PHYSICAL REVIEW B 82.075122 (2010) Methodologies Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds V.L.Chevrier.S.P.Ong.R.Armiento.M.K.Y.Chan.and G.Ceder HSE06 is as successful as GGA+U in predicting Jahn-Teller Depurtment of Muterials Science and Engineering.Massachusetts Institute of Technology.Cambridge,02139.USA (Received 12 February 2010:revised manuscript received 18 July 2010:published 12 August 2010) distortions,magnetic moments,and charge localization. TABLE I.Values of the (parameters in electron volt,adapted (a)GGA+U (b)HSE06 from Ref.3. HSE06 consistently predicts more accurate geometries than Olivine Layered Spinel both GGA and GGA+U Mn 4.5 48 Fe 4.3 HSE06 and GGA+U with a linear response U yield similar Co 5.7 5.1 Ni 61 6.4 accuracies for Li intercalation potentials. Isosurfaces of the change in charge density upon lithiation of Relative error of the optimized volumes compared NiPO4 to LiNiPO4 to experiment for the lithiated phases Average Li intercalation potentials vs.Li/Li,in volts 15 GGA● GGA GGA+U HSE06 Expt. 0.6 GGA-⊙ GGA+U LiCoO: 3.38 3.85 4.51 4.1 GGA+U△ 10 HSE06 LiNiO2 3.08 3.92 4.14 3.9 0.2 HSE06日 LiTiS, 1.91 (1.91) 206 21 0 回 LixTixO 1.05 (1.05) 1.19 1.3 LiMn2O 3.37 4.04 425 4.1 0.2 LiMnPO 2.99 4.01 3.87 4.1 04 LiFePO 2.84 3.47 3.33 3.5 LiCoPO 3.62 4.63 4.57 4.8 0,6 LiNiPO 4.15 5.00 541 53 0.8 Mean 2.93 3.54 3.70 3.69 -1 MAE 0.76 0.15 0.19 10 -1.2 Delithiation to LiTiO. L甜 LiNiPO is unstable upon delithiation,leading to a larger error in average intercalation potential. Mean absolute errorMethodologies ✓ HSE06 is as successful as GGA+U in predicting Jahn-Teller distortions, magnetic moments, and charge localization. ✓ HSE06 consistently predicts more accurate geometries than both GGA and GGA+U. ✓ HSE06 and GGA+U with a linear response U yield similar accuracies for Li intercalation potentials. Isosurfaces of the change in charge density upon lithiation of NiPO4 to LiNiPO4 Average Li intercalation potentials vs. Li/Li+ in volts Relative error of the optimized volumes compared to experiment for the lithiated phases