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I noticed that a lot of articles use DFT+U methods to calculate different formation energies when using regular DFT and DFT+U methods. For example, in the attached paper[1] on $\ce{In2O3}$, the enthalpy of formation was found to be $\pu{-9.86 eV}$ and $\pu{-10.41 eV}$ using LDA and LDA+U, respectively.

When calculating the formation energies using DFT+U, I am wondering if the energies of the elemental reference states ($\ce{In}$ and $\ce{O2}$ in the above case) also need to be calculated using DFT+U, or just from regular DFT, since they often do not have band gaps that DFT+U seeks to correct.

  1. Pakpoom Reunchan, Xin Zhou, Sukit Limpijumnong, Anderson Janotti, Chris G. Van de Walle, Vacancy defects in indium oxide: An ab-initio study, Current Applied Physics, Volume 11, Issue 3, Supplement, 2011, Pages S296-S300,DOI: 10.1016/j.cap.2011.03.051
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As far as my knowledge, they must be calculated using DFT+U. When you calculate the energy of $\ce{In}$ in its bulk state using DFT, it won't lead to the same value using DFT+U.

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To calculate formation energies from DFT+U, you must use a self consistent set of parameters. This is easy to visualize since you can imagine the reaction of InODFT -> InODFT+U, which will end up having some non-zero reaction energy. While this example is obviously incorrect, mixing energy differences with DFT+U corrections and non-corrected differences results in a similar picture, but is often less obvious.

There have been some attempts to mix these however and materials project has a small section on a mixing correction they have applied, however I do not know personally if this has been successful or not. Someone more familiar with materials project might know more.

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