The Jahn-Teller potential energy surface of the radical cation of tetrahedrane is explored by quantum chemical calculations and modeled analytically. The first- and second-order vibronic constants are evaluated. The rearrangement to the cyclobutadiene radical cation, which was previously predicted to occur with no activation, is investigated by the same quantum chemical method (CCSD (T)/cc-pVTZ//QCISD/6-31G*). It is shown that the localization of the HOMO which is necessary for adiabatic crossover requires some energy, which leads to a 0 K activation barrier of 4.3 kcal/mol for the process. It is concluded that the radical cations of substituted tetrahedranes should persist at low temperatures if they can be formed with little excess energy.