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.     

Ab initio study of the π–π interactions between CO2 and benzene,pyridine, and pyrrole

The π–π interactions between CO₂ and three aromatic molecules, namely benzene (C₆H₆), pyridine (C₅H₅N), and pyrrole (C₄H₅N), which represent common functional groups in metal‐organic/zeoliticimidazolate framework materials, were characterized using high‐level ab initio methods. The coupled‐cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second‐order M?ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2‐QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C₄H₅N > C₆H₆ ～ C₅H₅N and was roughly correlated with the aromaticity and the charge transfer between CO₂ and aromatic molecule in clusters. Compared with hydrogen‐bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2‐QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO₂ and aromatic molecules. © 2013 Wiley Periodicals, Inc.     

Reconciling Electrostatic and n→π* Orbital Contributions in Carbonyl Interactions

Interactions between carbonyl groups are prevalent in protein structures. Earlier investigations identified dominant electrostatic dipolar interactions, while others implicated lone pair n→π* orbital delocalisation. Here these observations are reconciled. A combined experimental and computational approach confirmed the dominance of electrostatic interactions in a new series of synthetic molecular balances, while also highlighting the distance‐dependent observation of inductive polarisation manifested by n→π* orbital delocalisation. Computational fiSAPT energy decomposition and natural bonding orbital analyses correlated with experimental data to reveal the contexts in which short‐range inductive polarisation augment electrostatic dipolar interactions. Thus, we provide a framework for reconciling the context dependency of the dominance of electrostatic interactions and the occurrence of n→π* orbital delocalisation in C=O???C=O interactions.     

Influence of the Li⋅⋅⋅π Interaction on the H/X⋅⋅⋅π Interactions in HOLi⋅⋅⋅C6H6⋅⋅⋅HOX/XOH (X=F,Cl, Br,I) Complexes

The influences of the Li???π interaction of C₆H₆???LiOH on the H???π interaction of C₆H₆???HOX (X=F, Cl, Br, I) and the X???π interaction of C₆H₆???XOH (X=Cl, Br, I) are investigated by means of full electronic second‐order Møller–Plesset perturbation theory calculations and “quantum theory of atoms in molecules” (QTAIM) studies. The binding energies, binding distances, infrared vibrational frequencies, and electron densities at the bond critical points (BCPs) of the hydrogen bonds and halogen bonds prove that the addition of the Li???π interaction to benzene weakens the H???π and X???π interactions. The influences of the Li???π interaction on H???π interactions are greater than those on X???π interactions; the influences of the H???π interactions on the Li???π interaction are greater than X???π interactions on Li???π interaction. The greater the influence of Li???π interaction on H/X???π interactions, the greater the influences of H/X???π interactions on Li???π interaction. QTAIM studies show that the intermolecular interactions of C₆H₆???HOX and C₆H₆???XOH are mainly of the π type. The electron densities at the BCPs of hydrogen bonds and halogen bonds decrease on going from bimolecular complexes to termolecular complexes, and the π‐electron densities at the BCPs show the same pattern. Natural bond orbital analyses show that the Li???π interaction reduces electron transfer from C₆H₆ to HOX and XOH.     

The nido‐Cage⋅⋅⋅π Bond: A Non‐covalent Interaction between Boron Clusters and Aromatic Rings and Its Applications

Non‐covalent interactions involving multicenter multielectron skeletons such as boron clusters are rare. Now, a non‐covalent interaction, the nido‐cage???π bond, is discovered based on the boron cluster C₂B₉H₁₂^? and an aromatic π system. The X‐ray diffraction studies indicate that the nido‐cage???π bonding presents parallel‐displaced or T‐shaped geometries. The contacting distance between cage and π ring varies with the type and the substituent of the aromatic ring. Theoretical calculations reveal that this nido‐cage???π bond shares a similar nature to the conventional anion???π or π???π bonds found in classical aromatic ring systems. This nido‐cage???π interaction induces variable photophysical properties such as aggregation‐induced emission and aggregation‐caused quenching in one molecule. This work offers an overall understanding towards the boron cluster‐based non‐covalent bond and opens a door to investigate its properties.     

A Computational Study on 3‐Azonia‐, 3‐Phosphonia‐, and 3‐Arsoniaspiro[2.2]pentanes and Related Three‐Membered Heterocycles

A theoretical study at the ab initio MP2/6‐311++G(d,p) level of theory is carried out to characterize several heterocyclic spiro[2.2]pentane cations with N, P, and As as spiro atoms. The strain and relative stability of the spiropentanes are obtained through isodesmic reactions. Nucleus‐independent chemical shifts (NICS) and 3D NICS isosurfaces show σ‐aromatic characteristics, similar to those found in cyclopropane. The interaction with the Cl^? anion, which results in four different stationary structures, is studied and characterized by means of the atoms in molecules methodology, and Cl ??? pnicogen, Cl ??? H, and Cl ??? C interactions are found. The most stable structure in all cases corresponds to opening of one of the three‐membered rings, due to the attack of the Cl atom, and C?Cl bond formation. Furthermore, the reaction with the 3‐boranuidaspiro[2.2]pentane anion results in the formation of a new compound through cleavage of one ring of both reactants.     

