Substituent effects in parallel-displaced pi-pi interactions

High-quality quantum-mechanical methods are used to examine how substituents tune pi-pi interactions between monosubstituted benzene dimers in parallel-displaced geometries. The present study focuses on the effect of the substituent across entire potential energy curves. Substituent effects are examined in terms of the fundamental components of the interaction (electrostatics, exchange-repulsion, dispersion and induction) through the use of symmetry-adapted perturbation theory. Both second-order M?ller-Plesset perturbation theory (MP2) with a truncated aug-cc-pVDZ' basis and spin-component-scaled MP2 (SCS-MP2) with the aug-cc-pVTZ basis are found to mimic closely estimates of coupled-cluster with perturbative triples [CCSD(T)] in an aug-cc-pVTZ basis. Substituents can have a significant effect on the electronic structure of the pi cloud of an aromatic ring, leading to marked changes in the pi-pi interaction. Moreover, there can also be significant direct interactions between a substituent on one ring and the pi-cloud of the other ring.     

The effect of multiple substituents on sandwich and T-shaped pi-pi interactions

Sandwich and T-shaped configurations of substituted benzene dimers were studied by second-order perturbation theory to determine how substituents tune pi-pi interactions. Remarkably, multiple substituents have an additive effect on the binding energy of sandwich dimers, except in some cases when substituents are aligned on top of each other. The energetics of substituted T-shaped configurations are more complex, but nevertheless a simple model that accounts for electrostatic and dispersion interactions (and direct contacts between substituents on one ring and hydrogen atoms on the other), provides a good match to the quantum mechanical results. These results provide insight into the manner by which substituents csan be utilized in supramolecular design.     

Unexpected substituent effects in offset pi-pi stacked interactions in water

We have measured the rotational barriers of meta- and para-substituted N-benzyl-2-(2-fluorophenyl)pyridinium bromides in aqueous solution by dynamic NMR as a model system for offset-stacking interactions in proteins. Because the benzyl ring can stack with the 2-fluorophenyl ring in the offset conformation in the ground state, but not the transition state, the rotational barrier reflects the magnitude of the stacking interaction. Only a small (0.1 kcal/mol) change in rotational barrier was found for para substituents relative to hydrogen. A much larger energy difference was found for electronegative meta substituents (up to 0.66 kcal/mol for CF3). Evidence suggests that this is due at least in part to an electrostatic interaction between electron-poor hydrogens on one ring with the electronegative substituents on the other ring.     

Substituent effects on aromatic stacking interactions

Synthetic supramolecular zipper complexes have been used to quantify substituent effects on the free energies of aromatic stacking interactions. The conformational properties of the complexes have been characterised using NMR spectroscopy in CDCl(3), and by comparison with the solid state structures of model compounds. The structural similarity of the complexes makes it possible to apply the double mutant cycle method to evaluate the magnitudes of 24 different aromatic stacking interactions. The major trends in the interaction energy can be rationalised using a simple model based on electrostatic interactions between the pi-faces of the two aromatic rings. However, electrostatic interactions between the substituents of one ring and the pi-face of the other make an additional contribution, due to the slight offset in the stacking geometry. This property makes aromatic stacking interactions particularly sensitive to changes in orientation as well as the nature and location of substituents.     

Substituent effects on edge-to-face aromatic interactions

Chemical double mutant cycles have been used to measure the magnitude of edge-to-face aromatic interactions in hydrogen-bonded zipper complexes as a function of substituents on both aromatic rings. The interaction energies vary depending on the combination of substituents from +1.0 kJ mol-1 (repulsive), to -4.9 kJ mol-1 (attractive). The results correlate with the Hammett substituent constants which indicates that electrostatic interactions are responsible for the observed differences in interaction energy. The experiments can be rationalised based on local electrostatic interactions between the protons on the edge ring and the pi-electron density on the face ring as well as global electrostatic interactions between the overall dipoles on the two aromatic groups.     

Intermolecular pi-pi interactions in solids

A parameter-free DFT/CCSD(T) correction scheme is proposed for precise calculations (close to CCSD(T) accuracy) of weakly bound molecular solids. The correction scheme has been tested for solid benzene and graphite. The CCSD(T)/CBS correction to planewave DFT calculations reproduces the experimentally determined lattice constants for solid benzene. The calculated cohesive energy of benzene (457 meV per molecule) compares well with the experimental values of the heat of sublimation (460-560 meV per molecule). For graphite, the correction yields structural parameters (a = 2.46 A, c = 6.60 A) in good agreement with experiment (a = 2.46 A, c = 6.67 A). The calculated exfoliation energy of 54 meV per atom agrees fairly well with the most recent experimental value of 52 +/- 5 meV per atom.     

