Intermolecular Covalent Interactions: Nature and Directionality

Energy decomposition analysis for excited states: an extension based on TDDFT

To enhance the understanding of photochemical reactivity and its mechanisms, it is essential to analyze bonding interactions in excited-state reactions. Such insights can aid in optimizing these reactions. This paper presents an energy decomposition analysis method for excited states (exc-EDA), integrating the ground state EDA approach by Morokuma, Ziegler and Rauk with time-dependent density functional theory (TDDFT). The methodology focuses on calculating excitation energies, particularly for the intermediate states of the EDA. We introduce two variants: the first uses non-relaxed excitation coefficients (exc-u-EDA), where the excitation coefficients of the excited fragment are used directly; the second optimizes these coefficients for the intermediate states (exc-r-EDA). Exc-EDA can be applied with various density functionals, but the accuracy depends on the functional's ability to describe the excited state properly. Smaller basis sets result in lower energy values due to fewer virtual orbitals, while larger basis sets produce consistent relative results but may involve different excited states in intermediate steps leading to artificial increase of energy terms in the EDA. The method's convergence behavior resembles that of TDDFT, with a computational cost approximately three times that of the underlying TDDFT calculation. At the current stage, the method requires that the excitation is localized on one of the fragments, but it also enables an analysis of the subsequent charge-transfer effects. Application of exc-EDA to singlet fission in pentacene clusters demonstrates its practical value, offering quantitative insights into excited-state bonding and revealing clear, intuitive trends.

"Hydridic Hydrogen-Bond Donors" Are Not Hydrogen-Bond Donors

Herein, we dismiss a recent proposal by Civiš, Hobza, and co-workers to modify the IUPAC definition of hydrogen bonds in order to expand the scope from protonic Y-Hδ+ to hydridic Y-Hδ- hydrogen-bond donor fragments [J. Am. Chem. Soc. 2023, 145, 8550]. Based on accurate Kohn-Sham molecular orbital (KS-MO) analyses, we falsify the conclusion that interactions involving protonic and hydridic hydrogens are both hydrogen bonds; they are not. Instead, our quantitative KS-MO, energy decomposition, and Voronoi deformation density analyses reveal two fundamentally different bonding mechanisms for protonic Y-Hδ+ and hydridic Y-Hδ- fragments which go with charge transfer in opposite directions. On one hand, we confirm the IUPAC definition for regular hydrogen bonds in the case of protonic Y-Hδ+ fragments. On the other hand, complexes involving Y-Hδ- fragments are, in fact, acceptors in other well-known families of Lewis-acid/base interactions, such as halogen bonds, chalcogen bonds, and pnictogen bonds. These mechanisms lead to the same spectroscopic phenomenon in both the Y-Hδ+ and Y-Hδ- fragments, that is, the redshift in the Y-H stretching frequency, which is, thus, not an exclusive indicator for hydrogen bonding.

Anion transporters based on halogen, chalcogen, and pnictogen bonds: towards biological applications

Motivated by their potential biological applications, anion receptors are increasingly explored as transmembrane transporters for anions. The vast majority of the reported anion transporters rely on hydrogen bonding to interact with the anions. However, in recent decades, halogen, chalcogen, and pnictogen bonding, collectively referred to as sigma-hole interactions, have received increasing attention. Most research efforts on these interactions have focused on crystal engineering, anion sensing, and organocatalysis. In recent years, however, these sigma-hole interactions have also been explored more widely in synthetic anion transporters. This perspective shows why synthetic transporters are promising candidates for biological applications. We provide a comprehensive review of the compounds used to transport anions across membranes, with a particular focus on how the binding atoms and molecular design affect the anion transport activity and selectivity. Few cell studies have been reported for these transporters based on sigma-hole interactions and we highlight the critical need for further biological studies on the toxicity, stability, and deliverability of these compounds to explore their full potential in biological applications, such as the treatment of cystic fibrosis.

