The Jahn-Teller potential energy surface of the radical cation of tetrahedrane
is explored by quantum chemical calculations and modeled analytically. The
firts- and second-order vibronic constants are evaluated. The rearrangement to
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 ) 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.