We have developed a novel semiclassical transition state theory (SC-TST) for truncated parabolic barriers, based on the formulation of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)]. Our SC-TST rate coefficient has the form k(SC-TST)=k(TST).Gamma, where Gamma depends on the zero point corrected barrier, Delta E-0, and the barrier curvature, \omega(F)double dagger\. Our rate expression is stable to arbitrarily low temperatures, as opposed to purely harmonic SC-TST, because we identify the maximum possible semiclassical action in the reaction coordinate. For low temperatures, we derive an analytical approximation for Gamma that is proportional to e(0)(beta Delta E). We develop a theory for the tunneling crossover temperature, T-x, yielding k(B)T(x)congruent to (h) over bar\omega(F)double dagger\Delta E-0/(2 pi Delta E-0-(h) over bar\omega(F)double dagger\ln 2), which generalizes the harmonic theory for systems with large but finite barriers. We have calculated rate coefficients and crossover temperatures for the O(1)--> O(4) jump in H-Y and D-Y zeolites, yielding T-x=368 K and 264 K, respectively. These results suggest that tunneling dominates proton transfer in H-Y up to and slightly above room temperature, and that true proton transfer barriers are being underestimated by neglecting tunneling in the interpretation of experimental mobility data. (C) 2000 American Institute of Physics. [S0021-9606(00)70915-9].