Ab-initio based 13C NMR shift calculations as a probe for carbocation structure. Homoaromaticity and rearrangements of the C9H9+ ion

Abstract

Geometries and energies of C₉H₉⁺ ions, in particular the 1,4-bishomotropylium cation (1) and the barbaralyl cation (3), have been calculated at the HF/6-31G(d) and MP2/6-31G(d)/HF/6-31G(d) level of theory. MP2 theory predicts, for 1, a folded structure (folding angle 93°) with distances r(2,9)=r(5,7) being ca. 2 Å. The corresponding parameters for the classic analogue of 1, the dihydroindenyl cation (2), are 114°(folding angle) and 2.34 Å[distance r(2,9)]. At MP2, 1 is 14 kcal mol^–1 more stable than 2. However, a comparison of the relative energies of various C₉H₉⁺ structure reveals that MP2/6-31G(d)/HF/6-31G(d) is not sufficient to provide a reliable prediction of the relative stabilities of these ions. More useful are IGLO/6-31G(d) values of ¹³C chemical shifts which characterize 1 to be a bishomoaromatic ion. Also, they confirm that a precursor of 1 is the barbaralyl cation 3 and that 3 can undergo sixfold degenerate divinycyclopropylcarbinyl rearrangements.