New permutation inversion (PI) symmetry groups are presented which can be used to symmetry classify the nuclear-rotational-vibrational-electronic- translational wave function (Ψnrvet) of an A2/A 2, A2/AB, A2/B2, or AB/AB collision system, where the diatomic electronic states can be of any spatial symmetry or spin multiplicity. A symmetry correlation scheme based on these PI groups is developed which connects symmetry distinct nuclear motion states of Ψnrvet at infinite diatom/diatom separation with distinct electronic symmetries of the system in the diatom/diatom interaction region. Consideration of the effect of isotopic substitution on the correlation indicates that a kinetic isotope effect which is based on symmetry rather than mass considerations can occur in reactions where (1) the molecules are identical, but in different electronic states, or (2) at least one of the reactants is in a degenerate electronic state. Application of the correlation scheme to the kinetics of the H2+/H2 proton/atom transfer reaction (and its isotopic analogs) indicates that the experimentally observed unusual isotope effects can be understood as a consequence of this new symmetry based kinetic isotope effect. The possibility of observing this effect in the reactions of more complex molecules is discussed briefly.