Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and nonhydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydrocarbon rubrene (orthorhombic 5,6,11,12-tetraphenyltetracene), a cocrystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HARADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Elementhydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.

There is a great variety of bond analysis tools that aim to extract information on the bonding situation from the molecular wavefunction. Because none of these can fully describe bonding in all of its complexity, it is necessary to regard a balanced selection of complementary analysis methods to obtain a reliable chemical conclusion. This is, however, not a feasible approach in most studies because it is a time-consuming procedure. Therefore, we provide the first comprehensive comparison of modern bonding analysis methods to reveal their informative value. The element-oxygen bond of neutral H XOH model compounds (X=Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl) is investigated with a selection of different bond analysis tools, which may be assigned into three different categories: i) real space bonding indicators (quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the Raub-Jansen index), ii) orbital-based descriptors (natural bond orbitals (NBO), natural resonance theory (NRT), and valence bond (VB) calculations), and iii) energy analysis methods (energy decomposition analysis (EDA) and the Q-analysis). Besides gaining a deep insight into the nature of the element-oxygen bond across the periodic table, this systematic investigation allows us to get an impression on how well these tools complement each other. Ionic, highly polarized, polarized covalent, and charge-shift bonds are discerned from each other.

Covalency and ionicity are orthogonal rather than antipodal concepts. We demonstrate for the case of siloxane systems [R Si-(O-SiR ) -O-SiR ] that both covalency and ionicity of the Si-O bonds impact on the basicity of the Si-O-Si linkage. The relationship between the siloxane basicity and the Si-O bond character has been under debate since previous studies have presented conflicting explanations. It has been shown with natural bond orbital methods that increased hyperconjugative interactions of LP(O)→σ*(Si-R) type, that is, increased orbital overlap and hence covalency, are responsible for the low siloxane basicity at large Si-O-Si angles. On the other hand, increased ionicity towards larger Si-O-Si angles has been revealed with real-space bonding indicators. To resolve this ostensible contradiction, we perform a complementary bonding analysis, which combines orbital-space, real-space, and bond-index considerations. We analyze the isolated disiloxane molecule H SiOSiH with varying Si-O-Si angles, and n-membered cyclic siloxane systems Si H O(CH ) . All methods from quite different realms show that both covalent and ionic interactions increase simultaneously towards larger Si-O-Si angles. In addition, we present highly accurate absolute hydrogen-bond interaction energies of the investigated siloxane molecules with water and silanol as donors. It is found that intermolecular hydrogen bonding is significant at small Si-O-Si angles and weakens as the Si-O-Si angle increases until no stable hydrogen-bond complexes are obtained beyond φ =168°, angles typically displayed by minerals or polymers. The maximum hydrogen-bond interaction energy, which is obtained at an angle of 105°, is 11.05 kJ mol for the siloxane-water complex and 18.40 kJ mol for the siloxane-silanol complex.

The second-order nucleophilic substitution (S 2) reaction at a silicon atom is scrutinized by means of snapshots along a pseudoreaction coordinate. Phosphine and fluoride represent both attacking and leaving groups in the modeled S 2 reaction. In the experimentally obtained 5-diphenylphosphinoacenaphth-6-yl-dimethylfluorosilane, 1, the phosphine and fluorosilane moieties are forced into immediate proximity through an acenaphthyl scaffold, that is, they exhibit peri interactions that serve as the model of the reactant ion-molecule complex and starting point for a theoretical potential-energy surface (PES) scan. Upon dissociation of fluoride, the experimentally obtained silylphosphonium cation 2 serves as a model of the product and end point of the PES scan. The pseudoreaction pathway is studied using geometric, energetic, spectroscopic, molecular-orbital, and topological real-space bonding indicators. It becomes evident that it is crucial to combine such methods to understand the pseudoreaction because they reveal different aspects based on different sensitivity to dispersive, electrostatic, and polar-covalent contributions to bonding, as shown by the reduced density gradient analysis. For example, atoms-in-molecules theory describes a late topological catastrophe, whereas the electron localizability indicator describes an early concerted reaction and natural resonance theory describes a more gradual change of properties. This case study encourages the use of a well-balanced toolbox equipped with complementary methods to emphasize different aspects of bonding.

There are many examples of atoms in molecules that violate Lewis’ octet rule, because they have more than four electron pairs assigned to their valence. These atoms are referred to as hypervalent. However, hypervalency may be regarded as an artifact arising from Lewis’ description of molecules, which is based on the assumption that electrons are localized in two‐center two‐electron bonds and lone pairs. In the present paper, the isoelectronic phosphate (PO43−), sulfate (SO42−) and perchlorate (ClO4−) anions were examined with respect to the concept of hypervalency. Lewis formulas containing a hypervalent central atom exist for all three anions. Based on X‐ray wavefunction refinements of high‐resolution X‐ray diffraction data of representative crystal structures (MgNH4PO4⋅6 H2O, Li2SO4⋅H2O, and KClO4), complementary bonding analyses were performed. In this way, experimental information from the new field of quantum crystallography validate long‐known facts, or refute long‐standing misunderstandings. It is shown that the P−O and S−O bonds are highly polarized covalent bonds and, thus, the increase in the valence population following three‐center four‐electron bonding is not sufficient to yield hypervalent phosphorus or sulfur atoms, respectively. However, for the highly covalent Cl−O bond, most bonding indicators imply a hypervalent chlorine atom.