The thermal motion of CD4+ in the gas phase at 4 and 40 K is studied by means of a molecular dynamics method using the MP2/6-31G(d,p) force field. The thermal motion of CD4+ in the temperature range from 4 to 40 K does not involve a deuterium permutation on the picosecond time scale. The electronic energy fluctuations of CD4+ due to thermal motion are less than 0.7 kcal/mol at 4 K and 1.6 kcal/mol at 40 K, which is less than the energy barrier (3.4 kcal/mol at MP2 level) required for the permutation between two energy minimum C-2 upsilon structures. On the basis of these calculations it is suggested that the observation of four equivalent hydrogen atoms in the ESR spectrum of CH4+ can be attributed to fast quantum tunneling, with an estimated rate of 4.3 X 10(6) s(-1) for CH4+ and 1.6 X 10(3) s(-1) for CD4+.