Computational and Spectroscopic Studies on the Formation of Halogen-Bonded Complexes Between Tertiary Amines and CBr4 and Application in the Light-Mediated Amino Acid Coupling

In recent years, halogen-bonded complexes (XBCs), in solution, have played a pivotal role in inducing photochemical organic reactions. In this work, we explore the ability of various tertiary amines to act as XB acceptors in the presence of the XB donor CBr4 by computational and spectroscopic studies. DFT studies clearly showcase the formation of XBCs between the studied tertiary amines and CBr4. Simultaneously, computational and experimental UV-Vis studies display intense red shifts that are consistent with charge transfer observed from tertiary amines to CBr4. A detailed NMR study revealed a clear chemical shift of the carbon carrying the bromine atoms upon mixing the XB acceptor with the donor, suggesting that this spectroscopic technique is indeed an experimental tool to identify the generation of XBCs. An application of the ability of such XBCs to activate a carboxylic acid under UVA irradiation or sunlight is presented for amino acid coupling. Among the various tertiary amines studied, the pair DABCO-CBr4 was found to work well for the photochemical amide bond formation. Direct infusion-HRMS studies allowed us to propose a general mechanism for the photochemical amino acid coupling in the presence of a tertiary amine and CBr4, initiated by the photoactivation of an XBC.

Expanding chalcogen bonds in thiophenes to interactions with halogens

Compounds containing the thiophene moiety find several applications in physics and chemistry, such as electrical conduction, which depends on specific conformations to properly exhibiting the desired properties. In turn, chalcogen bonding has found to modulate the conformation of some N-thiophen-2-ylfomamides. Since halogens participate in a kin interaction (halogen bonding) and are abundant in agrochemicals, pharmaceuticals, and materials, we have quantum-chemically explored the interaction between organic halogen and thiophene as a conformational modulator in some model compounds. Although such interaction indeed appears, as demonstrated by atoms in molecules and natural bond orbital analysis, it is inefficient to control the conformational equilibrium. An energy decomposition analysis scheme demonstrated that halomethane and thiophene tend to move away from one another due to a core component (Pauli repulsion and exchange), which is mainly due to a deformation term. Therefore, chalcogen bonds with halogens appear weaker than with other chalcogens.

The nature of metallophilic interactions in closed-shell d8-d8 metal complexes

We have quantum chemically analyzed the closed-shell d8-d8 metallophilic interaction in dimers of square planar [M(CO)2X2] complexes (M = Ni, Pd, Pt; X = Cl, Br, I) using dispersion-corrected density functional theory at ZORA-BLYP-D3(BJ)/TZ2P level of theory. Our purpose is to reveal the nature of the [X2(CO)2M]⋯[M(CO)2X2] bonding mechanism by analyzing trends upon variations in M and X. Our analyses reveal that the formation of the [M(CO)2X2]2 dimers is favored by an increasingly stabilizing electrostatic interaction when the M increases in size and by more stabilizing dispersion interactions promoted by the larger X. In addition, there is an overlooked covalent component stemming from metal-metal and ligand-ligand donor-acceptor interactions. Thus, at variance with the currently accepted picture, the d8-d8 metallophilicity is attractive, and the formation of [M(CO)2X2]2 dimers is not a purely dispersion-driven phenomenon.

Chalcogen Noncovalent Interactions between Diazines and Sulfur Oxides in Supramolecular Circular Chains

The noncovalent chalcogen interaction between SO2/SO3 and diazines was studied through a dispersion-corrected DFT Kohn-Sham molecular orbital together with quantitative energy decomposition analyses. For this, supramolecular circular chains of up to 12 molecules were built with the aim of checking the capability of diazine molecules to detect SO2/SO3 compounds within the atmosphere. Trends in the interaction energies with the increasing number of molecules are mainly determined by the Pauli steric repulsion involved in these σ-hole/π-hole interactions. But more importantly, despite the assumed electrostatic nature of the involved interactions, the covalent component also plays a determinant role in its strength in the involved chalcogen bonds. Noticeably, π-hole interactions are supported by the charge transfer from diazines to SO2/SO3 molecules. Interaction energies in these supramolecular complexes are not only determined by the S···N bond lengths but attractive electrostatic and orbital interactions also determine the trends. These results should allow us to establish the fundamental characteristics of chalcogen bonding based on its strength and nature, which is of relevance for the capture of sulfur oxides.

