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.     

Modeling pi-pi interactions with the effective fragment potential method: the benzene dimer and substituents

This study compares the results of the general effective fragment potential (EFP2) method to the results of a previous combined coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] and symmetry-adapted perturbation theory (SAPT) study [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690] on substituent effects in pi-pi interactions. EFP2 is found to accurately model the binding energies of the benzene-benzene, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile dimers, as compared with high-level methods [Sinnokrot and Sherrill, J. Am. Chem. Soc., 2004, 126, 7690], but at a fraction of the computational cost of CCSD(T). In addition, an EFP-based Monte Carlo/simulated annealing study was undertaken to examine the potential energy surface of the substituted dimers.     

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.     

Understanding of assembly phenomena by aromatic-aromatic interactions: benzene dimer and the substituted systems

Interactions involving aromatic rings are important in molecular/biomolecular assembly and engineering. As a consequence, there have been a number of investigations on dimers involving benzene or other substituted pi systems. In this Feature Article, we examine the relevance of the magnitudes of their attractive and repulsive interaction energy components in governing the geometries of several pi-pi systems. The geometries and the associated binding energies were evaluated at the complete basis set (CBS) limit of coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] using a least biased scheme for the given data set. The results for the benzene dimer indicate that the floppy T-shaped structure (center-to-center distance: 4.96 A, with an axial benzene off-centered above the facial benzene) is isoenergetic in zero-point-energy (ZPE) corrected binding energy (D0) to the displaced-stacked structure (vertical interplanar distance: 3.54 A). However, the T-shaped structure is likely to be slightly more stable (D0 approximately equal to 2.4-2.5 kcal/mol) if quadruple excitations are included in the coupled cluster calculations. The presence of substituents on the aromatic ring, irrespective of their electron withdrawing or donating nature, leads to an increase in the binding energy, and the displaced-stacked conformations are more stabilized than the T-shaped conformers. This explains the wide prevalence of displaced stacked structures in organic crystals. Despite that the dispersion energy is dominating, the substituent as well as the conformational effects are correlated to the electrostatic interaction. This electrostatic origin implies that the substituent effect would be reduced in polar solution, but important in apolar media, in particular, for assembling processes.     

Substituent effects in the benzene dimer are due to direct interactions of the substituents with the unsubstituted benzene

The prevailing views of substituent effects in the sandwich configuration of the benzene dimer are flawed. For example, in the polar/pi model of Cozzi and co-workers (J. Am. Chem. Soc. 1992, 114, 5729), electron-withdrawing substituents enhance binding in the benzene dimer by withdrawing electron density from the pi-cloud of the substituted ring, reducing the repulsive electrostatic interaction with the nonsubstituted benzene. Conversely, electron-donating substituents donate excess electrons into the pi-system and diminish the pi-stacking interaction. We present computed interaction energies for the sandwich configuration of the benzene dimer and 24 substituted dimers, as well as sandwich complexes of substituted benzenes with perfluorobenzene. While the computed interaction energies correlate well with sigmam values for the substituents, interaction energies for related model systems demonstrate that this trend is independent of the substituted ring. Instead, the observed trends are consistent with direct electrostatic and dispersive interactions of the substituents with the unsubstituted ring.     

Multicoefficient extrapolated density functional theory studies of pi...pi interactions: the benzene dimer

We report tests of new (2005) and established (1999-2003) multilevel methods against essentially converged benchmark results for nonbonded interactions in benzene dimers. We found that the newly developed multicoefficient extrapolated density functional theory (DFT) methods (which combine DFT with correlated wave function methods) give better performance than multilevel methods such as G3SX, G3SX(MP3), and CBS-QB3 that are based purely on wave function theory (WFT); furthermore, they have a lower computational cost. We conclude that our empirical approach for combining WFT methods with DFT methods is a very efficient and effective way for describing not only covalent interactions (as shown previously) but also nonbonded interactions.     

Calculation of intermolecular interactions in the benzene dimer using coupled-cluster and local electron correlation methods

Potential energy curves for the parallel-displaced, T-shaped and sandwich structures of the benzene dimer are computed with density fitted local second-order M?ller-Plesset perturbation theory (DF-LMP2) as well as with the spin-component scaled (SCS) variant of DF-LMP2. While DF-LMP2 strongly overestimates the dispersion interaction, in common with canonical MP2, the DF-SCS-LMP2 interaction energies are in excellent agreement with the best available literature values along the entire potential energy curves. The DF-SCS-LMP2 dissociation energies for the three structures are also compared with new complete basis set estimates of the interaction energies obtained from accurate coupled cluster (CCSD(T)) and DF-SCS-MP2 calculations. Since LMP2 is essentially free of basis set superposition errors, counterpoise corrections are not required. As a result, DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger pi-stacked systems such as truncated sections of DNA.     

