The improved canonical variational theory, presented previously for reaction rates in a classical mechanical world, has been extended to reactions in a quantum mechanical world where internal energies of reactants are quantized. A detailed discussion of vibrationally adiabatic models for transmission coefficients for conventional transition-state theory and three versions of variational transition-state theory are also presented. The relationship of the improved canonical variational transition-state theory to the classical limit of these transmission coefficients has been shown. The improved canonical variational theory and the new quantal and classical transmission coefficients are illustrated and tested by applications to quantal collinear and three-dimensional reactions rates for several reactions. Semiclassical approximations to the quantal transmission coefficients are also examined. Applications considered are collinear H + H/sub 2/ and isotopic analogs, Cl + H/sub 2/ and isotopic analogs, and I + H/sub 2/ and three-dimensional D + H/sub 2/, Cl + HD, I + H/sub 2/, I + D/sub 2/, O + H/sub 2/, and F + H/sub 2/.