Reaction pathways for the addition of ethylene, 1, to butadiene radical cation, 2, involving H-shifts have
been investigated at the coupled cluster UCCSD(T)/DZP//UMP2(fc)/DZP + ZPE level of theory. Activation
energies are relatively low for [1,2]- (10.0 kcal mol-1, TS-4/20) and [1,5]-hydrogen shifts (7.7 kcal mol-1,
TS-4/26) but are relatively high for [1,4]- (33.8 kcal mol-1, TS-4/14) and [1,3]-H shifts (e.g. 42.2 kcal mol-1,
TS-12/13; 57.2 kcal mol-1, TS-16/21). Several rearrangement reactions have been found to occur below the
energy limit of separated 1 + 2. The cyclopentenyl cation, [C5H7]+, 18, experimentally observed as reaction
product of the butadiene radical cation, 2, and ethylene, 1, in the gas phase may origin from various reaction
pathways. The following reaction sequence has been identified as the lowest in energy path from 1 + 2 to 18
with all relative energies (ΔE°) of transition structures below that of 1 + 2: (a) ethylene adds to the butadiene
radical cation to form an open-chain distonic intermediate, 4, that undergoes a [1,5]-H shift to the 1,4-hexadiene
radical cation, 26; (b) intramolecular [2+1] cycloaddition to methyl-cyclopenta-1,3-diyl intermediates, 22
and 24, which can interconvert through a bicyclo[2.1.0]pentane radical cation, 23; (c) [1,2]-H shift of 24 to
the 3-methyl cyclopentene radical cation, 16; (d) methyl radical loss to give cyclopenten-3-yl cation, 18.
Along this reaction pathway, ΔH
298 changes by −18.1 kcal mol-1 (ΔG
298 by −16.0 kcal mol-1) and only
transition structures low in energy (ΔH
298 is below that of 1 + 2; max. ΔG
298⧧ = 10.4 kcal mol-1 for [1,5]-H
shift relative to 1 + 2) are involved. Ethylene, 1, can also add to 2, simultaneously accepting a transferred
hydrogen to give a 1,3-hexadiene radical cation. Back dissociation of the latter into 1 + 2 is favored over
methyl radical loss.