Redox‐Switchable 20π‐, 19π‐, and 18π‐Electron 5,10,15,20‐Tetraaryl‐5,15‐diazaporphyrinoid Nickel(II) Complexes

The first examples of air‐stable 20π‐electron 5,10,15,20‐tetraaryl‐5,15‐diaza‐5,15‐dihydroporphyrins, their 18π‐electron dications, and the 19π‐electron radical cation were prepared through metal‐templated annulation of nickel(II) bis(5‐arylamino‐3‐chloro‐8‐mesityldipyrrin) complexes followed by oxidation. The neutral 20π‐electron derivatives are antiaromatic and the cationic 18π‐electron derivatives are aromatic in terms of the magnetic criterion of aromaticity. The meso N atoms in these diazaporphyrinoids give rise to characteristic redox and optical properties for the compounds that are not typical of isoelectronic 5,10,15,20‐tetraarylporphyrins.     

A Zwitterionic, 10 π Aromatic Hemisphere

A new concept in anionic 10 π aromaticity is described by the embedding of a compensating charge within an aromatic cyclononatetraenide ring by the symmetric superposition of an alkyl ammonium bridge. This is accomplished by the methylation of azatriquinacene to give a quaternary ammonium salt, followed by oxidation to the tetraene and final deprotonation. The resulting zwitterion is a stable [9]annulene with strong aromaticity as shown by its degree of C−C bond equalization and a nucleus‐independent chemical shift value lower than that of benzene. The solid‐state structure shows an eclipsed stacking motif with the electron‐poor ammonium methyl groups occupying the electron‐rich cavity of the aromatic bowl.     

Construction of Alkynylplatinum(II) Bzimpy‐Functionalized Metallacycles and Their Hierarchical Self‐Assembly Behavior in Solution Promoted by Pt⋅⋅⋅Pt and π–π Interactions

A family of new alkynylplatinum(II) 2,6‐bis(benzimidazol‐2′‐yl)pyridine (bzimpy)‐functionalized supramolecular metallacycles with different shapes and sizes have been successfully prepared by coordination‐driven self‐assembly. The obtained metallacycles showed switchable emission and a strong tendency to form intermolecular Pt???Pt and π–π stacking interactions in solution that were not displayed by their individual precursors. Further investigation revealed that the existence of the metallacyclic scaffold at the core could facilitate the formation of intermolecular Pt???Pt and π–π stacking interactions of peripheral alkynylplatinum(II) bzimpy units. Moreover, the shapes and sizes of the metallacyclic scaffold have a significant influence on the hierarchical self‐assembly behavior. Among the three metallacycles, hexagonal metallacycle A , with a relatively small size, could spontaneously self‐assemble into an aromatic guest stimuli‐responsive metallogel at room temperature without a heating–cooling process.     

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.     

π‐Hole Bonds: Boron and Aluminum Lewis Acid Centers

MP2/aug‐cc‐pVTZ calculations were performed on complexes of boron and aluminum trihydrides and trihalides with hydrogen cyanide (ZH₃‐NCH and ZX₃‐NCH; Z=B, Al; X=F, Cl). The complexes are linked through the B???N and Al???N interactions, which are named as triel bonds and which are classified as π‐hole bonds. It was found that they possess numerous characteristics of typical covalent bonds, since they are ruled mainly by processes of the electron charge shift from the Lewis base to the Lewis acid unit. Other configurations of the ZH₃‐NCH and ZX₃‐NCH complexes linked by the dihydrogen, hydrogen, and halogen bonds were found. However, these interactions are much weaker than the corresponding π‐hole bonds. The quantum theory of atoms in molecules and the natural bond orbital approaches were applied to characterize the complexes and interactions analyzed. The crystal structures of triel trihydrides and triel trihalides were also analyzed for comparison with the results of calculations.     

Herring‐bone π–π interactions in trans‐2,6‐diphenyl‐2,3,5,6‐tetrahydrothiapyran‐4‐one

The structure of the title compound, C₁₇H₁₆OS, is primarily stabilized by T‐shaped and parallel‐displaced aromatic clusters. The distances between the centroids of the aromatic pairs are in the range 4.34–5.30 Å. In the crystal packing, the mol­ecules dimerize by means of π–π interactions of both face‐to‐face and edge‐to‐face types, and the aromatic rings associate in a cyclic edge‐to‐face tetrameric arrangement of the herring‐bone type. These herring‐bone interactions appear to insulate hydrogen‐bond interactions in the crystal structure.     

