Ions in Crystals: The Topology of the Electron Density in Ionic Materials. 4. The Danburite (CaB2Si2O8) Case and the Occurrence of Oxide−Oxide Bond Paths in Crystals

Bader's Topological Bond Path Does Not Necessarily Indicate Stabilizing Interaction-Proof Studies Based on the Ng@[3n]cyclophane Endohedral Complexes

According to Bader's quantum theory of atoms in molecules (QTAIM), the simultaneous presence of a bond path and the corresponding bond critical point between any two atoms is both a necessary and sufficient condition for the atoms to be bonded to one another. In principle, this means that this pair of atoms should make a stabilizing contribution to the molecular system. However, the multitude of so-called counterintuitive bond paths strongly suggests that this statement is not necessarily true. Particularly 'troublesome' are endohedral complexes, in which encapsulation-enforced proximity between the trapped guest (e.g., an atom) and the host's cage system usually 'produces' many counterintuitive bond paths. In the author's opinion, the best evidence to demonstrate the repulsive nature of the intra-cage guest⋯host interaction is the use of some trapping systems containing small escape channels and then showing that the initially trapped entity spontaneously escapes outside the host's cage during geometry optimization of the initially built guest@host endohedral complex. For this purpose, a group of 24 Ng@[3n]cyclophane (3≤n≤6) endohedral complexes is used. As a result, arguments are presented showing that Bader's topological bond path does not necessarily indicate a stabilizing interaction.

Determining Repulsion in Cyclophane Cages

Superphane, i.e., [2.2.2.2.2.2](1,2,3,4,5,6)cyclophane, is a very convenient molecule in studying the nature of guest⋯host interactions in endohedral complexes. Nevertheless, the presence of as many as six ethylene bridges in the superphane molecule makes it practically impossible for the trapped entity to escape out of the superphane cage. Thus, in this article, I have implemented the idea of using the superphane derivatives with a reduced number of ethylene linkers, which leads to the [2n] cyclophanes where n<6. Seven such cyclophanes are then allowed to form endohedral complexes with noble gas (Ng) atoms (He, Ne, Ar, Kr). It is shown that in the vast majority of cases, the initially trapped Ng atom spontaneously escapes from the cyclophane cage, creating an exohedral complex. This is the best proof that the Ng⋯cyclophane interaction in endohedral complexes is indeed highly repulsive, i.e., destabilizing. Apart from the ‘sealed’ superphane molecule, endohedral complexes are only formed in the case of the smallest He atom. However, it has been shown that in these cases, the Ng⋯cyclophane interaction inside the cyclophane cage is nonbonding, i.e., repulsive. This highly energetically unfavorable effect causes the cyclophane molecule to ‘swell’.

Tracing electron density changes in langbeinite under pressure

Pressure is well known to dramatically alter physical properties and chemical behaviour of materials, much of which is due to the changes in chemical bonding that accompany compression. Though it is relatively easy to comprehend this correlation in the discontinuous compression regime, where phase transformations take place, understanding of the more subtle continuous compression effects is a far greater challenge, requiring insight into the finest details of electron density redistribution. In this study, a detailed examination of quantitative electron density redistribution in the mineral langbeinite was conducted at high pressure. Langbeinite is a potassium magnesium sulfate mineral with the chemical formula [K2Mg2(SO4)3], and crystallizes in the isometric tetartoidal (cubic) system. The mineral is an ore of potassium, occurs in marine evaporite deposits in association with carnallite, halite and sylvite, and gives its name to the langbeinites, a family of substances with the same cubic structure, a tetrahedral anion, and large and small cations. Single-crystal X-ray diffraction data for langbeinite have been collected at ambient pressure and at 1 GPa using a combination of in-house and synchrotron techniques. Experiments were complemented by theoretical calculations within the pressure range up to 40 GPa. On the basis of changes in structural and thermal parameters, all ions in the langbeinite structure can be grouped into 'soft' (potassium cations and oxygens) and 'hard' (sulfur and magnesium). This analysis emphasizes the importance of atomic basins as a convenient tool to analyse the redistribution of electron density under external stimuli such as pressure or temperature. Gradual reduction of completeness of experimental data accompanying compression did not significantly reduce the quality of structural, electronic and thermal parameters obtained in experimental quantitative charge density analysis.

Does the Presence of a Bond Path Really Mean Interatomic Stabilization? The Case of the Ng@Superphane (Ng = He, Ne, Ar, and Kr) Endohedral Complexes

Using a fairly structurally flexible and, therefore, very suitable for this type of research, superphane molecule, we demonstrate that the inclusion of a noble gas atom (Ng = He, Ne, Ar, and Kr) inside it and, thus, the formation of the Ng@superphane endohedral complex, leads to its ‘swelling’. Positive values of both the binding and strain energies prove that encapsulation and in turn ‘swelling’ of the superphane molecule is energetically unfavorable and that the Ng⋯C interactions in the interior of the cage are destabilizing, i.e., repulsive. Additionally, negative Mayer Bond Orders indicate the antibonding nature of Ng⋯C contacts. This result in combination with the observed Ng⋯C bond paths shows that the presence of a bond path in the molecular graph does not necessarily prove interatomic stabilization. It is shown that the obtained conclusions do not depend on the computational methodology, i.e., the method and the basis set used. However, on the contrary, the number of bond paths may depend on the methodology. This is yet another disadvantageous finding that does not favor the treatment of bond paths on molecular graphs as indicators of chemical bonds. The Kr@superphane endohedral complex features one of the longest C–C bonds ever reported (1.753 Å).

