Theoretical study of the geometrical and electronic structures and thermochemistry of spherophanes

A set of supramolecular cage-structures—spherophanes—was studied at the density functional B3LYP level. Full geometrical structure optimisations were made with 6–31G and 6–31G(d) basis sets followed by frequency calculations, and electronic energies were evaluated at B3LYP/6–31++G(d,p). Three different symmetries were considered: C1, Ci, and Oh. It was found that the bonds between the benzene rings are very long to allow π-electron delocalisation between them. These spherophanes show portal openings of 2.596 A in Spher1, 4.000 A in Meth2, 3.659 A in Oxa3, and 4.412 A in Thia4. From the point of view of potential host–guest interaction studies, it should also be noted that the atoms nearest to the centre of the cavities are carbons bonded to X groups. These supramolecules seem to exhibit relatively large gap HOMO−LUMO: 2.89 eV(Spher1), 5.26 eV(Meth2), 5.73 eV(Oxa3), and 4.82 eV(Thia4). The calculated ΔH°f (298.15 K) values at B3LYP/6–31G(d) are (in kcal mol−1) 750.98, 229.78, −10.97, and 482.49 for Spher1, Meth2, Oxa3, and Thia4, respectively. Using homodesmotic reactions, relative to Spher1, the spherophanes Meth2, Oxa3, and Thia4 are less strained by −399.13 kcal mol−1, −390.40 kcal mol−1, and −411.38 kcal mol−1, respectively. Their infrared and 13C NMR calculated spectra are reported.