Density functional calculations of the enthalpies of formation of rare-earth orthophosphates^†

Electronic structure calculations are carried out to estimate the enthalpies of formation of rare-earth orthophosphates from their oxides. The calculated enthalpies of formation are systematically less exothermic than the measured values. The discrepancy is almost entirely in the electronic total energy calculated from density functional theory, and appears to be intrinsic to the generalized-gradient exchange-correlation functional used. However, comparison with electronic structure calculation of the enthalpies of formation of alkaline earth oxyacid carbonates, silicates, and sulfates suggests that near chemical accuracy can be obtained for the enthalpies of formation of most of the compounds in the phosphate system by applying a scaling factor obtained from the simpler alkaline earth oxyacids. The increasingly exothermic ΔH^f_ox with increasing ionic radius (i.e., LaPO₄ is more exothermic than ScPO₄) results from the higher charge localization on the oxide anion (O²⁻) relative to the phosphate anion (PO₄³⁻), making it more favorable, in a relative sense, to pair the smaller cation with the oxide anion than with the phosphate anion. This effect is also manifested in ΔH^f_ox of the other oxyacids, such as carbonates, silicates, and sulfates.