Revealing electron conjugation through an observable

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, ρ, and its derivatives. Being completely independent from the tools used to get ρ, the SF represents a very useful descriptor, able in some 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 ρ derived from X-ray diffraction data. The potential uses of the SF are, however, yet not fully explored. In a preliminary work, we addressed the question of whether the SF is or is not capable to reveal electron conjugation [3]. Question arose because of a recent claim [4] according to which “π-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 is the null contribution from π molecular orbitals (MOs) to ρ in their nodal plane. However, since σ- and π-distributions are not independent, but self-consistently interrelated, we conjectured that some, albeit small, effect of electron conjugation could also be manifest when the rp lies in the π-nodal plane, even though π-orbitals do not obviously yield direct contributions to ρ in that plane. Results on a series of increasingly π-conjugated systems demonstrate that this is actually the case. By looking at the C-C bcp electron density for the shortest bond(s) in cyclohexene, cyclohexadiene, benzene, i.e. those bonds with largest double-bond character, one observes that both the SF and the SF% contributions of the C atoms other than those directly involved in such a bond increase with decreasing double bond character and electron localization of the bond. The enhanced S% value then becomes largely more evident when analysed using rps for which the effect of π-electron conjugation takes place directly through π-electron distribution rather than, indirectly, through σ-π electron interdependency. In this work, the analysis is extended to more complex systems, formed by more than one ring, with fully conjugated or partially interrupted sequence of formal double-bonds and with planar or non planar geometry. In the case of benzene, the analysis is also performed on a ρ derived through multipole refinement of a set of X-ray diffraction data taken on a benzene molecular crystal. In the inspected cases and regardless of the theoretical or experimental origin of ρ, the SF reveals capable to detect electron conjugation. Such an ability is independent from a σ and π separation of ρ, since the SF tool was applied to the total ρ. This observation is important in view of the possibility to recover electron conjugation effects using both ρ’s derived experimentally (hence without σ and π separation being allowed) and ρ’s where the departure from symmetry inhibits a proper separation of σ and π contributions. Using a MO approach, the σ and π contributions to the SF values can also be revealed and quantified. [1] R.F.W. Bader, C. Gatti, Chem Phys Lett 1998, 287, 233-238. [2] C. Gatti, F. Cargnoni et al., J Comput Chem 2003 24, 422-436. [3] C. Gatti, Struct Bond 2011 [4] L.J. Farrugia, P. Macchi, J. Phys. Chem. 2009, A113, 10058-10067.