Theoretical studies of carbocations in ion pairs. 5. Structures and interconversion of the 3-methyl-2-butyl cation and 2,3-dimethyl-1-protonated cyclopropane

The structures of carbocations formed in the ionization of 3-methyl-2-butyl precursors were investigated by high level ab initio MO calculations. The relative stability of the 3-methyl-2-butyl cation (3) increased upon placem ent in a dielectric medium using SCRF calculations, but the 2,3-dimethyl-1- protonated cyclopropanes (5) were still more stable, as they were in vacuum , introduction of negative point charges in single-point calculations on th e structures of isolated ions made the open ion more stable than the bridge d isomers and increased the stability difference favoring trans-5 over cis- 5. The structure and stabilities of 3 and trans-5 in ion pairs were examine d with two counterions successfully used in previous studies, trihydrofluor oborate (FBH3-, A) at short interionic distances (d) and dihydrolithiate (L iH2-, B) at longer distances. Optimization (MP2/6-31G*) of trans-5.A with t he anion free to move in a plane parallel to the C1C2C3 plane at d = 2.3 An gstrom gives 3.A as the only energy minimum. The position of the anion is d etermined by electrostatic interaction with C2 and hydrogen atoms at C1 and C5. At 2.6 Angstrom trans-5.A also opens, but the anion in the resulting 3 .A moves toward C1 and forms 3-methyl-1-butene by elimination. Rotation of the cation to the conformation in which the hydrogen at C3 of 3.A faces the anion at d = 2.6 Angstrom leads to 2-methyl-2-butene. Optimization at long er interionic distances with the anion (B) placed above C2, along a line pe rpendicular to the C1C2C3, plane, shows 3,B as the only stable entity up to d = 3.25 Angstrom. Both 3.B and trans-5.B were optimized at d = 3.3 Angstr om, where 3.B was more stable by 2.11 kcal/mol (MP4SDTQ(FC)/6-31G**//MP2(FC )/ 6-31G** + ZPE). At greater separation, rotation of C2-C3 brings one hydr ogen at C5 closer to the anion. At d = 3.8 Angstrom, ring closure in 3.B oc curs with participation of C5. rather than C4 which should bridge in an anc himerically assisted ionization. Another orientation of the anion was teste d, placing B on a line perpendicular to the C2,C3,C5 plane. Optimization of trans-5.B at d = 4.0 Angstrom led to 3.B but tmns-S.B could be optimized a t d = 4.5 Angstrom, where it was 7.1 kcal/mol less stable than 3.B. The cal culations indicate that there should be no anchimeric assistance by either methyl or hydrogen upon ionization of a 3-methyl-2-butyl precursor to ion p airs, in agreement with the previous study of this process in trifluoroacet ic add.