A theoretical investigation of the isopropylbenzenium ion system has been carried out with structures determined with B3LYP. Energies are calculated with the high accuracy composite methods, G3 (G3B3) and CBS (CBS-QB3). The main goal has been to resolve the following issue: Are there any stable ion pi-electron complexes of the type C6H6/C3H7+ or C6H7+/C3H6 in this system? Two minimum points on the potential energy surface (PES) corresponding to benzenium ion/propene complexes were found. Due to free internal rotation, they represent only one species. The barrier for forming an isopropylbenzenium ion from the complex is low, so the lifetime will be short. Computation of the IR spectrum of the complex shows that there is a very intense absorption line due to C-H stretching, in an otherwise empty region, that may be used to identify the complex, if present. No stable C6H6/C3H7+ complex was found, but a quasi-stable species structurally corresponding to the earlier described stable C6H6/C4H9+ complex was observed. A simplistic explanation why the benzene/isopropyl cation, in contrast to benzene/tert-butyl cation, does not form a stable ion/pi-electron complex is given.