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 Møller-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.

State-of-the-art electronic structure theory has been applied to generate potential energy curves for the sandwich, T-shaped, and parallel-displaced configurations of the simplest prototype of aromatic π−π interactions, the benzene dimer. Results were obtained using second-order Møller−Plesset perturbation theory (MP2) and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] with different augmented, correlation-consistent basis sets. At the MP2 level, the smallest basis set used (a modified aug-cc-pVDZ basis) underestimates the binding by ∼0.5 kcal mol-1 at equilibrium and by ∼1 kcal mol-1 at smaller intermonomer distances compared to results with a modified aug-cc-pVQZ basis (denoted aug-cc-pVQZ*). The best MP2 binding energies differ from the more accurate CCSD(T) values by up to 2.0 kcal mol-1 at equilibrium and by more than 2.5 kcal mol-1 at smaller intermonomer distances, highlighting the importance of going beyond MP2 to achieve higher accuracy in binding energies. Symmetry adapted perturbation theory is used to analyze interaction energies in terms of electrostatic, dispersion, induction, and exchange-repulsion contributions. The high-quality estimates of the CCSD(T)/aug-cc-pVQZ* potential energy curves for the benzene dimer presented here provide a better understanding of how the strength of π−π interactions varies with distance and orientation of the rings and will assist in the development of approximate methods capable of modeling weakly bound π−π systems.

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.

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.

State-of-the-art electronic structure methods have been applied to obtain the first high-quality theoretical results for substituent effects in π-stacking interactions. The sandwich configurations of benzene dimer, benzene−phenol, benzene−toluene, benzene−fluorobenzene, and benzene−benzonitrile have been studied using correlation consistent basis sets augmented by multiple diffuse functions, namely aug-cc-pVDZ and aug-cc-pVTZ, at the second-order perturbation theory (MP2) level. Coupled-cluster computations with perturbative triples [CCSD(T)] were performed and combined with the above MP2 calculations to estimate the CCSD(T)/aug-cc-pVTZ binding energies, which should be accurate within several tenths of a kcal mol-1. All substituted dimers bind more strongly than benzene dimer, with benzene−benzonitrile binding the most strongly. Both electrostatic and dispersion interactions contribute to the increased binding of the monosubstituted dimers.