High-level ab initio calculations show that the most stable stacking for benzene−cyclohexane is 17% stronger than that for benzene− benzene. However, as these systems are displaced horizontally the benzene− benzene attraction retains its strength. At a displacement of 5.0 Å, the benzene−benzene attraction is still ∼70% of its maximum strength, while benzene−cyclohexane attraction has fallen to ∼40% of its maximum strength. Alternatively, the radius of attraction (>2.0 kcal/mol) for benzene−benzene is 250% larger than that for benzene−cyclohexane. Thus, at relatively large distances aromatic rings can recognize each other, a phenomenon that helps explain their importance in protein folding and supramolecular structures.

Stacking interactions between six-membered resonance-assisted hydrogen-bridged (RAHB) rings and C6-aromatic rings have been studied by analyzing crystal structures in the Cambridge Structural Database and performing quantum chemical calculations.

Stacking interactions of resonance-assisted hydrogen-bridged rings are quite common, as 44% of their crystal structures show mutually parallel contacts. Highlevel quantum-chemical calculations by the CCSD(T)/CBS method indicate that these interactions are quite strong, up to −4.7 kcal/mol. This strength is comparable to the stacking interactions of saturated hydrogen-bridged rings (−4.9 kcal/mol), while it is substantially stronger than stacking interaction between two benzene molecules (−2.7 kcal/mol). Symmetry-adapted perturbation theory energy decomposition analysis shows that the dispersion component makes the major contribution in total interaction energy, but it is mostly canceled by the exchange-repulsion term in some systems, while electrostatic attraction terms are very significant in all systems. The electrostatic terms can be dominant or similar to the net dispersion term.

In the crystal structures of methylated cyclopentadienyl (Cp) complexes (MeCp, Me4Cp and Me5Cp) deposited in the Cambridge Structural Database, certain orientation types of stacked contacts can be noted as the most frequent. These orientation preferences can be well explained by the matching of oppositely charged regions of electrostatic potential. Parallel displaced stacking, large offset stacking and C—H…π interactions are the dominant interaction types that are responsible for the arrangement in the crystal structures of stacked methylated Cp complexes.

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The Cambridge Structural Database (CSD) is searched for mutual contacts between six-membered resonance-assisted hydrogenbridged rings (RAHB) (the example of a fragment is shown in Fig. 1a) [1] and for contacts between six-membered RAHB rings and C6-aromatic rings (Fig. 1b). There is a quite large prevalence of parallel contacts in the set of RAHB/RAHB contacts, since 91% from totally 678 contacts found are parallel contacts, mostly with antiparallel orientation of the rings [1]. At the other side, the prevalence of parallel contacts in the set of RAHB/C6-aromatic contacts is not so pronounced, since 59% from totally 677 contacts found are parallel contacts. The distances between the interacting ring planes are mostly between 3.0 and 4.0 Å, while horizontal displacements are mostly in the range 0.0-3.0 Å in both parallel RAHB/RAHB and RAHB/C6-aromatic contacts. Figure 1. The examples of fragments used in CSD search for a) six-membered RAHB/RAHB contacts; b) six-membered RAHB/C6aromatic contactsThe interaction energy calculations were performed on stacked dimer model systems based on abundance in the CSD. The strongest calculated RAHB/RAHB interaction is -4.7 kcal/mol, while the strongest calculated RAHB/benzene interaction is significantly weaker -3.7 kcal/mol. However, RAHB/RAHB stacking interactions can be stronger or weaker than the corresponding RAHB/benzene stacking interactions, depending on the RAHB ring system. The Symmetry Adopted Perturbation Theory (SAPT) calculations show that the dominant contribution in total RAHB/RAHB stacking interaction energy is the dispersion term, which can be mostly or completely cancelled by the exchange repulsion term, hence, the electrostatic term can be effectively dominant. Depending on the RAHB ring system, the electrostatic contribution can be practically equal to the net dispersion contribution (the sum of dispersion and exchange-repulsion terms) [1]. The electrostatic term is effectively dominant in all RAHB/benzene systems observed, due to the almost complete cancellation of the dispersion by the exchange-repulsion terms.

The stacking contacts between two resonance-assisted hydrogenbridged (RAHB) rings and stacking contacts between RAHB rings and C 6aromatic groups are frequently found at large horizontal displacements in the crystal structures found in the Cambridge Structural Database (CSD), particularly in the range of 4.0−6.0 and 5.5−6.5 Å, respectively. Ab initio calculations reveal that interactions at large offsets, although weaker than interactions at smaller offsets, can be significant, since a large portion of interaction energy (in some systems up to 66%) can be preserved upon shifting to larger offset values.