(289d) Not Just a Fitting Parameter: the Untold Story of DFT+U

For over twenty years, Hubbard-model-like “+U” corrections have been employed to augment practical density functional theory (DFT) in order to improve upon well-known problems of common exchange-correlation functionals in predicting band gaps and describing insulating ground states in transition-metal-containing materials.  While DFT+U continues to be successfully used to empirically adjust band gaps, the magnitude of a “+U” correction has long since been shown to be directly connected to the unphysical curvature inherent in an exchange-correlation functional. Nevertheless, DFT+U is often still commonly considered an empirical, stop-gap measure for the well-known failings of practical DFT in describing the localized character of the valence states of transition metals at low computational cost. I will review a more rigorous view in which the “+U” is actually a measure of system-dependent curvature that may be self-consistently calculated. Recent extensions generalize this approach to enable comparison of total energies for different electronic states and for variations in coordination and geometry that are both key for catalysis. For cases where a level of empiricism is desired, a practical approach for identifying the sensitivity of electronic structure to variations in calculated and applied values of U will be discussed. Finally, I will propose a scheme for obtaining an internally consistent, constant value of U across dramatic changes in hybridization by isolating the subset of orbitals to which Hubbard-model-like corrections are appropriate.