Understanding the Fundamental Role of π/π, σ/σ, and σ/π Dispersion Interactions in Shaping Carbon‐Based Materials

Noncovalent interactions involving aromatic rings, such as π‐stacking and CH/π interactions, are central to many areas of modern chemistry. However, recent studies proved that aromaticity is not required for stacking interactions, since similar interaction energies were computed for several aromatic and aliphatic dimers. Herein, the nature and origin of π/π, σ/σ, and σ/π dispersion interactions has been investigated by using dispersion‐corrected density functional theory, energy decomposition analysis, and the recently developed noncovalent interaction (NCI) method. Our analysis shows that π/π and σ/σ stacking interactions are equally important for the benzene and cyclohexane dimers, explaining why both compounds have similar boiling points. Also, similar dispersion forces are found in the benzene???methane and cyclohexane???methane complexes. However, for systems larger than naphthalene, there are enhanced stacking interactions in the aromatic dimers adopting a parallel‐displaced configuration compared to the analogous saturated systems. Although dispersion plays a decisive role in stabilizing all the complexes, the origin of the π/π, σ/σ, and σ/π interactions is different. The NCI method reveals that the dispersion interactions between the hydrogen atoms are responsible for the surprisingly strong aliphatic interactions. Moreover, whereas σ/σ and σ/π interactions are local, the π/π stacking are inherently delocalized, which give rise to a non‐additive effect. These new types of dispersion interactions between saturated groups can be exploited in the rational design of novel carbon materials.     

Hydro­gen bonding and π–π stacking in di­methyl­genistein

The title compound, 5‐hydroxy‐4′,7‐di­methoxy­isoflavone, C₁₇H₁₄O₅, is composed of a benzo­pyran­one moiety, a phenyl moiety and two methoxy groups. The benzo­pyran­one ring is not coplanar with the phenyl ring, the dihedral angle between them being 56.28 (3)°. The two methoxy groups are nearly coplanar with their corresponding rings, having C—C—O—C torsion angles of 2.9 (2) and 5.9 (2)°. The mol­ecules are linked by C—H·O hydrogen bonds into sheets containing classical centrosymmetric (8) rings. The sheets are further linked by aromatic π–π stacking interactions and C—H·O hydrogen bonds into a supramolecular structure.     

The tropolone–isobutylamine complex: a hydrogen‐bonded troponoid without dominant π–π interactions

Tropolone long has served as a model system for unraveling the ubiquitous phenomena of proton transfer and hydrogen bonding. This molecule, which juxtaposes ketonic, hydroxylic, and aromatic functionalities in a framework of minimal complexity, also has provided a versatile platform for investigating the synergism among competing intermolecular forces, including those generated by hydrogen bonding and aryl coupling. Small members of the troponoid family typically produce crystals that are stabilized strongly by pervasive π–π, C—H…π, or ion–π interactions. The organic salt (TrOH·iBA) formed by a facile proton‐transfer reaction between tropolone (TrOH) and isobutylamine (iBA), namely isobutylammonium 7‐oxocyclohepta‐1,3,5‐trien‐1‐olate, C₄H₁₂N⁺·C₇H₅O₂⁻, has been investigated by X‐ray crystallography, with complementary quantum‐chemical and statistical‐database analyses serving to elucidate the nature of attendant intermolecular interactions and their synergistic effects upon lattice‐packing phenomena. The crystal structure deduced from low‐temperature diffraction measurements displays extensive hydrogen‐bonding networks, yet shows little evidence of the aryl forces (viz. π–π, C—H…π, and ion–π interactions) that typically dominate this class of compounds. Density functional calculations performed with and without the imposition of periodic boundary conditions (the latter entailing isolated subunits) documented the specificity and directionality of noncovalent interactions occurring between the proton‐donating and proton‐accepting sites of TrOH and iBA, as well as the absence of aromatic coupling mediated by the seven‐membered ring of TrOH. A statistical comparison of the structural parameters extracted for key hydrogen‐bond linkages to those reported for 44 previously known crystals that support similar binding motifs revealed TrOH·iBA to possess the shortest donor–acceptor distances of any troponoid‐based complex, combined with unambiguous signatures of enhanced proton‐delocalization processes that putatively stabilize the corresponding crystalline lattice and facilitate its surprisingly rapid formation under ambient conditions.     

