Recent experimental work on the methanol-to-hydrocarbons (MTH) reaction in zeolite H-Beta suggests that the heptamethylbenzenium (heptaMB+) cation is an important intermediate. We have carried out quantum chemical calculations to investigate intramolecular isomerization reactions and eliminations of small alkenes such as ethene, propene, and isobutene from heptaMB+ isomers. Two types of reaction paths have been investigated for the alkene formation: One starting with an initial ring contraction, and one starting with an initial ring expansion of the heptaMB+ ion. The reaction starting with an initial ring contraction leads to a bicyclic species that may split off propene or, after further isomerizations, isobutene. Expansion to a seven-membered ring may, via further isomerizations, lead to formation of ethyl and isopropyl groups that may in turn be split off as ethene and propene. The calculations have been carried out at the B3LYP/cc-pVTZ//B3LYP/6-311G(d,p) level of theory with zero point energy corrections. Comparisons with experimental data are made where possible.