The heats of formation for the molecules BH3PH3, BH2PH2, HBPH, AlH3NH3, AlH2NH2, HAlNH, AlH3PH3, AlH2PH2, HAlPH, AIH(4)(-), PH3, PH4, and PH4+, as well as the diatomics BP, AlN, and AlP, have been calculated by using ab initio molecular orbital theory. The coupled cluster with single and double excitations and perturbative triples method (CCSD(T)) was employed for the total valence electronic energies. Correlation consistent basis sets were used, up through the augmented quadruple zeta, to extrapolate to the complete basis set limit. Additional d core functions were used for Al and P. Core/valence, scalar relativistic, and spin-orbit corrections were included in an additive fashion to predict the atomization energies. Geometries were calculated at the CCSD(T) level up through at least aug-cc-pVTZ and frequencies were calculated at the CCSD(T)/ aug-cc-pVDZ level. The heats of formation of the salts [BH4-][PH4+](s), [AlH4-][NH4'](s), and [AlH4-][PH4'](s) have been estimated by using an empirical expression for the lattice energy and the calculated heats of formation of the two component ions. The calculations show that both AlH3NH3(g) and [AIH4-][NH4'](S) can serve as good hydrogen storage systems that release H-2 in a slightly exothermic process. In addition, AlH3PH3 and the salts [AlH4-][PH4'] and [BH4-][PH4] have the potential to serve as H-2 storage systems. The hydride affinity of AlH3 is calculated to be -70.4 kcal/mol at 298 K. The proton affinity of PH3 is calculated to be 187.8 kcal/mol at 298 K in excellent agreement with the experimental value of 188 kcal/mol. PH4 is calculated to be barely stable with respect to loss of a hydrogen to form PH3.