Electronic structure of the benzene dimer cation

The benzene and benzene dimer cations are studied using the equation-of-motion coupled-cluster model with single and double substitutions for ionized systems. The ten lowest electronic states of the dimer at t-shaped, sandwich, and displaced sandwich configurations are described and cataloged based on the character of the constituent fragment molecular orbitals. The character of the states, bonding patterns, and important features of the electronic spectrum are explained using qualitative dimer molecular orbital linear combination of fragment molecular orbital framework. Relaxed ground state geometries are obtained for all isomers. Calculations reveal that the lowest energy structure of the cation has a displaced sandwich structure and a binding energy of 20 kcal/mol, while the t-shaped isomer is 6 kcal/mol higher. The calculated electronic spectra agree well with experimental gas phase action spectra and femtosecond transient absorption in liquid benzene. Both sandwich and t-shaped structures feature intense charge resonance bands, whose location is very sensitive to the interfragment distance. Change in the electronic state ordering was observed between sigma and piu states, which correlate to the B and C bands of the monomer, suggesting a reassignment of the local excitation peaks in the gas phase experimental spectrum.     

A density-functional study on pi-aromatic interaction: benzene dimer and naphthalene dimer

The long-range correction (LC) scheme of density-functional theory (DFT) was applied to the calculation of the pi-aromatic interaction of the benzene dimer and naphthalene dimer. In previous calculations, it was confirmed that the LC scheme [Iikura et al., J. Chem. Phys. 115, 3540 (2001)] gives very accurate potential- energy surfaces (PESs) of small van der Waals (vdW) complexes by combining with the Anderson-Langreth-Lundqvist (ALL) vdW correlation functional [Andersson et al., Phys. Rev. Lett. 76, 102 (1996)] (LC-DFT + ALL). In this study, LC-DFT+ALL method was examined by calculating a wide range of PES of the benzene dimer including parallel, T-shaped, and parallel-displaced configurations. As a result, we succeeded in reproducing very accurate PES within the energy deviance of less than 1 kcalmol in comparison with the results of high-level ab initio molecular-orbital methods at all reference points on the PES. It was also found that LC-DFT + ALL gave accurate results independent of exchange-correlation functional used, in contrast with the strong functional dependencies of conventional pure functionals. This indicates that both exchange repulsion and van der Waals attractive interactions should be correctly incorporated in conventional pure functionals in order to calculate accurate pi-aromatic interactions. We also found that LC-DFT + ALL method has a low basis-set dependency in the calculations of pi-aromatic interactions. The present scheme was also successfully applied to the pi,[ellipsis (horizontal)],pi stacking interactions of naphthalene dimer. This may suggest that LC-DFT + ALL method would be a powerful tool in the calculations of large molecules such as biomolecules.     

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 in pi-pi interactions: sandwich and T-shaped configurations

Sandwich and T-shaped configurations of benzene dimer, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile are studied by coupled-cluster theory to elucidate how substituents tune pi-pi interactions. All substituted sandwich dimers bind more strongly than benzene dimer, whereas the T-shaped configurations bind more or less favorably depending on the substituent. Symmetry-adapted perturbation theory (SAPT) indicates that electrostatic, dispersion, induction, and exchange-repulsion contributions are all significant to the overall binding energies, and all but induction are important in determining relative energies. Models of pi-pi interactions based solely on electrostatics, such as the Hunter-Sanders rules, do not seem capable of explaining the energetic ordering of the dimers considered.     

Aggregation of imine-based metallo-supramolecular architectures through pi-pi interactions

The design of supramolecular architectures based on isoquinoline-imine ligand systems is described. The isoquinoline affords an extended pi surface and the use of this surface to obtain self-recognition and consequent pi-pi aggregation is investigated. The approach is effective in that each of four complexes is observed to aggregate through these interactions. Other pi-pi interactions can interfere with the aggregation indicating that a larger pi-surface may be required to obtain complete control over the aggregation of the units.     