Pnictogen bond-driven control of the molecular interaction between organophosphorus and acetylcholinesterase enzyme

This study addresses a comprehensive assessment of the interaction between chemical warfare agents (CWA) and acetylcholinesterase (AChE) systems, focus on the intriguing pnictogen-bond interaction (PnB). Utilizing the crystallographic data from the Protein Data Bank pertaining to the AChE-CWA complex involving Sarin (GB), Cyclosarin (GF), 2-[fluoro(methyl)phosphoryl]oxy-1,1-dimethylcyclopentane (GP) and venomous agent X (VX) agents, the CWA is systematically displaced by increments of 0.1 Å along the PO bond axis, extending its distance by 4 Å from the original position. The AIM analysis was carried out and consistently revealed the presence of a significant interaction along the PO bond. Investigating the intrinsic nature of the PnB, the NBO and the EDA analysis unearthed the contribution of orbital factors to the overall energy of the system. Strikingly, this observation challenges the conventional σ-hole explanation commonly associated with such interactions. This finding adds a layer of complexity to understanding of PnB, encouraging further exploration into the underlying mechanisms governing these intriguing chemical phenomena.

Acidity of Isomorphic Substituted Zeolites with B, Al and Ga Revisited

Isomorphic substitution of zeolites with B, Al and Ga is a widely used approach in catalysis. The experimentally reported trend of their acidities decreases in the order: Al>Ga>B. However, a consistent explanation is still lacking in the literature. To bring more understanding of this trend, density functional theory computations were conducted on several model systems. First, the acidity of small clusters with two (2T) and five (5T) tetrahedral sites was analyzed. These systems were then projected onto three large void structures: H-[A]-BEA (52T), H-[A]-FAU (84T) and H-[A]-MOR (112T) with A=B, Al, Ga. Our electron density and Interacting Quantum Atom analyses show that the acidity of Al zeolites originates from the much stronger O-Al bond, which is dominated by the electrostatic attraction. The bridging hydroxyl therefore donates more charge density to the metal, the proton becomes more positive and consequently more acidic. Ga zeolites are more acidic than B zeolites due to the greater covalent nature on the O-Ga bond. The resulting acidity, as seen by ammonia, depends on both the acidic oxygen and the charge distribution of the surrounding oxygens exerted by the substituents.

Multiple hydrogen-bonded dimers: are only the frontier atoms relevant?

Non-frontier atom exchanges in hydrogen-bonded aromatic dimers can induce significant interaction energy changes (up to 6.5 kcal mol-1). Our quantum-chemical analyses reveal that the relative hydrogen-bond strengths of N-edited guanine-cytosine base pair isosteres, which cannot be explained from the frontier atoms, follow from the charge accumulation in the monomers.

A Deeper Insight into the Supramolecular Activation of Oxidative Addition Reactions Involving Pincer-Rhodium(I) Complexes

The factors governing the acceleration of the oxidative addition of methyl iodide to pincer rhodium(I)-complexes induced by coronene have been computationally explored in detail using quantum chemical methods. Both the parent reaction and the coronene-mediated process proceed via a stepwise SN2-type mechanism. It is found that the acceleration of the process derives from the formation of an initial supramolecular complex, mainly stabilized by electrostatic and π-π interactions, which significantly increases the electron richness of the complex. The impact of this effect on the reaction barrier has been quantitatively analyzed by applying the activation strain model in combination with the energy decomposition analysis method. In addition, the influence of other polycyclic aromatic hydrocarbons on the oxidative reaction has been also considered.