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Experimental charge density of grossular under pressure - a feasibility study

X-ray diffraction studies of crystals under pressure and quantitative experimental charge density analysis are among the most demanding types of crystallographic research. A successful feasibility study of the electron density in the mineral grossular under 1 GPa pressure conducted at the CRISTAL beamline at the SOLEIL synchrotron is presented in this work. A single crystal was placed in a diamond anvil cell, but owing to its special design (wide opening angle), short synchrotron wavelength and the high symmetry of the crystal, data with high completeness and high resolution were collected. This allowed refinement of a full multipole model of experimental electron distribution. Results are consistent with the benchmark measurement conducted without a diamond-anvil cell and also with the literature describing investigations of similar structures. Results of theoretical calculations of electron density distribution on the basis of dynamic structure factors mimic experimental findings very well. Such studies allow for laboratory simulations of processes which take place in the Earth's mantle.

On the Uselessness of Bond Paths Linking Distant Atoms and on the Violation of the Concept of Privileged Exchange Channels

We refer to frequently used determinants suggesting dominant interactions between distant atoms in various dimers. First of all, we show, against the still-prevailling opinion, that, in general, bond paths have nothing in common with dominant intermolecular interactions and therefore they are useless in such cases. Quite the contrary, reliable information about dominant intermolecular interactions can be obtained by means of electrostatic potential maps, which very convincingly explain mutual orientation of molecules in a dimer. For the first time, numerous examples of interactions that violate both the concept of privileged exchange channels proposed by Pendás and his collaborators as well as inequalities obtained by Tognetti and Joubert for the β parameter related to secondary interactions are presented. The possible cause of this violation is suggested. We also show that the so-called counterintuitive bond paths result from quite natural behavior of the electron density gradient vector, i. e. searching for those areas of space that are characterized by large values of electron density or the most expanded its distributions.

Bond paths between distant atoms do not necessarily indicate dominant interactions

The goal of the article is to revive discussion on the interpretation of bond paths linking distant atoms, particularly tracing weak interactions in dimers. According to the Pendás' concept of privileged exchange channel, a bond path is formed between this pair of competing atoms, which is associated with larger value of the exchange energy. We point out that, due to the short-range nature of the exchange energy, bond paths linking distant atoms clearly become doubtful indicators of dominant intermolecular interactions, particularly if some other characteristics (geometric, spectroscopic, based on electrostatic parameters, etc.) indicate other intermolecular interactions as dominant. Several such cases are thoroughly investigated. We show that electrostatic parameters are much more reliable indicators of dominant intermolecular interactions than bond paths. Then, we pay attention that the presence of ("unexpected", i.e., not necessarily indicating dominant intermolecular interactions) bond paths between pairs of atoms featuring highly expanded charge distributions can be easily explained by visual exploration of isodensity contour plots. As always pointing in the direction of the steepest increase, the gradient vector of the electron density favors areas of its high values gaining higher exchange energy, yet being blind to highly electron deficient areas nearby, which, however, can quite often be involved in dominant intermolecular interactions as strongly suggested by many other bonding analysis. We also suggest that an interatomic component of Hellmann-Feynman force would most likely be the most reliable indicator of attractive or repulsive character of individual interatomic interaction. © 2018 Wiley Periodicals, Inc.

A bond path and an attractive Ehrenfest force do not necessarily indicate bonding interactions: case study on M2X2 (M = Li, Na, K; X = H, OH, F, Cl)

Interactions in dimers of model alkali metal derivatives M(2)X(2) (M = Li or Na or K; X = H or F, Cl, OH) are studied in the frame of the quantum theory of atoms in molecules (QTAIM) using the interacting quantum atoms approach (IQA). Contrary to opinion prevalent in QTAIM studies, the interaction between two anions linked by a bond path is demonstrated to be strongly repulsive. One may therefore say that a bond path does not necessarily indicate bonding interactions. The interactions between two anions or two cations that are not linked by a bond path are also strongly repulsive. The repulsive anion-anion and cation-cation interactions are outweighed by much stronger attractive anion-cation interactions, and the model molecules are therefore in a stable state. The attractive Ehrenfest forces (calculated in the frame of the QTAIM) acting across interatomic surfaces shared by anions in the dimers do not reflect the repulsive interactions between anions. Probable reasons of this disagreement are discussed. The force exerted on the nucleus and the electrons of a particular atom by the nucleus and the electrons of any another atom in question is proposed. It is assumed that this force unambiguously exposes whether basins of two atoms are attracted or repelled by each other in a polyatomic molecule.

Are halide...halide contacts a feature of rock-salts only?

The electron density distribution function in the crystalline hydroxylammonium chloride obtained using the high-resolution X-ray diffraction technique was analyzed by means of Bader's "atoms in molecule" theory. The anion-anion interactions in the crystal of this ionic material were examined and the energy of the Cl-...Cl- contacts was estimated on the basis of the experimental data. The results obtained coincide well with the theoretical calculations and the X-ray diffraction data for the rock-salts. The existence of such type of interactions was shown to be not the unique feature of inorganic salts with point charge cations.