A multidimensional transition state theory (TST) approach is formulated for the study of elementary jumps involved in the diffusion of a gaseous penetrant in a glassy polymer, taking explicitly into account the coupling between polymer and penetrant degrees of freedom along each jump. In this approach, an initial picture of states (local minima of the potential energy of the polymer + penetrant system) and “macrostates” (i.e., collections of states communicating over barriers small relative to kBT) is obtained through geometric analysis of accessible volume in representative glassy polymer configurations. Saddle points of the potential energy are computed using the “necks” between accessible volume clusters as initial guesses and progressively augmenting the set of degrees of freedom with respect to which the saddle point is calculated. Starting from the saddle points, states and reaction paths are then mapped out in the multidimensional space of penetrant and polymer degrees of freedom, using Fukui's int...