Comparison of N···I and N···O Halogen Bonds in Organoiodine Cocrystals of Heterocyclic Aromatic Diazine Mono-N-oxides

A series of cocrystals of halogen bond donors 1,4-diiodotetrafluorobenzene (p-F4DIB) and tetraiodoethylene (TIE) with five aromatic heterocyclic diazine mono-N-oxides based on pyrazine, tetramethylpyrazine, quinoxaline, phenazine, and pyrimidine as halogen bonding acceptors were studied. Structural analysis of the mono-N-oxides allows comparison of the competitive occurrence of N···I vs O···I interactions and the relative strength and directionality of these two types of interactions. Of the aromatic heterocyclic diazine mono-N-oxide organoiodine cocrystals examined, six exhibited 1:1 stoichiometry, forming chains that utilized both N···I and O···I interactions. Two cocrystals presented 1:1 stoichiometry with exclusive O···I interactions. Two cocrystals displayed a 2:1 stoichiometry-one characterized solely by O···I interactions and the other solely by N···I interactions. We have also compared these interactions to those present in the corresponding diazines, some of which we report here and some which have been previously reported. In addition, a computational analysis using density functional theory (M062X/def2-SVPD) was performed on these two systems and has been compared to the experimental results. The calculated complex formation energies were, on average, 4.7 kJ/mol lower for the I···O halogen bonding interaction as compared to the corresponding N···I interaction. The average I···O interaction distances were calculated to be 0.15 Å shorter than the corresponding I···N interactions.

Decoding energy decomposition analysis: Machine-learned Insights on the impact of the density functional on the bonding analysis

The concept of chemical bonding is a crucial aspect of chemistry that aids in understanding the complexity and reactivity of molecules and materials. However, the interpretation of chemical bonds can be hindered by the choice of the theoretical approach and the specific method utilized. This study aims to investigate the effect of choosing different density functionals on the interpretation of bonding achieved through energy decomposition analysis (EDA). To achieve this goal, a data set was created, representing four bonding groups and various combinations of functionals and dispersion correction schemes. The calculations showed significant variation among the different functionals for the EDA terms, with the dispersion correction terms exhibiting the highest variability. More information was extracted by using machine learning in combination with dimensionality reduction on the data set. Results indicate that, despite the differences in the EDA terms obtained from different functionals, the functional has the least significant impact, suggesting minimal influence on the bonding interpretation.

The Cambridge Structural Database and structural dynamics

With the availability of the computer readable information in the Cambridge Structural Database (CSD), wide ranging, largely automated comparisons of fragment, molecular, and crystal structures have become possible. They show that the distributions of interatomic distances, angles, and torsion angles for a given structural fragment occurring in different environments are highly correlated among themselves and with other observables such as spectroscopic signals, reaction and activation energies. The correlations often extend continuously over large ranges of parameter values. They are reminiscent of bond breaking and forming reactions, polyhedral rearrangements, and conformational changes. They map-qualitatively-the regions of the structural parameter space in which molecular dynamics take place, namely, the low energy regions of the respective (free) energy surfaces. The extension and continuous nature of the correlations provides an organizing principle of large groups of structural data and suggests a reconsideration of traditional definitions and descriptions of bonds, "nonbonded" and "noncovalent" interactions in terms of Lewis acids interacting with Lewis bases. These aspects are illustrated with selected examples of historic importance and with some later developments. It seems that the amount of information in the CSD (and other structural databases) and the knowledge on the nature of, and the correlations within, this body of information should allow one-in the near future-to make credible interpolations and possibly predictions of structures and their properties with machine learning methods.

