Formation enthalpies by mixing GGA and GGA+Ucalculations

Standard approximations to the density functional theory exchange-correlation functional have been extraordinary successful, but calculating formation enthalpies of reactions involving compounds with both localized and delocalized electronic states remains challenging. In this work we examine the shortcomings of the generalized gradient approximation (GGA) and GGA$+$$U$ in accurately characterizing such difficult reactions. We then outline a methodology that mixes GGA and GGA$+$$U$ total energies (using known binary formation data for calibration) to more accurately predict formation enthalpies. We demonstrate that for a test set of 49 ternary oxides, our methodology can reduce the mean absolute relative error in calculated formation enthalpies from approximately 7.7--21% in GGA$+$$U$ to under 2%. As another example we show that neither GGA nor GGA$+$$U$ alone accurately reproduces the Fe-P-O phase diagram; however, our mixed methodology successfully predicts all known phases as stable by naturally stitching together GGA and GGA$+$$U$ results. As a final example we demonstrate how our technique can be applied to the calculation of the Li-conversion voltage of LiFeF${}_{3}$. Our results indicate that mixing energies of several functionals represents one avenue to improve the accuracy of total energy computations without affecting the cost of calculation.