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.

The CH···HC interaction in biphenyl is a delocalized, molecular-wide and entirely non-classical interaction: Results from FALDI analysis.

In this study we aim to determine the origin of the electron density describing a CH···HC interaction in planar and twisted conformers of biphenyl. In order to achieve this, the fragment, atomic, localized, delocalized, intra- and inter-atomic (FALDI) decomposition scheme was utilized to decompose the density in the inter-nuclear region between the ortho-hydrogens in both conformers. Importantly, the structural integrity, hence also topological properties, were fully preserved as no 'artificial' partitioning of molecules was implemented. FALDI-based qualitative and quantitative analysis revealed that the majority of electron density arises from two, non-classical and non-local effects: strong overlap of ortho CH σ-bonds, and long-range electron delocalization between the phenyl rings and ortho carbons and hydrogens. These effects resulted in a delocalized electron channel, that is, a density bridge or a bond path in a QTAIM terminology, linking the H-atoms in the planar conformer. The same effects and phenomena are present in both conformers of biphenyl. We show that the CH···HC interaction is a molecular-wide event due to large and long-range electron delocalization, and caution against approaches that investigate CH···HC interactions without fully taking into account the remainder of the molecule.

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 ß 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.

FALDI-based criterion for and the origin of an electron density bridge with an associated (3,-1) critical point on Bader's molecular graph.

The total electron density (ED) along the λ2 -eigenvector is decomposed into contributions which either facilitate or hinder the presence of an electron density bridge (DB, often called an atomic interaction line or a bond path). Our FALDI-based approach explains a DB presence as a result of a dominating rate of change of facilitating factors relative to the rate of change of hindering factors; a novel and universal criterion for a DB presence is, thus, proposed. Importantly, facilitating factors show, in absolute terms, a concentration of ED in the internuclear region as commonly observed for most chemical bonds, whereas hindering factors show a depletion of ED in the internuclear region. We test our approach on four intramolecular interactions, namely (i) an attractive classical H-bond, (ii) a repulsive O⋅⋅⋅O interaction, (iii) an attractive Cl⋅⋅⋅Cl interaction, and (iv) an attractive CH⋅⋅⋅HC interaction. (Dis)appearance of a DB is (i) shown to be due to a "small" change in molecular environment and (ii) qualitatively and quantitatively linked with specific atoms and atom-pairs. The protocol described is equally applicable (a) to any internuclear region, (b) regardless of what kind of interaction (attractive/repulsive) atoms are involved in, (c) at any level of theory used to compute the molecular structure and corresponding wavefunction, and (d) equilibrium or nonequilibrium structures. Finally, we argue for a paradigm shift in the description of chemical interactions, from the ED perspective, in favor of a multicenter rather than diatomic approach in interpreting ED distributions in internuclear regions. © 2018 Wiley Periodicals, Inc.

A comparison of energetic criteria to probe the stabilizing interaction resulting from a bond path between congested atoms.

Four energetic criteria, all rooted in the partitioning of a molecule into atomic basins based on the properties of the electron density, are compared and correlated with the presence of a bond path between two nonbonded atoms in a series of sterically crowded derivatives of the same tetracyclododecane molecule. It was found that there is no correlation between the selected energetic criteria and the existence of a bond path between the congested atoms, nor with the existence of Ehrenfest force, virial, or Coulomb potential paths between those atoms.

Hydride-Triel Bonds.

In this article, we present the results of our comprehensive studies of 72 dimers of the R3XXH⋯YR3Y type (X = Si, Ge; Y = B, Al, Ga; RX = H, Cl, Me; RY = H, F, Cl, Me) and featuring hydride-triel bonds (i.e., charge-inverted hydrogen bonds). Influence of X and Y atoms as well as RX and RY substituents on various properties of these dimers is investigated in detail. In particular the strength of the H⋯Y hydride-triel bonds is paid a close attention and it is shown that hydride-triel bonds can be strong enough to considerably determine structure and properties of molecular systems. In addition, properties of the investigated dimers are largely governed by the charge transfer from the Lewis base to the Lewis acid, which is particularly important if more bulky and polarizable RY and Y atoms are present in the YR3Y molecule. Several excellent linear (R2 close to 1) and exponential correlations between pairs of diverse parameters are presented. Few instances are discussed where somewhat unexpected bond paths exist between two atoms featuring partial negative charges (e.g., between hydride hydrogen and halogen and between lateral sides of two halogens) showing that in some cases a bond path prefers to link two closely spaced electron-rich atoms instead of two atoms that are expected to form a bond. © 2018 Wiley Periodicals, Inc.

The barrier to the methyl rotation in Cis-2-butene and its isomerization energy to Trans-2-butene, revisited.

We respond to the two questions posed by Weinhold, Schleyer, and McKee (WSM) in their study of cis-2-butene (Weinhold et al., J Comput Chem 2014, 35, 1499), in which they solicit explanations for the relative conformational energies of this molecule in terms of the Quantum Theory of Atoms in Molecules (QTAIM). WSM requested answers to the questions: (1) why is cis-2-butene less stable than trans-2-butene despite the presence of a hydrogen-hydrogen (H⋯H) bond path in the former but not in the latter if the H⋯H bond path is stabilizing? (2) Why is the potential well of the conformational global minimum of cis-2-butene only 0.8 kcal/mol deep when the H⋯H bonding is stabilizing by 5 kcal/mol? Both questions raised by WSM are answered by considering the changes in the energies of all atoms as a function of the rotation of one of the two methyl groups from the minimum-energy structure, which exhibits the H⋯H bond path, to the transition state, which is devoid of this bond path. It is found that the stability gained by the H⋯H bonding interaction is cancelled by the destabilization of one of the ethylenic carbon atoms which, alone, destabilizes the system by as much as 5 kcal/mol in the global minimum conformation. Further, it is found that the 1.1 kcal/mol stability of trans-2-butene with respect to the cis-isomer is driven by the considerable destabilization of the ethylenic carbons by 11 kcal/mol, while the changes in the atomic energies of the other corresponding atoms in the two isomers account for the observed different stabilities. The error introduced into QTAIM atomic energies by neglecting the virials of the forces on the nuclei for partially optimized structures is discussed.