Source Function applied to experimental densities reveals subtle electron-delocalization effects and appraises their transferability properties in crystals

Abstract

The Source Function (SF), introduced in 1998 by Richard Bader and Carlo Gatti, is succinctly reviewed and a number of paradigmatic applications to in vacuo and crystal systems are illustrated to exemplify how the SF may be used to discuss chemical bonding in both conventional and highly challenging cases. The SF enables the electron density to be seen at a point determined by source contributions from the atoms or a group of atoms of a system, and it is therefore well linked to the chemist's awareness that any local property and chemical behaviour is to some degree influenced by all the remaining parts of a system. The key and captivating feature of the SF is that its evaluation requires only knowledge of the electron density (ED) of a system, thereby enabling a comparison of ab initio and X-ray diffraction derived electron density properties on a common and rigorous basis. The capability of the SF to detect electron-delocalization effects and to quantify their degree of transferability is systematically explored in this paper through the analysis and comparison of experimentally X-ray derived Source Function patterns in benzene, naphthalene and (±)-8'-benzhydrylideneamino-1,1'-binaphthyl-2-ol (BAB) molecular crystals. It is shown that the SF tool recovers the characteristic SF percentage patterns caused by π-electron conjugation in the first two paradigmatic aromatic molecules in almost perfect quantitative agreement with those obtained from ab initio periodic calculations. Moreover, the effect of chemical substitution on the degree of transferability of such patterns to the benzene- and naphthalene-like moieties of BAB is neatly shown and quantified by the observed systematic deviations, relative to benzene and naphthalene, of only those SF contributions from the substituted C atoms. Finally, the capability of the SF to reveal electron-delocalization effects is challenged by using a promolecule density, rather than the proper quantum mechanical density, to determine the changes in SF patterns along the cyclohexene, 1,3-cyclohexadiene and benzene molecule series. It is shown that, differently from the proper quantum density, the promolecular density is unable to reproduce the SF trends anticipated by the increase of electron delocalization along the series, therefore ruling out the geometrical effect as being the only cause for the observed SF patterns changes.

Electron Density Studies in Materials Research

“…[1d, e, 24] However,t heser equire information about either the first or second order reduced density matrix, and are thus not experimentally accessible, so they will not be considered in detail in this review.N evertheless, results based on the source function have been shownt oc orrelate well with those based on density matrices, so it is possible to retrieve importanti nformation about delocalization based purely on the ED. [25]…”

An Electron Density Source‐Function Study of DNA Base Pairs in Their Neutral and Ionized Ground States†

“…The source function (SF) introduces a novel perspective and one rich of chemical insight on how the electron density (ED) of a system originates . In particular, it shows, within a cause–effect view, how the various atoms or groups of atoms in the system contribute to determine the electron density at a given point of the system.…”

“…In particular, it shows, within a cause–effect view, how the various atoms or groups of atoms in the system contribute to determine the electron density at a given point of the system. If such point is a BCP, assumed as the most representative electron density location for a given chemical interaction, the pattern of the atomic SF contributions provides a visible representation of the more or less delocalized nature of the interaction …”

“…Though not explored here, it is worth mentioning that the SF analysis represents a natural choice for comparing, on the same grounds, results from studies of intermolecular interactions using experimentally and theoretically derived electron densities . In fact, SF values are also amenable to experimental determination provided an accurate ∇ 2 ρ distribution derived from high‐quality single‐crystal X‐ray diffraction intensity data is available [eqs. ].…”

“…This present work explores the effect of ionization on the hydrogen bonding interactions in the canonical (WC) base pairs using the tools of Bader's quantum theory of atoms in molecules (QTAIM) in conjunction with the analysis of the Bader–Gatti source function …”