Hydrogen‐Bonded Organic Aromatic Frameworks for Ultralong Phosphorescence by Intralayer π–π Interactions

Ultralong organic phosphorescence (UOP) based on metal‐free porous materials is rarely reported owing to rapid nonradiative transition under ambient conditions. In this study, hydrogen‐bonded organic aromatic frameworks (HOAFs) with different pore sizes were constructed through strong intralayer π–π interactions to enable ultralong phosphorescence in metal‐free porous materials under ambient conditions for the first time. Impressively, yellow UOP with a lifetime of 79.8 ms observed for PhTCz‐1 lasted for several seconds upon ceasing the excitation. For PhTCz‐2 and PhTCz‐3, on account of oxygen‐dependent phosphorescence quenching, UOP could only be visualized in N₂, thus demonstrating the potential of phosphorescent porous materials for oxygen sensing. This result not only outlines a principle for the design of new HOFs with high thermal stability, but also expands the scope of metal‐free luminescent materials with the property of UOP.     

Enhanced Aerogen–π Interaction by a Cation–π Force

The interaction between a noble gas atom and an aromatic π‐electron system, which mainly originates from the London dispersion force, is very weak and has not attracted enough attention yet. Herein, we reported a type of notably enhanced aerogen–π interaction between cation–π systems and noble gas atoms. The binding strength of a divalent cation–π system with a xenon atom is comparable to a moderate hydrogen bond (up to ca. 7 kcal mol^?1), whereas krypton and argon atoms produce slightly weaker interactions. Energy‐decomposition analysis reveals that the induction interaction is responsible for the stabilization of divalent cation–π?Xe species besides the dispersion interaction. Our results might be helpful to increase the understanding of some unsolved mysteries of aerogens.     

Phenylcarbamoylated β‐CD: π‐Acidic and π‐basic chiral selectors for HPLC

Two types of chiral stationary phases for HPLC based on π‐acidic or π‐basic perphenylcarbamoylated β‐CDs were synthesized. The relative structural features of the two effective chiral selectors are discussed and compared in both normal‐phase and RP modes. In addition, the nature and concentration of alcoholic modifiers were varied for optimal separation in normal phase and the structural variation of the analytes was also examined. The results showed that hydrogen bonding, steric effect and π‐acidic–π‐basic interaction contributed greatly to enantioseparation. Upon comparison, some of the differences in the separation behavior of the two types of chiral stationary phases might be due to the π‐acidic or π‐basic phenylcarbamate groups.     

Hydrogen Bond and π–π Interactions in a 3D Supramolecular Structure Containing 1D Helical Chains

The reaction of 2, 2′‐bipyridine‐6, 6′‐dicarboxylic acid (H₂bpdc) with zinc nitrate and different rare earth chlorides generates two novel three‐dimensional supramolecules Zn(6‐bpc)₂ · 2H₂O ( 1 ) and Ce(bpdc)₂ · H₂O ( 2 ) (6‐Hbpc = 2, 2′‐bipyridine‐6‐carboxylic acid). The left‐and right‐handed helical chains give rise to a 3D supramolecular framework through hydrogen‐bond and weak π–π interactions in complex 1 . Interestingly, the decarboxylation occurred and the bpdc ligand was transformed into 6‐bpc species under the hydrothermal reaction in the presence of Nd^III ions, while the decarboxylation did not occur when Ce^III ions were used. In the structure of 2 , one central Ce(IV) atom coordinates to two bpdc ligands, resulting in a discrete molecule. These discrete units are further extended into a 3D supramolecular structure through intermolecular hydrogen bonds and π–π interactions.     

Hydrogen bonding and π–π stacking in 6‐hydroxy­biochanin A monohydrate

In the lattice of the title compound (systematic name: 5,6,7‐trihydroxy‐4′‐meth­oxy­isoflavone monohydrate), C₁₆H₁₂O₆·H₂O, the isoflavone mol­ecules are linked into chains through R₄³(17) motifs composed via O—H⋯O and C—H⋯O hydrogen bonds. Centrosymmetric R₄²(14) motifs assemble the chains into sheets. Hydrogen‐bonding and aromatic π–π stacking inter­actions lead to the formation of a three‐dimensional network structure.     

C—H⋯π and π–π interactions in the supramolecular structure of 3‐methyl‐1,4‐diphenyl‐1H‐pyrazolo[3,4‐b]pyridine

The supramolecular structure of the title compound, C₁₉H₁₅N₃, is defined by π–π‐stacking and C—H?π interactions. There are no conventional hydrogen bonds in the structure.     

