The dehydrogenation enthalpies of Ca(AlH(4))(2), CaAlH(5), and CaH(2)+6LiBH(4) have been calculated using density functional theory calculations at the generalized gradient approximation level. Harmonic phonon zero point energy (ZPE) corrections have been included using Parlinski's direct method. The dehydrogenation of Ca(AlH(4))(2) is exothermic, indicating a metastable hydride. Calculations for CaAlH(5) including ZPE effects indicate that it is not stable enough for a hydrogen storage system operating near ambient conditions. The destabilized combination of LiBH(4) with CaH(2) is a promising system after ZPE-corrected enthalpy calculations. The calculations confirm that including ZPE effects in the harmonic approximation for the dehydrogenation of Ca(AlH(4))(2), CaAlH(5), and CaH(2)+6LiBH(4) has a significant effect on the calculated reaction enthalpy. The contribution of ZPE to the dehydrogenation enthalpies of Ca(AlH(4))(2) and CaAlH(5) calculated by the direct method phonon analysis was compared to that calculated by the frozen-phonon method. The crystal structure of CaAlH(5) is presented in the more useful standard setting of P2(1)c symmetry and the phonon density of states of CaAlH(5), significantly different to other common complex metal hydrides, is rationalized.