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I am reviewing some information in the Materials Project and notice that they do not use DFT+U to model copper oxides. Since the methodology for fitting U is largely based on the 2006 Ceder paper, I am curious why this was omitted.

Is DFT+U just not needed for copper oxides? This is very surprising to me as most other 3d transition metals benefit from U corrections.

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Just to add to Anyon's answer:

Since there may be practical considerations for using DFT+$U$ in a database like the Materials Project (i.e. a value you're confident will give you generally correct properties in high-throughput calculations, is there a literature reference or other justification for the value, etc.) I would in general not assume that they didn't perform DFT+$U$ because it doesn't help.

There can be situations where somewhat counter-intuitively, DFT+$U$ and even hybrid functionals can give worse results for some properties of correlated materials than a normal GGA calculation. For example, see the strongly correlated metal LaNiO$_3$ (HSE and DFT+$U$). Keep in mind that DFT+$U$(or hybrids for that matter) do not improve the treatment of correlation, they reduce self-interaction error. It also depends on how the correction is applied and how the value of $U$ was determined.

LaCuO$_3$ is also a metallic oxide. I did some calculations on this material and found ACBN0's method of calculating $U$ on both Cu and O provided better structural agreement with experiment than PBE. I didn't check other magnetic configurations to see if the experimentally observed order is the lowest energy though.

Of course, how you define 'worse' is based on what properties you want to look at. This is different for say, lattice parameters and geometry, vs. asking if you can predict the most stable magnetic configuration or not, vs. K-S gap, vs. defect formation energies, and so on... For these types of databases I suppose you want a balanced approach, another factor to consider when deciding to include a $U$ correction there or not.

So for a shorter answer: you have to look deeper for some in-depth studies of a material to really know. If those don't exist, you can try to find the answer with your own calculations!

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I can't speak as to how the Materials Project selects what information to display, but it's clear that the Hubbard $U$ (or rather the correlations/interactions it attempts to capture) generally is important for copper oxides. This is very clear in the cuprate high-$T_c$ superconductors, which are often modeled as doped antiferromagnetic insulators. The $U$ also helps in the case of simple copper oxides CuO, and Cu$_4$O$_3$, but standard DFT + U is no panaceum and has problems with Cu$_2$O, as discussed recently in Phys. Rev. B 99, 035154 (2019) (alternate link at Cardiff repository).

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