Photocontrol Over Self‐Assembled Nanostructures of π–π Stacked Dyes Supported by the Parallel Conformer of Diarylethene

Diarylethenes (DAEs) have rarely been used in the design of photoresponsive supramolecular assemblies with a well‐defined morphology transition owing to rather small structural changes upon photoisomerization. A supramolecular design based on the parallel conformation of DAEs enables the construction of photoresponsive dye assemblies that undergo remarkable nanomorphology transitions. The cooperative stacking of perylene bisimide (PBI) dyes was used to stabilize the parallel conformer of DAE through complementary hydrogen bonds. Atomic force microscopy, UV/Vis spectroscopy, and molecular modeling revealed that our DAE and PBI building blocks coassembled in nonpolar solvent to form well‐defined helical nanofibers featuring J‐type dimers of PBI dyes. Upon irradiating the coassembly solution with UV and visible light in turn, a reversible morphology change between nanofibers and nanoparticles was observed. This system involves the generation of a new self‐assembly pathway by means of photocontrol.     

Comparison of halogen bonding and van der Waals and π–π interactions in 4,5‐dibromo‐2‐hexyloxyphenol

The title compound, C₁₂H₁₆BrO₂, is an interesting case of a simple organic molecule making use of five different types of intra‐ and intermolecular interactions (viz. conventional and nonconventional hydrogen bonds, and π–π, Br...Br and Br...O contacts), all of them relevant in the molecular and crystal structure geometry. The molecules are strictly planar, with an intramolecular O—H...O hydrogen bond, and associate into two‐dimensional structures parallel to (01) through two different types of halogen bonding. The planar structures, in turn, stack parallel to each other interlinked by C—H...π and π–π contacts. Also discussed are the relevant structural features leading to the rather low melting point of the compound.     

The Effects of Substituents on the Geometry of π–π Interactions

We have designed and utilized a simple molecular recognition system to study the substituent effects in aromatic interactions. Recently, we showed that 3‐ and 3,5‐disubstituted benzoyl leucine diethyl amides with aromatic rings of varying electronic character organized into homochiral dimers in the solid state through a parallel displaced π–π interaction and two hydrogen bonds, but no such homochiral dimerization was observed for the unsubstituted case. This phenomenon supports the hypothesis that substituents stabilize π–π interactions regardless of their electronic character. To further investigate the origin of substituent effects for π–π interactions, we synthesized and crystallized a series of 4‐substituted benzoyl leucine diethyl amides. Surprisingly, only two of the 4‐substituted compounds formed homochiral dimers. A comparison among the 4‐substituted compounds that crystallized as homochiral dimers and their 3‐substituted counterparts revealed that there are differences in regard to the geometry of the aromatic rings with respect to each other, which depend on the electronic nature and location of the substituent. The crystal structures of the homochiral dimers that showed evidence of direct, local interactions between the substituents on the aromatic rings also displayed nonequivalent dihedral angles in the individual monomers. The crystallographic data suggests that such “flexing” may be the result of the individual molecules orienting themselves to maximize the local dipole interactions on the respective aromatic rings. The results presented here can potentially have broad applicability towards the development of molecular recognition systems that involve aromatic interactions.     

The peptide NCbz‐Val‐Tyr‐OMe and aromatic π–π interactions

The peptide N‐benzyloxycarbonyl‐L‐valyl‐L‐tyrosine methyl ester or NCbz‐Val‐Tyr‐OMe (where NCbz is N‐benzyloxycarbonyl and OMe indicates the methyl ester), C₂₃H₂₈N₂O₆, has an extended backbone conformation. The aromatic rings of the Tyr residue and the NCbz group are involved in various attractive intra‐ and intermolecular aromatic π–π interactions which stabilize the conformation and packing in the crystal structure, in addition to N—H...O and O—H...O hydrogen bonds. The aromatic π–π interactions include parallel‐displaced, perpendicular T‐shaped, perpendicular L‐shaped and inclined orientations.     

Observation of CH⋅⋅⋅π Interactions between Methyl and Carbonyl Groups in Proteins

Protein structure and function is dependent on myriad noncovalent interactions. Direct detection and characterization of these weak interactions in large biomolecules, such as proteins, is experimentally challenging. Herein, we report the first observation and measurement of long‐range “through‐space” scalar couplings between methyl and backbone carbonyl groups in proteins. These J couplings are indicative of the presence of noncovalent C−H⋅⋅⋅π hydrogen‐bond‐like interactions involving the amide π network. Experimentally detected scalar couplings were corroborated by a natural bond orbital analysis, which revealed the orbital nature of the interaction and the origins of the through‐space J couplings. The experimental observation of this type of CH⋅⋅⋅π interaction adds a new dimension to the study of protein structure, function, and dynamics by NMR spectroscopy.     