Control over the Self‐Assembly Modes of PtII Complexes by Alkyl Chain Variation: From Slipped to Parallel π‐Stacks

We report the self‐assembly of a new family of hydrophobic, bis(pyridyl) Pt^II complexes featuring an extended oligophenyleneethynylene‐derived π‐surface appended with six long (dodecyloxy ( 2 )) or short (methoxy ( 3 )) side groups. Complex 2 , containing dodecyloxy chains, forms fibrous assemblies with a slipped arrangement of the monomer units (d_Pt???Pt≈14 Å) in both nonpolar solvents and the solid state. Dispersion‐corrected PM6 calculations suggest that this organization is driven by cooperative π–π, C?H???Cl and π–Pt interactions, which is supported by EXAFS and 2D NMR spectroscopic analysis. In contrast, nearly parallel π‐stacks (d_Pt???Pt≈4.4 Å) stabilized by multiple π–π and C?H???Cl contacts are obtained in the crystalline state for 3 lacking long side chains, as shown by X‐ray analysis and PM6 calculations. Our results reveal not only the key role of alkyl chain length in controlling self‐assembly modes but also show the relevance of Pt‐bound chlorine ligands as new supramolecular synthons.     

Role of Intramolecular Aromatic π–π Interactions in the Self‐Assembly of Di‐l‐Phenylalanine Dipeptide Driven by Intermolecular Interactions: Effect of Alanine Substitution

Although the role of intermolecular aromatic π–π interactions in the self‐assembly of di‐l ‐phenylalanine (l ‐Phe‐l ‐Phe, FF), a peptide that is known for hierarchical structure, is well established, the influence of intramolecular π–π interactions on the morphology of the self‐assembled structure of FF has not been studied. Herein, the role of intramolecular aromatic π–π interactions is investigated for FF and analogous alanine (Ala)‐containing dipeptides, namely, l ‐Phe‐l ‐Ala (FA) and l ‐Ala‐l ‐Phe (AF). The results reveal that these dipeptides not only form self‐assemblies, but also exhibit remarkable differences in structural morphology. The morphological differences between FF and the analogues indicate the importance of intramolecular π–π interactions, and the structural difference between FA and AF demonstrates the crucial role of the nature of intramolecular side‐chain interactions (aromatic–aliphatic or aliphatic–aromatic), in addition to intermolecular interactions, in deciding the final morphology of the self‐assembled structure. The current results emphasise that intramolecular aromatic π–π interaction may not be essential to induce self‐assembly in smaller peptides, and π (aromatic)–alkyl or alkyl–π (aromatic) interactions may be sufficient. This work also illustrates the versatility of aromatic and a combination of aromatic and aliphatic residues in dipeptides in the formation of structurally diverse self‐assembled structures.     

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.     

Are water–aromatic complexes always stabilized due to π–H interactions? LMP2 study

Eight complexes of various aromatic molecules with water have been studied theoretically at the local Møller–Plesset 2nd order theory (LMP2)/aug‐cc‐pVTZ(‐f)//LMP2/6‐31+G* level of theory. Two types of complexes can be formed, depending on the electronic structure of aromatic molecules. Donor hydrocarbons form A‐type complexes, while aromatics bearing electron‐withdrawing substituents form B‐type complexes. A‐type complexes are stabilized due to π–H interactions with the OH bond pointing to the aromatic molecule plane, while B‐type complexes have geometry with the oxygen atom pointing to the aromatic molecule plane stabilized by the interaction of highest occupied molecular orbital (HOMO) of water molecule with π* orbitals of the aromatics. It has been found that a (? HOMO–lowest unoccupied molecular orbital (LUMO)/2 value of aromatic molecule, which can be called “molecular electronegativity,” is useful to predict the type of complex formed by aromatic molecule and water. Aromatic hydrocarbons with “molecular electronegativity” of <0.15 tend to form A‐type complexes, while aromatic molecules with “molecular electronegativity” of <0.15 a.u. form B‐type complexes. The binding energy of water–aromatic complexes undergoes a minimum in the area of switching from A‐type to B type complexes, which can be rationalize in terms of frontier orbital interactions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A Platinum(II) Terpyridine Metallogel with an L‐Valine‐Modified Alkynyl Ligand: Interplay of Pt⋅⋅⋅Pt, π–π and Hydrogen‐Bonding Interactions

