On the Interpretation of the Source Function

Nucleophilicity and electrophilicity of the C(sp3)–H bond: methane and ethane binary complexes with iodine

Cooperativity is key to the ability of saturated hydrocarbons to act both as nucleophilic and electrophilic centres.

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

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.

Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges

Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.

Heteroaromaticity approached by charge density investigations and electronic structure calculations

In this paper we present the results of a high-resolution single crystal X-ray diffraction experiment at 15 K on a benzothiazol-substituted phosphane and a subsequent charge density study based on multipole refinement and a topological analysis according to Bader's quantum theory of atoms in molecules. Although two valence shell charge concentrations (VSCCs) in the non-bonding region of each phosphorus and sulfur atom were found, the integration of both heteroatomic basins emphasizes charge depletion. Nevertheless they are attractive for C-H···P and C-H···S hydrogen bonding in the solid state. The nature of the P-C bonds and the question of aromaticity in the heterocycles were subject to our investigations. The ellipticities along the bonds were analysed to approach delocalization. The source function is employed to visualise atomic contributions to aromaticity. Theoretical calculations have been carried out to compute nuclear chemical shifts, induced ring currents and a variety of delocalization indices. All applied measures for delocalization point in the same direction: while heteroaromaticity is present in the benzothiazolyl substituents, the bridging P-C bonds are only involved marginally, almost preventing total conjugation of the phosphane. The charge density distributions around the phosphorus and the sulfur atoms have very similar features but turn out to be chemically very different from each other. Commonly used simplifying concepts have difficulties in providing a comprehensive view on the electronic situation in the molecule. Our results raise doubts on the validity of the common interpretation of VSCCs as one-to-one representations of Lewis lone pairs.

On the physical role of exchange in the formation of an intramolecular bond path between two electronegative atoms

In this paper, we present a detailed energetic decomposition of intramolecular O···X interactions (X being O, S, or a halogen atom) based on the interacting quantum atoms approach of Pendás and co-workers. The nature of these interactions (repulsive or attractive, more or less electrostatic) is discussed in the framework of Bader's atoms in molecules theory, a particular emphasis being put on delocalization (measured by delocalization indexes and in terms of the source function) and on the exchange contributions. Notably, the concept of exchange channels introduced by Pendás and collaborators provides means of rationalizing and predicting the presence of bond critical points, enhancing the physical meaning of bond paths.

Advances in understanding of chemical bonding: inputs from experimental and theoretical charge density analysis

The development of charge density analysis has undergone a major renaissance in the last two decades. In recent years, the characterization of bonding features associated with atoms in molecules and in crystals has been explored using high-resolution X-ray diffraction data (laboratory or synchrotron) complemented by high level ab initio theoretical calculations. The extraction of one electron topological properties, namely, electrostatic charges, dipole moment and higher moments, electrostatic potential, electric field gradients, in addition to evaluation of the local kinetic and potential energy densities, have contributed toward an understanding of the electron density distributions in molecular solids. New topological descriptors, namely, the source function (SF) and electron localization function (ELF) provide additional information as regards characterization of the topology of the electron density. In addition, delocalization indices have also been developed to account for bonding features pertinent to M-M bonds. The evaluation of these properties have contributed significantly toward the understanding of intra- and intermolecular bonding features in organic, inorganic, and biomolecules in the crystalline phase, with concomitant applications in the understanding of chemical reactivity and material/biological properties. In recent years, the focus has strongly shifted toward the understanding of structure-property relationships in organometallic complexes containing labile M-C bonds in the crystal structure with subsequent implications in catalysis. This perspective aims to highlight the major developments in electron density measurements in the past few years and provides pointers directed toward the potential use of this technique in future applications for an improved understanding of chemical bonding in systems that have been unexplored.

Meaningful structural descriptors from charge density

This paper provides a short introduction to the basics of electron density investigations. The two predominant approaches for the modelling and various interpretations of electron density distributions are presented. Their potential translations into chemical concepts are explained. The focus of the article lies on the deduction of chemical properties from charge density studies in some selected main group compounds. The relationship between the obtained numerical data and commonly accepted simple chemical concepts unfortunately is not always straightforward, and often the chemist relies on heuristic connections rather than rigorously defined ones. This article tries to demonstrate how charge density analyses can shed light on aspects of chemical bonding and reactivity resulting from the determined bonding situation. Sometimes this helps to identify misconceptions and sets the scene for new unconventional synthetic approaches.