Substituent effects on the edge-to-face aromatic interactions

The edge-to-face interactions for either axially or facially substituted benzenes are investigated by using ab initio calculations. The predicted maximum energy difference between substituted and unsubstituted systems is approximately 0.7 kcal/mol (approximately 1.2 kcal/mol if substituents are on both axially and facially substituted positions). In the case of axially substituted aromatic systems, the electron density at the para position is an important stabilizing factor, and thus the stabilization/destabilization by substitution is highly correlated to the electrostatic energy. This results in its subsequent correlation with the polarization and charge transfer. Thus, the stabilization/destabilization by substitution is represented by the sum of electrostatic energy and induction energy. On the other hand, the facially substituted aromatic system depends on not only the electron-donating ability responsible for the electrostatic energy but also the dispersion interaction and exchange repulsion. Although the dispersion energy is the most dominating interaction in both axial and facial substitutions, it is almost canceled by the exchange repulsion in the axial substitution, whereas in the facial substitution, together with the exchange repulsion it augments the electrostatic energy. The systems with electron-accepting substituents (NO2, CN, Br, Cl, F) favor the axial substituent conformation, while those with electron-donating substituents (NH2, CH3, OH) favor the facial substituent conformation. The interactions for the T-shape complex systems of an aromatic ring with other counterpart such as H2, H2O, HCl, and HF are also studied.     

Implementation of pi-pi interactions in molecular dynamics simulation

No explicit pi-pi interaction term has been incorporated in the conventional molecular dynamics (MD) simulation programs in spite of its significant role in the folding of biomolecules and the clustering of organic chemicals. In this article, we propose a technique to emphasize the effect of pi-pi interactions using a function of energy and implement it into an MD simulation program. Several trial calculations show that the pi-pi incorporated program gives improved results consistent with experimental data on atom geometry and has no unfavorable interference with the conventional computational framework. This indicates an importance of the explicit consideration of pi-pi interactions in MD simulation.     

Substituent effects on non-covalent interactions with aromatic rings: insights from computational chemistry

Non-covalent interactions with aromatic rings pervade modern chemical research. The strength and orientation of these interactions can be tuned and controlled through substituent effects. Computational studies of model complexes have provided a detailed understanding of the origin and nature of these substituent effects, and pinpointed flaws in entrenched models of these interactions in the literature. Here, we provide a brief review of efforts over the last decade to unravel the origin of substituent effects in π-stacking, XH/π, and ion/π interactions through detailed computational studies. We highlight recent progress that has been made, while also uncovering areas where future studies are warranted.     

Interplay between cation-pi, anion-pi and pi-pi interactions.

The interplay between three important noncovalent interactions involving aromatic rings is studied by means of high level ab initio calculations. They demonstrate that very strong synergic effects are present in complexes where either cation–π or anion–π and π‐‐π interactions coexist. These strong synergic effects have been studied using the “atoms in molecules” theory and the physical nature of the interactions investigated by means of the molecular interaction potential with polarization (MIPp).     

Substituent effects in cyclohexenes

Summary The effects of the C¹-CH₃ group in the¹³C spectra of trans-4,5-dimethylcyclohex-4-ene-1,2-dicarboxylic and syn-txans-⁴-octalin-1,2-dicarboxylic acid and their diesters show the existence in solution of a considerable proportion of the trans-a,a forms of these compounds.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1310–1312, June, 1980.     

Dibenzoeilatin: a novel ligand exhibiting remarkable complementary pi-pi stacking interactions

The complex [Ru(bpy)2(dbneil)][PF6]2 forms discrete dimers in solution held by strong pi-pi stacking interactions via its distorted dibenzoeilatin ligand, indicating that planarity is not an obligatory requirement for achieving strong pi-stacking, as long as complementarity between the stacking moieties can be achieved.     

High-accuracy quantum mechanical studies of pi-pi interactions in benzene dimers

Although supramolecular chemistry and noncovalent interactions are playing an increasingly important role in modern chemical research, a detailed understanding of prototype noncovalent interactions remains lacking. In particular, pi-pi interactions, which are ubiquitous in biological systems, are not fully understood in terms of their strength, geometrical dependence, substituent effects, or fundamental physical nature. However, state-of-the-art quantum chemical methods are beginning to provide answers to these questions. Coupled-cluster theory through perturbative triple excitations in conjunction with large basis sets and extrapolations to the complete basis set limit have provided definitive results for the binding energy of several configurations of the benzene dimer, and benchmark-quality ab initio potential curves are being used to calibrate new density functional and force-field models for pi-pi interactions. Studies of substituted benzene dimers indicate flaws in the conventional wisdom about substituent effects in pi-pi interactions. Three-body and four-body interactions in benzene clusters have also been examined.     

Substituent effects on noncovalent halogen/π interactions: Theoretical study

Noncovalent halogen/π interactions of FCl with substituted benzenes have been investigated using ab initio calculations. It was shown that the predicted maximum interaction energy gap between the substituted and unsubstituted systems amounts to 1.14 kcal/mol, and therefore substituents on benzene have a pronounced effect on the strength of halogen/π interactions. While the presence of electron‐donating groups (NH₂, CH₃, and OH) on benzene enhances the interaction energy appreciably, an opposite effect is observed for electron‐accepting groups (NO₂, CN, Br, Cl, and F). The large gain of the attraction by electron correlation illustrates that the stabilities of the systems considered arise primarily from the dispersion interaction. Beside the dispersion interaction, the charge‐transfer interaction also plays an important role in halogen/π interactions, as a charge density analysis suggested. To provide more insight into the nature of halogen/π interactions, topological analysis of the electron density distribution and properties of bond critical points were determined in terms of the atoms in molecules (AIM) theory. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