Ab initio and AIM studies on typical π‐type and pseudo‐π‐type halogen bonds: Comparison with hydrogen bonds

Series of typical π‐type and pseudo‐π‐type halogen‐bonded complexes B ··· ClY and B ··· BrY and hydrogen‐bonded complex B ··· HY (B = C₂H₄, C₂H₂, and C₃H₆; Y = F, Cl, and Br) have been investigated using the MP2/aug‐cc‐pVDZ method. A striking parallelism was found in the geometries, vibrational frequencies, binding energies, and topological properties between B ··· XY and B ··· HY (X = Cl and Br). It has been found that the lengths of the weak bond d(X ··· π)/d(H ··· π), the frequencies of the weak bond ν(X ··· π)/ν(H ··· π), the frequency shifts Δν(X? Y)/Δν(H? Y), the electron densities at the bond critical point of the weak bonds ρ_c(X ··· π)/ρ_c(H ··· π), and the electron density changes Δρ_c(X? Y)/Δρ_c(H? Y) could be used as measures of the strengths of typical π‐type and pseudo‐π‐type halogen/hydrogen bonds. The typical π‐type and pseudo‐π‐type halogen bond and hydrogen bond are noncovalent interactions. For the same Y, the halogen bond strengths are in the order B ··· ClY < B ··· BrY. For the same X, the halogen bond strength decreases according to the sequence F > Cl > Br that is in agreement with the hydrogen bond strengths B ··· HF > B ··· HCl > B ··· HBr. All of these typical π‐type and pseudo‐π‐type hydrogen‐bonded and halogen‐bonded complexes have the “conflict‐type” structure. Contour maps of the Laplacian of π electron density indicate that the formation of B ··· XY halogen‐bonded complex and B ··· HY hydrogen‐bonded complex is very similar. Charge transfer is observed from B to XY/HY and both the dipolar polarization and the volume of the halogen atom or hydrogen atom decrease on B ··· XY/B ··· HY complex formation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structure determination of three furan‐substituted benzimidazoles and calculation of π–π and C—H...π interaction energies

The synthesis and structural characterization of 2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazole [C₁₆H₁₂N₂O₂, (I)], 2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazol‐3‐ium chloride monohydrate [C₁₆H₁₃N₂O₂⁺·Cl⁻·H₂O, (II)] and the hydrobromide salt 5,6‐dimethyl‐2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazol‐3‐ium bromide [C₁₈H₁₇N₂O₂⁺·Br⁻, (III)] are described. Benzimidazole (I) displays two sets of aromatic interactions, each of which involves pairs of molecules in a head‐to‐tail arrangement. The first, denoted set (Ia), exhibits both intermolecular C—H...π interactions between the 2‐(furan‐2‐yl) (abbreviated as Fn) and 1‐(furan‐2‐ylmethyl) (abbreviated as MeFn) substituents, and π–π interactions involving the Fn substituents between inversion‐center‐related molecules. The second, denoted set (Ib), involves π–π interactions involving both the benzene ring (Bz) and the imidazole ring (Im) of benzimidazole. Hydrated salt (II) exhibits N—H...OH₂...Cl hydrogen bonding that results in chains of molecules parallel to the a axis. There is also a head‐to‐head aromatic stacking of the protonated benzimidazole cations in which the Bz and Im rings of one molecule interact with the Im and Fn rings of adjacent molecules in the chain. Salt (III) displays N—H...Br hydrogen bonding and π–π interactions involving inversion‐center‐related benzimidazole rings in a head‐to‐tail arrangement. In all of the π–π interactions observed, the interacting moieties are shifted with respect to each other along the major molecular axis. Basis set superposition energy‐corrected (counterpoise method) interaction energies were calculated for each interaction [DFT, M06‐2X/6‐31+G(d)] employing atomic coordinates obtained in the crystallographic analyses for heavy atoms and optimized H‐atom coordinates. The calculated interaction energies are −43.0, −39.8, −48.5, and −55.0 kJ mol⁻¹ for (Ia), (Ib), (II), and (III), respectively. For (Ia), the analysis was used to partition the interaction energies into the C—H...π and π–π components, which are 9.4 and 24.1 kJ mol⁻¹, respectively. Energy‐minimized structures were used to determine the optimal interplanar spacing, the slip distance along the major molecular axis, and the slip distance along the minor molecular axis for 2‐(furan‐2‐yl)‐1H‐benzimidazole.     

