Local environment dependent GGA plus U method for accurate thermochemistry of transition metal compounds

We present a framework to carry out highly accurate GGA+U thermochemistry calculations by deriving effective U values from experimental data. The U values predicted in this approach are applied to metal cations, and depend not only on (i) the chemical identity and the band to which the U correction is applied, but also on the local environment of the metal described by (ii) its oxidation state and (iii) the surrounding ligand. We predict such local environment dependent (LD) U values for the common oxidation states of 3d metals M = Ti, V, Cr, Mn, Fe, Co, and Ni in their oxides and fluorides. We implement the GGA/GGA+U mixing method [Jain et al. Phys. Rev. B 84, 045115 (2011)] to establish the total energy compatibility among the GGA+U calculations involving M treated with different LD-U values. Using the presented framework, formation enthalpies of 52 transition metal bearing oxides (which are not used during the LD-U parametrization) are predicted with a remarkably small mean absolute error of similar to 19 meV/atom, which is on the order of the experimental chemical accuracy. In addition, we present applications of the method in redox processes of important 3d-metal oxide and fluoride systems such as LixCoO2, LixV6O13, LixFeF3, and VO1.5+x, and show that LD-GGA+U can overcome several drawbacks of using constant-U values in conventional GGA+U.