From subtle to substantial: role of metal ions on pi-pi interactions

Quantum chemistry calculations reveal that the subtle pi-pi interactions, usually in the range 2-4 kcal/mol, will become substantially significant, from 6 to 17 kcal/mol, in the presence of metal ion. The metal ions have higher affinity toward a pi-pi dimer compared to a single pi-moiety. Considering the widespread occurrence of cation-pi-pi motifs in chemistry and biology, as evident from the database analysis, we propose that the two key noncovalent forces, which govern the macromolecular structure, cation-pi and pi-pi, work in concert.     

Substituent effects in C6F6-C6H5X stacking interactions

Parallel displaced and sandwich configurations of hexafluorobenzene-substituted benzene dimers are studied by ab initio molecular orbital methods up to the MP2(full)/aug-cc-pVDZ level of theory to reveal how substituents influence pi-pi interactions. Two minimum energy configurations are found, one with the substituent group away from the pi-face of the hexafluorobenzene ring (2a-f) and the other with the substituent group on top of the pi-face of the hexafluorobenzene (3a-f). Higher binding energies are predicted for dimers with the substituent on the pi-face (3a-f). All sandwich dimers (4a-e) are found to be saddle points on the potential energy surfaces. A parallel-displaced minimum energy configuration is also predicted for the parent complex, C6F6-C6H6, which is in contrast to predictions based on quadrupole moments of benzene and hexafuorobenzene. The preference for the parallel displaced, rather than the sandwich configuration, is rationalized based on the smaller interplanar distance in the former. The closeness of contact in the parallel-displaced dimers leads to greater binding energies. The shape of the electron density isosurface of the monomers is suggested to provide a guide for the prediction of how arenes stack with one another. A large difference in binding energy between the C6F6 complex of aniline (3e) and N,N-dimethylaniline (3f) is calculated, and charge-transfer interactions are suggested to play a role in the latter.     

Estimates of the ab initio limit for pi-pi interactions: the benzene dimer

State-of-the-art electronic structure methods have been applied to the simplest prototype of aromatic pi-pi interactions, the benzene dimer. By comparison to results with a large aug-cc-pVTZ basis set, we demonstrate that more modest basis sets such as aug-cc-pVDZ are sufficient for geometry optimizations of intermolecular parameters at the second-order M?ller-Plesset perturbation theory (MP2) level. However, basis sets even larger than aug-cc-pVTZ are important for accurate binding energies. The complete basis set MP2 binding energies, estimated by explicitly correlated MP2-R12/A techniques, are significantly larger in magnitude than previous estimates. When corrected for higher-order correlation effects via coupled cluster with singles, doubles, and perturbative triples [CCSD(T)], the binding energies D(e) (D(0)) for the sandwich, T-shaped, and parallel-displaced configurations are found to be 1.8 (2.0), 2.7 (2.4), and 2.8 (2.7) kcal mol(-1), respectively.     

Anion-pi and pi-pi cooperative interactions regulating the self-assembly of nitrate-triazine-triazine complexes

We theoretically investigate the cooperative enhancement of the interactions between anions and electron-deficient aromatics by pi-pi stacking, focusing on the recent crystallographic observation of anion-pi-pi interactions in a synthesized coordination compound based on 1,3,5-triazine moieties. Using a combination of state-of-the-art dispersion-corrected density functional and quantum Monte Carlo calculations, we rationalize the unusual structural features observed in this nitrate-triazine-triazine complex. We show that the triazine rings are staggered and bent and slip with respect to each other with the nitrate bound off-center in a T-like configuration. Our results indicate that this pi-pi stacking is not simply enforced by the coordination of the triazines within the particular crystal structure but is regulated by cooperative anion-pi and pi-pi interactions. In the nitrate-triazine-triazine complex, this cooperative effect amounts to 6% of the total binding energy. Ways to further increase this energetic enhancement in the design of anion-host architectures are discussed.     

Beyond the benzene dimer: an investigation of the additivity of pi-pi interactions

The benzene dimer is the simplest prototype of pi-pi interactions and has been used to understand the fundamental physics of these interactions as they are observed in more complex systems. In biological systems, however, aromatic rings are rarely found in isolated pairs; thus, it is important to understand whether aromatic pairs remain a good model of pi-pi interactions in clusters. In this study, ab initio methods are used to compute the binding energies of several benzene trimers and tetramers, most of them in 1D stacked configurations. The two-body terms change only slightly relative to the dimer, and except for the cyclic trimer, the three- and four-body terms are negligible. This indicates that aromatic clusters do not feature any large nonadditive effects in their binding energies, and polarization effects in benzene clusters do not greatly change the binding that would be anticipated from unperturbed benzene-benzene interactions, at least for the 1D stacked systems considered. Three-body effects are larger for the cyclic trimer, but for all systems considered, the computed binding energies are within 10% of what would be estimated from benzene dimer energies at the same geometries.