The structures, relative energies, and interconversion
barriers and pathways for several isomeric
C5H11
+ 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.