Interplay of π-Electron Delocalization and Strain in [<i>n</i>](2,7)Pyrenophanes

The geometries of a series of [n](2,7)pyrenophanes (n = 6−12) were optimized at the B3LYP/6-311G** DFT level. The X-ray crystal structures determined for the [9](2,7)- and [10](2,7)pyrenophanes agreed excellently with the computed structures. The degree of nonplanarity of the pyrene moiety depends on the number of CH2 groups in the aliphatic bridge and, as analyzed theoretically, influences the strain energy and the extent of π-electron delocalization in the pyrene fragment. Various indices, e.g., the relative aromatic stabilization energies (ΔASE), magnetic susceptibility exaltations (Λ), nucleus-independent chemical shifts (NICS), and the harmonic oscillator model of aromaticity (HOMA) were used to quantify the change in aromatic character of the pyrene fragment. ΔASE and relative Λ values (with respect to planar pyrene) were evaluated by homodesmotic equations comparing the bent pyrene unit with its bent quinoid dimethylene-substituted analog. The bend angle, α, ΔASE, and Λ were linearly related. The aromaticity decreases smoothly and regularly over a wide range of bending, but the magnitude of the change is not large. The differences between planar pyrene (α = 0°) and the most distorted pyrene unit (α = 39.7° in [6](2,7)pyrenophane) are only 15.8 kcal/mol (ΔASE) and 18.8 cgs-ppm (Λ). Also, the geometry-based HOMA descriptor changes by only 0.07 unit. The local NICS descriptors of aromatic character also correlate very well with the global indices of aromaticity. In line with the known reactivity of pyrenophanes, the variations of NICS(1), a measure of π-electron delocalization, were largest for the outer, biphenyl-type rings. The strain energies of the pyrene fragments were much larger and varied more than those evaluated for the bridge. Both strain energies were interrelated (correlation coefficient R = 0.979) and depend on the bend angle, α.