Source function applied to experimental densities reveals subtle electron delocalization effects and appraises their transferability properties in crystals
The Source Function (SF) [1] enables the electron density (ED) to be seen at a point as determined by source contributions from the atoms of a system, and it is therefore well linked to the chemist\u2019s awareness that any local property and chemical behaviour is to some degree influenced by all the remaining parts of a system [1-3]. The key feature of the SF is that its evaluation requires only knowledge of the ED of a system, enabling a comparison of ab initio and X-ray diffraction derived ED properties on a common, rigorous basis. We here apply the SF descriptor to X-ray derived EDs as a mean to reveal electron-delocalization effects (EDEs) in crystals. Use of the SF to detect them has been firmly assessed for isolated molecules and for theoretically-derived EDs [2,4-5], but extending to crystals and experimental EDs, although being reported at two conferences [6-7] and in two papers discussing heteroaromaticity in a benzothiazol-substituted phosphane [8] or antiaromaticity in cyclopentadienone derivatives [9] needs to be fully demonstrated. Still unanswered questions are whether the EDs from X-ray data may be accurate enough to reveal the subtle features caused by electron pairing and whether these are not only detectable, but also reproducible and transferable, whenever appropriate. To provide an answer we analyse the experimental SF patterns in benzene (BZ), naphthalene (NT) and (+/-)-8\u2019-benzhydrylideneamino-1,1\u2019-binaphtyl-2-ol (BAB) molecular crystals. We find that the SF tool recovers the characteristic SF% patterns caused by pi-electron conjugation in the first two paradigmatic aromatic molecules in almost perfect quantitative accord with those from ab initio periodic calculations [10]. Moreover, the effect of chemical substitution on the transferability of such patterns to the BZ- and NT-like moieties of BAB is neatly spotted by the observed systematic deviations, relative to BZ and NT, of only those SF contributions from the substituted C atoms [10]. The capability of the SF to reveal EDEs by using a promolecule ED (PED), rather than the \u201ctrue\u201d ED, is then tested; the PED seems unable to reproduce the SF trends anticipated by the increase of electron delocalization [10].
The SF has wider applications than those related to the nature of chemical bonds in more or less conventional situations [2-3]. Detection of EDEs is one such new direction, another being the extension of the SF machinery to retrieve the atomic sources of the spin ED [5,11].
Acknowledgements
Prof. Sine Larsen and Prof. Mark Spackman are both warmly thanked for providing us with, respectively, the 135 K X-ray diffraction dataset of naphthalene crystal and the 110 K X-ray diffraction data set of benzene. The Danish National Research Foundation is also thanked for partial funding of this work through the Center for Materials Crystallography (DNRF93).
References
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