Lone pair-pi and pi-pi interactions play an important role in proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET), a class of formal hydrogen atom transfer (HAT) reactions, is of widespread interest because it is implicated in a broad range of chemical and biochemical processes. PCET is typically differentiated from HAT by the fact that it occurs when a proton and electron are transferred between different sets of molecular orbitals. Previous theoretical work predicted that hydrogen bonding between reactants is a necessary but not sufficient condition for H exchanges to take place by PCET. This implies that HAT is the only mechanism for H exchange between two carbon atoms. In this work, we present computational results that show that the H exchange in the tert-butylperoxyl/phenol couple, a prototypical antioxidant exchange reaction, occurs by PCET and that the transfer of the electron can occur via an oxygen lone pair-ring pi overlap. We then show that the H exchange in a model for the tyrosyl/tyrosine couple, which is implicated in ribonucleotide reductase chemistry, occurs via PCET and that one path for the electron transfer is provided by a strong pi-stacking interaction. Finally, we show that a pi-stacking interaction in the benzyl/toluene couple, a system in which there is no H-bonding, can result in this exchange occurring via PCET to some extent. Collectively, these results indicate that PCET reactions are not unique to systems that can engage in H-bonding and that lone pair-pi and pi-pi interactions in these systems may be more important than previously understood.     

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.     

Aromatic-aromatic interactions in proteins: beyond the dimer

Aromatic residues are key widespread elements of protein structures and have been shown to be important for structure stability, folding, protein-protein recognition, and ligand binding. The interactions of pairs of aromatic residues (aromatic dimers) have been extensively studied in protein structures. Isolated aromatic molecules tend to form higher order clusters, like trimers, tetramers, and pentamers, that adopt particular well-defined structures. Taking this into account, we have surveyed protein structures deposited in the Protein Data Bank in order to find clusters of aromatic residues in proteins larger than dimers and characterized them. Our results show that larger clusters are found in one of every two unique proteins crystallized so far, that the clusters are built adopting the same trimer motifs found for benzene clusters in vacuum, and that they are clearly nonlocal brining primary structure distant sites together. We extensively analyze the trimers and tetramers conformations and found two main cluster types: a symmetric cluster and an extended ladder. Finally, using calmodulin as a test case, we show aromatic clsuters possible role in folding and protein-protein interactions. All together, our study highlights the relevance of aromatic clusters beyond the dimer in protein function, stability, and ligand recognition.     

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.     

Direct infrared absorption spectroscopy of benzene dimer

The direct infrared (IR) absorption spectrum of benzene dimer formed in a free-jet expansion was recorded in the 3.3 μm region for the first time. This has led to the observation of the C-H stretching fundamental mode ν(13) (B(1u)), which is both IR and Raman forbidden in the monomer. Moreover, the IR forbidden and Raman allowed ν(7) (E(2g)) mode has been observed as well. These two modes were found to be red-shifted along with the IR allowed ν(20) (E(1u)) mode, as previously reported by Erlekam et al. [Erlekam; Frankowski; Meijer; Gert von Helden J. Chem. Phys.2006, 124, 171101], using ion-dip spectroscopy, contrary to the blue-shift predicted earlier by theoretical studies. The observation of the ν(13) band indicates that the symmetry is reduced in the dimer, confirming the T-shaped structure observed by Erlekam et al. Our experimental results have not provided any direct evidence for the presence of the parallel displaced geometry, the main objective of the present work, as predicted by theoretical calculations.     

Electronic states of the benzene dimer: a simple case of complexity

Electronic structure calculations of the excited states of the benzene dimer using equation-of-motion coupled-cluster method are reported. The calculations reveal large density of electronic states, including multiple valence, Rydberg, and mixed Rydberg-valence states. The calculations of the oscillator strengths for the transitions between the excimer state (i.e., the lowest excited state of the dimer, 1(1)B(1g)) and other excited states allowed us to identify the target state responsible for the excimer absorption as the E(1u) state of a mixed Rydberg-valence character at 3.04 eV above the excimer (1(1)B(1g)). Although at D(6h) the 1(1)B(1g) → E(1u) transition is symmetry-forbidden, small geometric displacements (to D(2h)) that have a negligible effect on the excitation energy split this degenerate state into the dark (4B(3u)) and bright (4B(2u)) components (oscillator strength of 0.3 au). The excitation energy for this transition depends strongly on the dimer structure, which explains the broad character of the experimentally observed excimer absorption spectrum.