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 LiFeF3. 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.
Kohn W., Sham L. J., Self-Consistent Equations Including Exchange and Correlation Effects, 10.1103/physrev.140.a1133
Langreth David C., Perdew John P., Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works, 10.1103/physrevb.21.5469
Anisimov Vladimir I, Aryasetiawan F, Lichtenstein A I, First-principles calculations of the electronic structure and spectra of strongly correlated systems: theLDA+Umethod, 10.1088/0953-8984/9/4/002
Rohrbach A, Hafner J, Kresse G, Electronic correlation effects in transition-metal sulfides, 10.1088/0953-8984/15/6/325
Heyd Jochen, Peralta Juan E., Scuseria Gustavo E., Martin Richard L., Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, 10.1063/1.2085170
D. Rappoport, Computational Inorganic and Bioinorganic Chemistry (2009)
Csonka Gábor I., Perdew John P., Ruzsinszky Adrienn, Philipsen Pier H. T., Lebègue Sébastien, Paier Joachim, Vydrov Oleg A., Ángyán János G., Assessing the performance of recent density functionals for bulk solids, 10.1103/physrevb.79.155107
Zhou F., Cococcioni M., Marianetti C. A., Morgan D., Ceder G., First-principles prediction of redox potentials in transition-metal compounds withLDA+U, 10.1103/physrevb.70.235121
Anisimov Vladimir I., Zaanen Jan, Andersen Ole K., Band theory and Mott insulators: HubbardUinstead of StonerI, 10.1103/physrevb.44.943
Wang Lei, Maxisch Thomas, Ceder Gerbrand, Oxidation energies of transition metal oxides within theGGA+Uframework, 10.1103/physrevb.73.195107
Zhou F., Cococcioni M., Marianetti C. A., Morgan D., Ceder G., First-principles prediction of redox potentials in transition-metal compounds withLDA+U, 10.1103/physrevb.70.235121
Franchini C., Podloucky R., Paier J., Marsman M., Kresse G., Ground-state properties of multivalent manganese oxides: Density functional and hybrid density functional calculations, 10.1103/physrevb.75.195128
Jain Anubhav, Hautier Geoffroy, Moore Charles J., Ping Ong Shyue, Fischer Christopher C., Mueller Tim, Persson Kristin A., Ceder Gerbrand, A high-throughput infrastructure for density functional theory calculations, 10.1016/j.commatsci.2011.02.023
Mattsson Ann E., Armiento Rickard, Paier Joachim, Kresse Georg, Wills John M., Mattsson Thomas R., The AM05 density functional applied to solids, 10.1063/1.2835596
Quintal Miriam M., Karton Amir, Iron Mark A., Boese A. Daniel, Martin Jan M. L., Benchmark Study of DFT Functionals for Late-Transition-Metal Reactions†, 10.1021/jp054449w
Curtarolo Stefano, Morgan Dane, Ceder Gerbrand, Accuracy of ab initio methods in predicting the crystal structures of metals: A review of 80 binary alloys, 10.1016/j.calphad.2005.01.002
Lany Stephan, Semiconductor thermochemistry in density functional calculations, 10.1103/physrevb.78.245207
Heyd Jochen, Scuseria Gustavo E., Ernzerhof Matthias, Hybrid functionals based on a screened Coulomb potential, 10.1063/1.1564060
Heyd Jochen, Scuseria Gustavo E., Ernzerhof Matthias, Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)], 10.1063/1.2204597
Chevrier V. L., Ong S. P., Armiento R., Chan M. K. Y., Ceder G., Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds, 10.1103/physrevb.82.075122
