The Significance of Ionic Bonding in Sulfur Dioxide: Bond Orders from X‐ray Diffraction Data

Abstract

Lewis diagrams and the octet rule [1] are central concepts in chemistry. Hypervalent molecules break the octet rule because they contain atoms with more than four electron pairs in their valence shell. [2] To describe them with the Lewis model requires hybridization schemes involving d orbitals (sp 3 d or sp 3 d 2 hybrids). [3, 4] The problem is that the formation of these hybrid orbitals requires large promotion energies. [5] Therefore, the significance of ionic resonance diagrams, which obviate the need for hypervalency, has long been discussed. [4] In this context, the electronic structure of SO 2 has been controversial. SO 2 can be described as a hypervalent molecule (Figure 1, left). Apart from d-orbital hybridization, multiple covalent bonding in SO 2 may be explained by three-center p pp p interactions of the sulfur 3p p orbital with non-bonding oxygen p p electrons (this interpretation goes back to Ref. [6]).However, other non-hypervalent ionic resonance structures can be formulated that preserve the octet rule ( Figure 1).The neutral Lewis structure is thought to be dominant, as the SÀO bond length in SO 2 is shorter than that in sulfur monoxide, SO (1.4299(3) in SO 2 from this study, compared to 1.481 for SO [7] ). The bond dissociation energy is also higher in SO 2 than in SO (547.3(8) kJ mol À1 vs. 517.1(8) kJ mol À1 [8] ). Furthermore, O 3 and O 2 , which are valence-isoelectronic with SO 2 and SO, have no available d orbitals, so they cannot be hypervalent, implying bond orders no higher than 1.5 and 2.0, respectively. This is consistent with the fact that the O À O distance in O 3 (1.2717(2) [9] ) is longer than in O 2 (1.15(8) , [10] 1.207 [7] ), in direct contrast with SO 2 relative to SO. This could support the notion that multiple covalent bonding is significant in SO 2 . Indeed, a large number of textbooks [11,12] adhere to this conclusion; for example, in ref. [12] it is stated that the S À O bond order is "at least 2".The simple empirical analysis above is in sharp contrast to the fact that computational studies have found significant ionic contributions to the SÀO bond, and very little sulfur dorbital participation. [13] Today, there is agreement among theoreticians that the role of d orbitals in the formation of bonds involving second and higher row elements is predominantly one of polarization functions, not of hybridization involving d orbitals. [5,14] In fact, the shorter and stronger bonds in SO 2 compared to SO (which is formally a double bond) support the conclusion that there are significant noncovalent contributions to the bonding. Indeed, calculations employing the electron localization function have shown that the polarity of a bond only depends on the electronegativity differences of the bonded atoms, so that molecules formerly classified as being hypervalent can be readily described with various ionic resonance structures. [15] So from a computational viewpoint, hypervalency is avoided by introducing ionic bonds.Experimentally, it has hitherto been difficult to obtain i...

Hirshfeld Atom Refinement

“…In the present form, the term X-ray wavefunction refinement (XWR) refers to the subsequent execution of an iterative HAR, as introduced in this study, and an X-ray constrained wavefunction fitting procedure, introduced earlier by Jayatilaka (1998) and Jayatilaka & Grimwood (2001). The idea of XWR was first introduced by Grabowsky et al (2012), and put into context with other methods by Grabowsky et al (2013) and Schmøkel et al (2013). The present XWR protocol was used by Chęciń ska et al (2013) and Zakrzewska et al (2013), but could also be understood as the first cycle of a future iterative XWR.…”

“…(iii) The data sets of urea (Birkedal et al, 2004) and benzene (Bü rgi et al, 2002), as well as all other data sets of compounds that have been subjected to HAR in different studies for different purposes Chęciń ska et al, 2013;Grabowsky et al, 2012), are highresolution data sets (d < 0.5 Å ) originally collected for experimental electron density studies. It is unclear to what extent the use of lower-resolution data affects the accuracy of hydrogen and non-hydrogen parameters within the framework of HAR.…”

New Look on 3-Hydroxyiminoflavanone and Its Palladium(II) Complex: Crystallographic and Spectroscopic Studies, Theoretical Calculations and Cytotoxic Activity

“…While two models of electron-density distribution were considered for compound 1, i.e., an experimental model obtained from X-ray wavefunction refinement (1-XWR) [22] and a theoretical one derived by DFT-geometry optimization (1-OPT), only a theoretical electron-density model was available for compound 2. Table 3 presents the topological properties of the bonds derived from QTAIM space partitioning and a set of ELI-D derived properties from the models of 1 and 2.…”

“…In the fitting procedure, the obtained wavefunction was constrained to the experimental data by introducing the Lagrange parameter; final λ = 0.10. Both steps of X-ray wavefunction refinement [22] (XWR = HAR + XCW) were performed using blyp/cc-pVTZ [44][45][46] level of theory within the Tonto [47] software package. In order to simulate the effect of the crystal environment, a cluster of charges and dipoles around the central molecule was introduced: all molecules with at least one atom within a radius of 8 Å around the central molecule were included in the surrounding cluster.…”

Structure, charge density and energetic features of quinoline derivatives

“…The derivatives differ in the substituent at position 8 which is either a halogen atom (Cl, Br, I) or -S-Ph moiety. Highresolution X-ray measurements were performed in each case, resulting in experimental data of varying quality, possibly characterized by the presence of anharmonic motion, which makes them suitable for verifying capabilities of two different charge density models compared in this work.The refinement methods applied during X-ray data processing were: the multipole refinement (MR) in Hansen and Coppens formalism [1] and the X-ray wavefunction refinement (XWR) [2] implementing Hirshfeld partition of ED. The latter technique includes two steps: (a) Hirshfeld atom refinement (HAR) being only structural refinement and (b) X-ray constrained wavefunction fitting introducing experimental contribution to ED.…”