The potential energy surface relating to the C7H11+ bicyclobutonium cation and its isomers was investigated in the gas phase using the ab initio and density functional calculations. The unsymmetrical bicyclobutonium ion 5 was identified with the MP2/6-31G* method as a global minimum, which is slightly more stable by 0.8 kcal/mol than the boat conformer of the bicyclo[3.1.0]heptyl-1-carbinyl cation 6. Similar results were obtained when larger basis sets, such as 6-311+G**, were used to optimize the geometries. However, the energy gap between the bicyclobutonium ion 5 and the chair conformer of cyclopropylcarbinyl cation 6 became even smaller when the MP4(SDQ)/6-31G* method was used. The small differences in terms of relative energies between these minima located at the MP2/6-31G* and MP4(SDQ)/6-31G* levels reflect the flat profile of the corresponding part of C7H11+ potential energy surfaces. The geometries of other types of C7H11+ isomeric carbocations were also optimized such as the allyl cation 7, the chair conformer of bicyclo[3.1.0]heptyl-1-carbinyl ion 8, and p-complex 9, with the latter species being clearly less stable by 15.2 kcal/mol than 5. Becke's hybrid density functional, B3LYP, combined with the 6-31G* and 6-311+G** basis sets, was also utilized to investigate the C7H11+ potential energy surface. The majority of B3LYP results were comparable to those obtained with the post Hartree–Fock methods; however, the unsymmetrical bicyclobutonium ion 5 could not be found with this density functional method. Low energy barriers separate the two cyclopropylcarbinyl cations 6 and 8, preventing them from rearranging into the bicyclobutonium type of ion 5. A much higher barrier is found for the rearrangement of the two cyclopropylcarbinyl cations 6 and 8 into allyl and p-complex species. The carbocation with the positive charge localized at the bridgehead position does not represent a minimum at any level of theory used throughout this investigation.