No abstract

No abstract

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.

The structure of the tert-butyl cation (1) ion-paired with the trihydrofluoroborate anion (A), previously shown to be appropriate for such studies, was investigated by ab initio calculations, as a function of the interionic distance in the ion pair (d). At short distance (d ) 2.25 Å), the lowest energy cation conformation was a slightly distorted C s form. At intermediate distances (d ) 2.60, 2.95, 3.30, and 3.65 Å), the preferred geometry had a C 3V conformation, and at d ) 4.0 Å the cation adopted again a C s -type conformation, but the anion was no longer in the space above the carbon skeleton of the cation and it was tilted, interacting strongly with only one of the hydrogen atoms. Finally, at d ) 4.5 Å, the anion moved to the side of the cation, also interacting with only one hydrogen atom, whereas the cation adopted an asymmetric geometry, close to the C 3h form preferred by the isolated carbocation. Examination of spectral properties could indicate the average or most probable interionic distance in solution. Thus, the Raman spectrum had been interpreted as indicating a C 3V form of the cation, which suggests an interionic distance in the intermediate range. The insensitivity of cation structure to the nature of the anion for interionic distances beyond recombination range has been established by a comparison of anion A with the tetrafluoroborate anion (B). Optimization of the cation geometry in the triple ion A.1.A, held at the interionic distance found in the crystal, showed that the C s form with two hydrogens facing the farthest anion was the most stable, but the C s form with two hydrogens facing the nearest anion was almost equal in energy and the two C 3V forms (three hydrogens facing the farthest and the nearest anion, respectively) were only slightly less stable. The preferred geometry of the cation in the triple ion was the same as that found previously in a more complex aggregate, in which the cation and the two anions were allowed to move freely. This result shows that geometry optimizations at fixed interionic distances give reliable structures for carbocations in ion pairs or aggregates. The similar stability of the C s and C 3V conformations in the triple ion is in agreement with the identification of two sets of hydrogens, each twisted by 60°against the second set, for two of the methyl groups of the tert-butyl cation in the crystal.

No abstract