Improper self-energy

Fig. 5. Graphs contributing to the improper and proper self-energy, respectively, derived from the graphs in Fig. 1.

One such varied implementation that has recently gained in popularity (especially for transition metals) is the use of LDA and GGA with the addition of a Hubbard U correction [34, 35], often denoted with a +U. In this XC functional, the base LDA or GGA functional is used with the addition of a mean-field term for the Coulomb energy that aids in correcting improper self-interactions. This additional term can lead to more accurate spin states and band gaps and computationally isn t much more expensive than the underlying XC functional. One major drawback, however, is that there is no fundamental parameterization, so terms are often treated as adjustable parameters. This drastically hurts the predictive ability of the DFT model and means that some external experimental values must be included to help with parameterization. Fully self-consistent parameterizations of the Hubbard correction terms are a field of much current research and if shown to give accurate results with no a priori fitting needed would be incredibly useful for the study of metal oxides and oxide film formation. 

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