Long but Strong C-C Single Bonds: Challenges for Theory

Theoretical challenges in describing molecules with anomalously long single C-C bonds are analyzed in terms of the relative contributions of stabilizing and destabilizing intramolecular interactions. Diamondoid dimers that are stable despite the presence of C-C bonds up to 1.7 Å long, as well as other bulky molecules stabilized due to intramolecular noncovalent interactions (London dispersions) are discussed. The unexpected stability of highly crowded molecules, such as diamondoid dimers and tert-butyl-substituted hexaphenylethanes, calls for reconsideration of the "steric effect" traditionally thought to destabilize the molecule. Alternatively, "steric attraction" helps to understand bonding in sterically overloaded molecules, whose structural and energetic analysis requires a proper theoretical description of noncovalent interactions.

Affinity of Telluronium Chalcogen Bond Donors for Lewis Bases in Solution: A Critical Experimental-Theoretical Joint Study

Telluronium salts [Ar2 MeTe]X were synthesized, and their Lewis acidic properties towards a number of Lewis bases were addressed in solution by physical and theoretical means. Structural X-ray diffraction analysis of 21 different salts revealed the electrophilicity of the Te centers in their interactions with anions. Telluroniums' propensity to form Lewis pairs was investigated with OPPh3 . Diffusion-ordered NMR spectroscopy suggested that telluroniums can bind up to three OPPh3 molecules. Isotherm titration calorimetry showed that the related heats of association in 1,2-dichloroethane depend on the electronic properties of the substituents of the aryl moiety and on the nature of the counterion. The enthalpies of first association of OPPh3 span -0.5 to -5 kcal mol-1 . Study of the affinity of telluroniums for OPPh3 by state-of-the-art DFT and ab-initio methods revealed the dominant Coulombic and dispersion interactions as well as an entropic effect favoring association in solution. Intermolecular orbital interactions between [Ar2 MeTe]+ cations and OPPh3 are deemed insufficient on their own to ensure the cohesion of [Ar2 MeTe ⋅ Bn ]+ complexes in solution (B=Lewis base). Comparison of Grimme's and Tkatchenko's DFT-D4/MBD-vdW thermodynamics of formation of higher [Ar2 MeTe ⋅ Bn ]+ complexes revealed significant molecular size-dependent divergence of the two methodologies, with MBD yielding better agreement with experiment.

Crystal Clear: Decoding Isocyanide Intermolecular Interactions through Crystallography

The isocyanide group is the chameleon among the functional groups in organic chemistry. Unlike other multiatom functional groups, where the electrophilic and nucleophilic moieties are typically separated, isocyanides combine both functionalities in the terminal carbon. This unique feature can be rationalized using the frontier orbital concept and has significant implications for its intermolecular interactions and the reactivity of the functional group. In this study, we perform a Cambridge Crystallographic Database-supported analysis of isocyanide intramolecular interactions to investigate the intramolecular interactions of isocyanides in the solid state, excluding isocyanide-metal complexes. We discuss examples of different interaction classes, including the isocyanide as a hydrogen bond acceptor (RNC···HX), halogen bonding (RNC···X), and interactions involving the isocyanide and carbon atoms (RNC···C). The latter interaction serves as an intriguing illustration of a Bürgi-Dunitz trajectory and represents a crucial experimental detail in the well-known multicomponent reactions such as the Ugi- and Passerini-type mechanisms. Understanding the spectrum of intramolecular interactions that isocyanides can undergo holds significant implications in fields such as medicinal chemistry, materials science, and asymmetric catalysis.

