On the Importance of Electron Correlation Effects for the π‐π Interactions in Cyclophanes

Abstract

Correlated ab initio quantum chemical methods based on second-order perturbation theory and density functional theory (DFT) together with large atomic orbital (AO) basis sets are used to calculate the structures of four cyclophanes with two aromatic rings and one sulphur-containing phane with one aromatic ring. The calculated geometrical data for [2.2]paracyclophane, cyclophane (superphane), 8,16-dimethyl[2.2]metacyclophane, 16-methyl[2.2]metaparacyclophane, and 2,6,15-trithia[3(4,10)][7]metacyclophane are compared to experimental data from X-ray crystal structure determinations. In all cases, very accurate theoretical predictions are obtained from the recently developed spin-component-scaled MP2 (SCS-MP2) method, in which the deviations are within the experimental accuracy and expected crystal-packing or vibrational effects. Especially the inter-ring distances, which are determined by a detailed balance between attractive van der Waals (dispersive) and repulsive (Pauli) contributions, are very sensitive to the level of theory employed. While standard MP2 theory in general overestimates the dispersive interactions (pi-pi correlations) between the two aromatic rings leading to too short distances (between 3 and 8 pm), the opposite is observed for DFT methods (errors up to 15 pm). This indicates that an explicit account of dispersive-type electron correlation effects between the clamped aromatic units is essential for a quantitative description of cyclophane structures. In order to distinguish these effects from "normal" van der Waals interactions, the term "overlap-dispersive" interaction may be employed. The popular B3 LYP hybrid density functional offers no advantage over the pure PBE functional that at least qualitatively accounts for some of the dispersive effects. The use of properly polarized AO basis sets of at least valence-triple-zeta quality is strongly recommended to obtain quantitative predictions with traditional wave function methods.

Do Special Noncovalent π–π Stacking Interactions Really Exist?

“…For systems with about ten carbon atoms or less, there is little theoretical evidence for a special role of the p orbitals. This view is supported by experimental phasechange data for hydrocarbons, and even extreme cases, such as intramolecular p-p stacking in cyclophanes, [29] fit in. Thus, the term "p-p stacking" should be used as a geometrical descriptor of the interaction mode in unsaturated molecules and to understand p-p interactions as a special type of electron correlation (dispersion) effect that can only act in large unsaturated systems when they are spatially close, which is only possible in the stacked orientation.…”

Modulation of Stacking Interactions by Transition‐Metal Coordination: Ab Initio Benchmark Studies

“…In its original form proposed by Grimme, the scaling parameters were optimised to improve on MP2 for a wide range of thermodynamic, kinetic and geometrical properties. [30] Three further variants of SCS have been employed, all specifically optimised for description of non-covalent interactions. The first, termed SCSN, uses new scaling parameters to improve DF-LMP2/AVTZ* prediction of binding energy for stacked nucleic acid base pairs.…”

N,N‐Dimethylaminopropylsilane: A Case Study on the Nature of Weak Intramolecular Si⋅⋅⋅N Interactions

“…The shortest Si···N distance is predicted by the MP2 calculation; this again reflects the importance of dispersion interactions, which are known to be overestimated by MP2. [14] Si···N potential-energy curve of 3 a: The ab initio Si···N deformation potential of 3 a (Figure 10) is very shallow. Any Scheme 2.…”