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 electron correlation, at the MP2/6-31G** level. The aggregate size was defined 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 was collinear and normal to these planes, the angles between each of the three C+−C bonds and an axis perpendicular to the planes were equal, and the ions in the central triple ion moved freely along this axis. Starting from the C 3h form preferred by the isolated carbocation, geometry optimization led to a C s conformation, by methyl group rotation. The C 3v form of the cation maintained its conformation upon optimization. The stabilities of these two conformations cannot be fairly compared, because the interionic equilibrium distances are different. (The aggregate with a C 3v cation is lower in energy by 1.9 kcal/mol at L = 12.658 Å). At the second level of complexity, no restraint was placed upon carbocation orientation. The C 3v form did not change from the previous case, but in the C s form the plane of the cation was tilted by 16−18° from the perpendicular orientation and 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 relative to the Li planes. The C s aggregate geometry was unchanged, but the C 3 v aggregate exhibited a very flat energy surface, optimizing ultimately with the cation within coordinating distance (1.655 Å) from the F atom 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 different relative orientations of near-equal energy and with the same carbocation geometry occurred, but in the end optimization gave an aggregate with the same cation geometry and about the same relative orientation of ions as in the previous case. Thus, the geometry of the cation shows little sensitivity to the degree of freedom of movement of ions within the aggregate. Optimization of a triple ion with frozen interionic distances gave the same structure for the carbocation as the aggregate which got optimized to the same interionic distances, thus showing that geometry optimizations at fixed interionic distances give reliable structures for carbocations in ion pairs or aggregates.