Density functional theory, DFT, and high-level conventional ab initio calculations, together with RRKM calculations, have been employed to study the nature of the transition state geometry for 1,2 elimination of HF from 1,1,1-trifluoroethane-d(0),-d(3); these serve as test cases for 1,2-HF elimination from fluorocarbons. Quantities calculated include structural parameters, bond indices, energies, atomic charges, vibrational frequencies, and moments of inertia for the reactant and the transition state geometry. The threshold energies for HF and DF elimination were computed and the vibrational frequencies and moments of inertia data were used with the RRKM theory to calculate the entropies of activation, preexponential factors for thermal activation, and also rate constants and the kinetic isotope effect for both thermally and chemically activated 1,1,1-trifluoroethane-d(0),-d(3). Of all the methods, employed, the hybrid DFT methods incorporating either the three-parameter exchange functional of Becke with the correlation functional of Perdew and Wang or the correlation functional of Lee, Yang, and Parr were found to give results more consistent with the experimental studies. Both the 6-31G(d',p') and cc-PVDZ basis sets gave comparable agreement with experiment and suggest that basis sets of double-zeta quality in the valence region, which include polarization functions, appear to be adequately flexible to describe the systems studied here. There appears to be little to be gained in going from the computationally efficient DFT calculations to the computationally very expensive methods such as G2 or MP2.