Effect of electron-withdrawing substituents on the epoxide ring: an experimental and theoretical electron density analysis of a series of epoxide derivatives

A series of acceptor-substituted epoxide derivatives is scrutinized by means of experimental and theoretical electron-density investigations. Due to the possibility of nucleophilic ring-opening, the epoxide ring is not only a very useful functional group in organic synthesis, but acceptor-substituted epoxides are valuable building blocks for the design of protease inhibitors. Therefore, the electron-density analysis in this work focuses on two main aspects that can contribute to rational drug design: (i) the quantification of the electron-withdrawing substituent effects on the epoxide ring and (ii) the intermolecular interactions involving the epoxide ring in combination with different substituents. It can be shown that the electron-withdrawing properties of the substituents cause an elongation of the C-C bonds in the epoxide rings and the loss of electron density can be measured by an analysis of critical points, atomic charges, and the source function. The different strengths of the substituents are reflected in these properties. Covalent and electrostatic contributions to the intermolecular interactions and thus the lattice energies are depicted on different molecular surfaces.

Metal-metal and metal-ligand bonding at a QTAIM catastrophe: a combined experimental and theoretical charge density study on the alkylidyne cluster Fe3(μ-H)(μ-COMe)(CO)10

The charge density in the tri-iron methoxymethylidyne cluster Fe(3)(μ-H)(μ-COMe)(CO)(10) (1) has been studied experimentally at 100 K and by DFT calculations on the isolated molecule using the Quantum Theory of Atoms in Molecules (QTAIM). The COMe ligand acts as a nearly symmetric bridge toward two of the Fe atoms (Fe-C = 1.8554(4), 1.8608(4) Å) but with a much longer interaction to the third Fe atom, Fe-C = 2.6762(4) Å. Complex 1 provides a classic example where topological QTAIM catastrophes render an exact structure description ambiguous. While all experimental and theoretical studies agree in finding no direct metal-metal interaction for the doubly bridged Fe-Fe vector, the chemical bonding between the Fe(CO)(4) unit and the Fe(2)(μ-H)(μ-COMe)(CO)(6) moiety in terms of conventional QTAIM descriptors is much less clear. Bond paths implying direct Fe-Fe interactions and a weak interaction between the COMe ligand and the Fe(CO)(4) center are observed, depending on the experimental or theoretical density model examined. Theoretical studies using the Electron Localizability Indicator (ELI-D) suggest the metal-metal bonding is more significant, while the delocalization indices imply that both Fe-Fe bonding and Fe···C(alkylidyne) bonding are equally important. The source functions at various interfragment reference points are similar and highly delocalized. The potential-energy surface (PES) for the migration of the alkylidyne group from a μ(2) to a semi-μ(3) coordination mode has been explored by DFT calculations on 1 and the model complexes M(3)(μ-H)(μ-CH)(CO)(10) (M = Fe, 2; Ru, 3; and Os, 4). These calculations confirm a semi-μ(3) bridging mode for the alkylidyne ligand as the minimum-energy geometry for compounds 2-4 and demonstrate that, for 1, both Fe-Fe and Fe···C(alkylidyne) interactions are important in the cluster bonding. The PES between μ(2) and semi-μ(3) alkylidyne coordination for 1 is extremely soft, and the interconversion between several topological isomers is predicted to occur with almost no energy cost. Analysis of the density ρ(r) and the Laplacian of the density ▽(2)ρ(r(b)) in the methoxymethylidyne ligand is consistent with a partial π-bond character of the C-O bond, associated with an sp(2) hybridization for these atoms.

Real-space indicators for chemical bonding. Experimental and theoretical electron density studies of four deltahedral boranes

In an approach combining high-resolution X-ray diffraction at low temperatures with density functional theory calculations, two closo-borates, B(12)H(12)(2-) (1) and B(10)H(10)(2-) (2), and two arachno-boranes, B(10)H(12)L(2) [L = amine (3) or acetonitrile (4)], were analyzed by means of the atoms-in-molecules (AIM) theory and electron localizability indicator (ELI-D). The two-electron three-center (2e3c) bonds of the borane cages are investigated with the focus on real-space indicators for chemical bonding and electron delocalization. In compound 2, only two of the three expected bond critical points (bcp's) are found. However, a weakly populated ELI-D basin is found for this pair of adjacent B atoms and the delocalization index and the Source contributions are on the same order of magnitude as those for the other pairs. The opposite situation is found in the arachno-boranes, where no ELI-D basins are found for two types of B-B pairs, which, in turn, exhibit a bcp. However, again the delocalization index is on the same order of magnitude for this bonding interaction. The results show that an unambiguous real-space criterion for chemical bonding is not given yet for this class of compounds. The arachno-boranes carry a special B-B bond, which is the edge of the crown-shaped molecule. This bond is very long and extremely curved inward the B-B-B ring. Nevertheless, the corresponding bond ellipticity is quite small and the ELI-D value at the attractor position of the disynaptic valence basin is remarkably larger than those for all other B-B valence basins. Furthermore, the value of the ED is large in relation to the B-B bond length, so that only this bond type does not follow a linear relationship of the ED value at the bcp versus B-B bond distances, which is found for all other B-B bcp's. The results indicate that both 2e2c and 2e3c bonding play a distinct role in borane chemistry.