Blueshift in Trifurcated Hydrogen Bonds: A Tradeoff between Tetrel Bonding and Steric Repulsion

We have quantum chemically investigated the origin of the atypical blueshift of the H-C bond stretching frequency in the hydrogen-bonded complex X- •••H3 C-Y (X, Y=F, Cl, Br, I), as compared to the corresponding redshift occurring in Cl- •••H3 N and Cl- •••H3 C-H, using relativistic density functional theory (DFT) at ZORA-BLYP-D3(BJ)/QZ4P. Previously, this blueshift was attributed, among others, to the contraction of the H-C bonds as the H3 C moiety becomes less pyramidal. Herein, we provide quantitative evidence that, instead, the blueshift arises from a direct and strong X- •••C interaction of the HOMO of A- with the backside lobe on carbon of the low-lying C-Y antibonding σ* LUMO of the H3 C-Y fragment. This X- •••C bond, in essence a tetrel bond, pushes the H atoms towards a shorter H-C distance and makes the H3 C moiety more planar. The blueshift may, therefore, serve as a diagnostic for tetrel bonding.

A Holistic View of the Interactions between Electron-Deficient Systems: Clustering of Beryllium and Magnesium Hydrides and Halides

In the search for common bonding patterns in pure and mixed clusters of beryllium and magnesium derivatives, the most stable dimers and trimers involving BeX2 and MgX2 (X = H, F, Cl) have been studied in the gas phase using B3LYP and M06-2X DFT methods and the G4 ab initio composite procedure. To obtain some insight into their structure, stability, and bonding characteristics, we have used two different energy decomposition formalisms, namely MBIE and LMO-EDA, in parallel with the analysis of the electron density with the help of QTAIM, ELF, NCIPLOT, and AdNDP approaches. Some interesting differences are already observed in the dimers, where the stability sequence observed for the hydrides differs entirely from that of the fluorides and chlorides. Trimers also show some peculiarities associated with the presence of compact trigonal cyclic structures that compete in stability with the more conventional hexagonal and linear forms. As observed for dimers, the stability of the trimers changes significantly from hydrides to fluorides or chlorides. Although some of these clusters were previously explored in the literature, the novelty of this work is to provide a holistic approach to the entire series of compounds by using chemical bonding tools, allowing us to understand the stability trends in detail and providing insights for a significant number of new, unexplored structures.

The borderless world of chemical bonding across the van der Waals crust and the valence region

The definition of the van der Waals crust as the spherical section between the atomic radius and the van der Waals radius of an element is discussed and a survey of the application of the penetration index between two interacting atoms in a wide variety of covalent, polar, coordinative or noncovalent bonding situations is presented. It is shown that this newly defined parameter permits the comparison of bonding between pairs of atoms in structural and computational studies independently of the atom sizes.

Origin of the Bürgi-Dunitz Angle

The Bürgi-Dunitz (BD) angle plays a pivotal role in organic chemistry to rationalize the nucleophilic addition to carbonyl groups. Yet, the origin of the obtuse trajectory of the nucleophile remains incompletely understood. Herein, we quantify the importance of the underlying physical factors quantum chemically. The obtuse BD angle appears to originate from the concerted action of a reduced Pauli repulsion between the nucleophile HOMO and carbonyl π bond, a more stabilizing HOMO-π*-LUMO(C=O) interaction, as well as a more favorable electrostatic attraction.

Noncovalent Interactions in Hydrated Nitrosonium Ion Clusters Mediated by Hydrogen-Bonded Water Networks

As important species in the D region of the ionosphere, hydrated nitrosonium ion clusters [NO⁺(H₂O)_n] are also archetypal and concise models to illustrate effects of different solvent shells. We have investigated noncovalent interactions in NO⁺(H₂O)₃ and NO⁺(H₂O)₄ isomers with high levels of ab initio and symmetry-adapted perturbation theory (SAPT) methods. On the basis of our computations, the exchange energies become much more repulsive, whereas the induction energies are significantly more attractive for the noncovalent interactions of NO⁺ with hydrogen-bonded water chains. Combined with analyses of the electron densities for the NO⁺(H₂O)₃ and NO⁺(H₂O)₄ isomers, we propose that the counteracting effect of the exchange and induction energies could be deemed as an index for the tendency to form the HO-NO covalent bond. Moreover, we have also found that the third-order induction terms are very important to evaluate reasonable charge transfer energies with the SAPT computations.