A series of platinum(II) terpyridine complexes with L ‐valine‐modified alkynyl ligands has been synthesized. A complex with an unsubstituted terpyridine and one valine unit on the alkynyl is shown to be capable of gel formation, which is in sharp contrast to the gelation properties of the corresponding organic counterparts. Upon sol–gel transition, a drastic color change from yellow to red is observed, which is indicative of the involvement of Pt ??? Pt interactions. Through the concentration‐ and temperature‐dependent UV/Vis absorption, emission, circular dichroism, and ¹H NMR studies, the contribution of hydrogen bonding, Pt ??? Pt and π–π stacking interactions as driving forces for gelation have been established, and the importance of maintaining a delicate balance between different intermolecular forces has also been illustrated.     

Homonuclear chalcogen–chalcogen bond interactions in complexes pairing YO3 and YHX molecules (Y = S,Se; X = H,Cl, Br,CCH, NC,OH, OCH3): Influence of substitution and cooperativity

MP2/aug‐cc‐pVTZ calculations are performed on complexes of YO₃ (Y = S, Se) with a series of electron‐donating chalcogen bases YHX (X = H, Cl, Br, CCH, NC, OH, OCH₃). These complexes are formed through the interaction of a positive electrostatic potential region (π‐hole) on the YO₃ molecule with the negative region in YHX. Interaction energies of the binary O₃Y???YHX complexes are in the range of ?4.37 to ?12.09 kcal/mol. The quantum theory of atoms in molecules and the natural bond orbital analysis were applied to characterize the nature of interactions. It was found that the formation and stability of these binary complexes are ruled mainly by electrostatic effects, although the electron charge transfer from YHX to YO₃ unit also seems to play an important role. In addition, mutual influence between the Y???N and Y???Y interactions is studied in the ternary HCN???O₃Y???YHX complexes. The results indicate that the formation of a Y???N interaction tends to weaken Y???Y bond in the ternary systems. Although the Y???Y interaction is weaker than the Y???N one, however, both types of interactions seem to compete with each other in the HCN???O₃Y???YHX complexes. © 2016 Wiley Periodicals, Inc.     

Tuning of Supramolecular Architectures of l‐Valine‐Containing Dicyanoplatinum(II) 2,2′‐Bipyridine Complexes by Metal–Metal, π–π Stacking,and Hydrogen‐Bonding Interactions

A series of newly synthesized dicyanoplatinum(II) 2,2′‐bipyridine complexes exhibits self‐assembly properties in solution after the incorporation of the l ‐valine amino units appended with various hydrophobic motifs. These l ‐valine‐derived substituents were found to have critical control over the aggregation behaviors of the complexes in the solution state. On one hand, one of the complexes was found to exhibit interesting circularly polarized luminescence (CPL) signals at low temperature due to the formation of chiral spherical aggregates in the temperature‐dependent studies. On the other hand, systematic transformation from less uniform aggregates to well‐defined fibrous and rod‐like structures via Pt???Pt and π–π stacking interactions has also been observed in the mixed‐solvent studies. These changes were monitored by UV/Vis absorption, emission, circular dichroism (CD), and CPL spectroscopies, and morphologies were studied by electron microscopy.     

Competition Between π–π and CH/π Interactions: A Comparison of the Structural and Electronic Properties of Alkoxy‐Substituted 1,8‐Bis((propyloxyphenyl)ethynyl)naphthalenes

The structural and electronic consequences of π–π and C?H/π interactions in two alkoxy‐substituted 1,8‐bis‐ ((propyloxyphenyl)ethynyl)naphthalenes are explored by using X‐ray crystallography and electronic structure computations. The crystal structure of analogue 4 , bearing an alkoxy side chain in the 4‐position of each of the phenyl rings, adopts a π‐stacked geometry, whereas analogue 8 , bearing alkoxy groups at both the 2‐ and the 5‐positions of each ring, has a geometry in which the rings are splayed away from a π‐stacked arrangement. Symmetry‐adapted perturbation theory analysis was performed on the two analogues to evaluate the interactions between the phenylethynyl arms in each molecule in terms of electrostatic, steric, polarization, and London dispersion components. The computations support the expectation that the π‐stacked geometry of the alkoxyphenyl units in 4 is simply a consequence of maximizing π–π interactions. However, the splayed geometry of 8 results from a more subtle competition between different noncovalent interactions: this geometry provides a favorable anti‐alignment of C?O bond dipoles, and two C?H/π interactions in which hydrogen atoms of the alkyl side chains interact favorably with the π electrons of the other phenyl ring. These favorable interactions overcome competing π–π interactions to give rise to a geometry in which the phenylethynyl substituents are in an offset, unstacked arrangement.