Secondary and Tertiary 2-Methylbutyl Cations. 3. Theoretical Study of Structures and Interconversions of C₅H₁₁⁺ Ions in the Gas Phase¹a

The structures, relative energies, and interconversion barriers and pathways for several isomeric C 5 H 11 + carbocations were investigated by high level ab initio MO calculations with inclusion of electron correlation. The energy minima found were two conformations of the tertiary 2-methyl-2-butyl cation ( 2 ), bisected ( 2 b ) and asymmetric ( 2 as ), and three 1-protonated (corner-protonated) cyclopropanes: trans -2,3-dimethyl ( trans - 8 ), cis -2,3-dimethyl ( cis - 8 ), and 1,2-dimethyl ( 9 ).The bridged ions trans - 8, cis - 8, and 9 are higher in energy than the tertiary ion by 8.3, 9.2, and 10.6 kcal/mol, respectively, at the MP4SDTQ(FC)/6-31G**//MP2(FC)/6-31G** level, or 9.6, 10.6 and 12.4 kcal/mol after correcting for the zero-point energies (ZPE). Various conformations of the “open” 3-methyl-2-butyl cation correspond to transition states for the interconversion of the tertiary ion 2 as and the two 1-protonated-2,3-dimethylcyclopropanes. Hydrogen shift in 2 as can lead only to the cis -2,3-dimethyl isomer, cis - 8; trans - 8 is formed only from the cis isomer by ring opening and reclosure. The 1,3-protonated-1,2-dimethylcyclopropane ( 10 ) (edge-protonated) is the transition state for the interconversion of trans - 8, and the third corner-protonated cyclopropane isomer (1-protonated-1,2-dimethylcyclopropane, 9 ). The latter can be regarded as the cyclic form of the 2-pentyl cation or of the 2-methyl-1-butyl cation. The calculations thus agree with the results of the experimental study on the cations generated in trifluoroacetic by predicting the existence of more than one “2-methylbutyl” cation, but disagree on another point, by predicting that the other cation besides 2 has a symmetrical structure, 8 .