The Bright Future of Unconventional σ/π‐Hole Interactions

Non‐covalent interactions play a crucial role in (supramolecular) chemistry and much of biology. Supramolecular forces can indeed determine the structure and function of a host–guest system. Many sensors, for example, rely on reversible bonding with the analyte. Natural machineries also often have a significant non‐covalent component (e.g. protein folding, recognition) and rational interference in such ‘living’ devices can have pharmacological implications. For the rational design/tweaking of supramolecular systems it is helpful to know what supramolecular synthons are available and to understand the forces that make these synthons stick to one another. In this review we focus on σ‐hole and π‐hole interactions. A σ‐ or π‐hole can be seen as positive electrostatic potential on unpopulated σ* or π⁽*⁾ orbitals, which are thus capable of interacting with some electron dense region. A σ‐hole is typically located along the vector of a covalent bond such as X?H or X?Hlg (X=any atom, Hlg=halogen), which are respectively known as hydrogen and halogen bond donors. Only recently it has become clear that σ‐holes can also be found along a covalent bond with chalcogen (X?Ch), pnictogen (X?Pn) and tetrel (X?Tr) atoms. Interactions with these synthons are named chalcogen, pnigtogen and tetrel interactions. A π‐hole is typically located perpendicular to the molecular framework of diatomic π‐systems such as carbonyls, or conjugated π‐systems such as hexafluorobenzene. Anion–π and lone‐pair–π interactions are examples of named π‐hole interactions between conjugated π‐systems and anions or lone‐pair electrons respectively. While the above nomenclature indicates the distinct chemical identity of the supramolecular synthon acting as Lewis acid, it is worth stressing that the underlying physics is very similar. This implies that interactions that are now not so well‐established might turn out to be equally useful as conventional hydrogen and halogen bonds. In summary, we describe the physical nature of σ‐ and π‐hole interactions, present a selection of inquiries that utilise σ‐ and π‐holes, and give an overview of analyses of structural databases (CSD/PDB) that demonstrate how prevalent these interactions already are in solid‐state structures.     

Three N2‐benzoyl­oxybenz­amidines: sheet structures built from hard and soft hydrogen bonds and aromatic π–π stacking interactions

Molecules of the title compounds N²‐(benzoyl­oxy)­benz­ami­dine, C₁₄H₁₂N₂O₂, (I), N²‐(2‐hydroxy­benzoyl­oxy)­benz­ami­dine, C₁₄H₁₂N₂O₃, (II), and N²‐benzoyloxy‐2‐hydroxybenzamidine, C₁₄H₁₂N₂O₃, (III), all have extended chain conformations, with the aryl groups remote from one another. In (I), the mol­ecules are linked into chains by a single N—H⋯N hydrogen bond [H⋯N = 2.15 Å, N⋯N = 3.029 (2) Å and N—H⋯N = 153°] and these chains are linked into sheets by means of aromatic π–π stacking interactions. There is one intramolecular O—H⋯O hydrogen bond in (II), and a combination of one three‐centre N—H⋯(N,O) hydrogen bond [H⋯N = 2.46 Å, H⋯O = 2.31 Å, N⋯N = 3.190 (2) Å, N⋯O = 3.146 (2) Å, N—H⋯N = 138° and N—H⋯O = 154°] and one two‐centre C—H⋯O hydrogen bond [H⋯O = 2.46 Å, C⋯O = 3.405 (2) Å and C—H⋯O = 173°] links the mol­ecules into sheets. In (III), an intramolecular O—H⋯N hydrogen bond and two N—H⋯O hydrogen bonds [H⋯O = 2.26 and 2.10 Å, N⋯O = 2.975 (2) and 2.954 (2) Å, and N—H⋯O = 138 and 163°] link the molecules into sheets.     

A labeling study of π-cycloheptatrienetricarbonylchromium(0)

Peaks of different intensities in the mass spectra of π-toluenetricarbonylchromium and π-cycloheptatrienetricarbonylchromium were studied by deuterium labeling of the latter compound. Incomplete hydrogen randomization in cycloheptatriene ligands preceding different reactions was observed, in contrast to the results for cycloheptatriene itself.