Ong Shyue Ping, Chevrier Vincent L., Ceder Gerbrand, Comparison of small polaron migration and phase separation in olivine LiMnPO4and LiFePO4using hybrid density functional theory, 10.1103/physrevb.83.075112
Kresse G., Furthmüller J., Efficient iterative schemes forab initiototal-energy calculations using a plane-wave basis set, 10.1103/physrevb.54.11169
Kresse G., Furthmüller J., Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, 10.1016/0927-0256(96)00008-0
Langreth David C., Mehl M. J., Beyond the local-density approximation in calculations of ground-state electronic properties, 10.1103/physrevb.28.1809
Perdew John P., Burke Kieron, Ernzerhof Matthias, Generalized Gradient Approximation Made Simple, 10.1103/physrevlett.77.3865
Kresse G., Joubert D., From ultrasoft pseudopotentials to the projector augmented-wave method, 10.1103/physrevb.59.1758
Monkhorst Hendrik J., Pack James D., Special points for Brillouin-zone integrations, 10.1103/physrevb.13.5188
G. Bergerhoff, Journal of Chemical Information and Computer Sciences, 23, 66 (1983)
Fiz Karlsruhe, The Inorganic Crystal Structure Database
Setyawan Wahyu, Curtarolo Stefano, High-throughput electronic band structure calculations: Challenges and tools, 10.1016/j.commatsci.2010.05.010
Dudarev S. L., Botton G. A., Savrasov S. Y., Humphreys C. J., Sutton A. P., Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, 10.1103/physrevb.57.1505
Curtarolo Stefano, Morgan Dane, Persson Kristin, Rodgers John, Ceder Gerbrand, Predicting Crystal Structures with Data Mining of Quantum Calculations, 10.1103/physrevlett.91.135503
Zhou Fei, Cococcioni Matteo, Kang Kisuk, Ceder Gerbrand, The Li intercalation potential of LiMPO4 and LiMSiO4 olivines with M=Fe, Mn, Co, Ni, 10.1016/j.elecom.2004.09.007
O. Kubaschewski, Materials Thermochemistry (1993)
Rzyman K., Moser Z., Miodownik A.P., Kaufman L., Watson R.E., Weinert M., Enthalpies of formation of AlFe: Experiment versus theory, 10.1016/s0364-5916(01)00007-4
Kubaschewski O, Dench W.A, The heats of formation in the systems titanium-aluminium and titanium-iron, 10.1016/0001-6160(55)90038-9
Ping Ong Shyue, Wang Lei, Kang Byoungwoo, Ceder Gerbrand, Li−Fe−P−O2Phase Diagram from First Principles Calculations, 10.1021/cm702327g
Cabana Jordi, Monconduit Laure, Larcher Dominique, Palacín M. Rosa, Beyond Intercalation-Based Li-Ion Batteries: The State of the Art and Challenges of Electrode Materials Reacting Through Conversion Reactions, 10.1002/adma.201000717
Badway F., Cosandey F., Pereira N., Amatucci G. G., Carbon Metal Fluoride Nanocomposites, 10.1149/1.1602454
Doe Robert E., Persson Kristin A., Meng Y. Shirley, Ceder Gerbrand, First-Principles Investigation of the Li−Fe−F Phase Diagram and Equilibrium and Nonequilibrium Conversion Reactions of Iron Fluorides with Lithium, 10.1021/cm801105p
Aydinol M. K., Kohan A. F., Ceder G., Cho K., Joannopoulos J., Ab initiostudy of lithium intercalation in metal oxides and metal dichalcogenides, 10.1103/physrevb.56.1354
Loschen Christoph, Carrasco Javier, Neyman Konstantin M., Illas Francesc, First-principlesLDA+UandGGA+Ustudy of cerium oxides: Dependence on the effective U parameter, 10.1103/physrevb.75.035115
Bibliographic reference
Anubhav Jain ; Hautier, Geoffroy ; Shyue Ping Ong ; Charles J. Moore ; Christopher C. Fischer ; et. al. Formation enthalpies by mixing GGA and GGA + U calculations. In: Physical Review. B, Condensed Matter, Vol. 84, p. 045115 1-10 (2011)