalization has been carefully addressed [3,4]. Question arose because of a recent claim [5] according to which "pi-electron delocalization in the benzene ring is not manifest in the SF when the reference point (rp) - the point at which the atomic sources for its density are calculated - is taken at the C-C bond critical point (bcp)". Reasoning behind this statement was the null contribution from pi-molecular orbitals (MOs) to rho in their nodal plane. In all inspected cases and regardless of the theoretical or experimental derivation of rho, the answer to the question referred to above seems instead to be convincingly positive. Such a SF ability to reveal electron delocalization is independent from a sigma and pi separation of rho, since the SF tool was applied to the total rho. This observation is important in view of the possibility to recover electron delocalization effects using both rho's derived experimentally (hence without sigma and pi separation being allowed) and rho's where the departure from symmetry inhibits a proper separation of sigma and pi contributions. Using a MO approach, the sigma and pi contributions to the SF values can also be revealed and quantified. [1]Bader, R.F.W., Gatti, C. Chem. Phys. Lett. 1998, 287, 233-238. [2] Gatti, C., Cargnoni, F., Bertini, L. J Comput Chem 2003, 24, 422-436. [3]Gatti, C. Struct. Bond. 2011, 1 $DOI: 10.1007/430_2010_31 2. [4]Monza, E., Gatti, C., Lo Presti, L., Ortoleva, E. J. Phys. Chem. A 2011, 115, 12864-12878. [5]Farrugia, L.J., P. Macchi, J. Phys. Chem. 2009, A113, 10058-10067.