Theoretical studies of carbocations in ion pairs. Part 3. The tert-butyl cation in an ionic aggregate

The structure of the tert-butyl cation in the five-ion aggregate Li+.H3BF-. Me3C+.FBH3-.Li+ was studied by high level ab initio MO calculations, with e lectron correlation, at the MP2/6-31G** level. The aggregate size was defin ed by the distance L between two parallel planes. One Li+ ion moves freely within each plane. At the first level of complexity, each Li..B..F group wa s collinear and normal to these planes, the angles between each of the thre e C+-C bonds and an axis perpendicular to the planes were equal, and the io ns in the central triple ion moved freely along this axis. Starting from th e C-3h form preferred by the isolated carbocation, geometry optimization le d to a C-s conformation, by methyl group rotation, The C-3v form of the cat ion maintained its conformation upon optimization. The stabilities of these two conformations cannot be fairly compared, because the interionic equili brium distances are different. (The aggregate with a C-3v cation is lower i n energy by 1.9 kcal/mol at L = 12.658 Angstrom). At the second level of co mplexity, no restraint was placed upon carbocation orientation. The C-3v fo rm did not change from the previous case, but in the C-s form the plane of the cation was tilted by 16-18 degrees from the perpendicular orientation a nd the bond lengths and angles for the C-H's facing the closest anion were slightly changed. In the third stage, the Li..B..F axes could also tilt rel ative to the Li planes. The C-s aggregate geometry was unchanged, but the C -3v aggregate exhibited a very flat energy surface, optimizing ultimately w ith the cation within coordinating distance (1.655 Angstrom) from the F ato m of the nearest anion. Finally, the collinearity of the Li..B..F group was also released for the C-s aggregate. The oscillation between slightly diff erent relative orientations of near-equal energy and with the same carbocat ion geometry occurred, but in the end optimization gave an aggregate with t he same cation geometry and about the same relative orientation of ions as in the previous case. Thus, the geometry of the cation shows little sensiti vity to the degree of freedom of movement of ions within the aggregate. Opt imization of a triple ion with frozen interionic distances gave the same st ructure for the carbocation as the aggregate which got optimized to the sam e interionic distances, thus showing that geometry optimizations at fixed i nterionic distances give reliable structures for carbocations in ion pairs or aggregates.