Question about the MP-Advanced Correction value for Fe oxides


in order to understand the MP correction schemes for the formation energies of transition metal oxides I studied the PRB papers of Wang (2006) and Jain (2011), and used the total energies given on the MP pages first for Manganese oxides to reproduce the Advanced Correction value for Mn (-1.68 eV per Mn), which worked out perfectly. So I think I am applying the procedure correctly.

But applying the same method to the iron oxides (FeO, Fe2O3, Fe3O4) did not lead to the correction value of -2.733 eV per Fe which is given on the MP pages, but to -2.27 eV instead. I also found the information online, that Fe3O4 was excluded from the fitting, but this changed the value only to -2.24 eV. I used the experimental standard formation enthalpies as follows: FeO: -272 kJ/mol, Fe2O3: -824.2 kJ/mol, Fe3O4: -1118,4 kJ/mol. These values are taken from wikipedia, and they deviate only within 2 kJ/mol (or 0.02 eV/f.u.) from those given by the NIST Chemistry WebBook ( so I think they are reliable.

Using the correction value of -2.27 eV [A] reproduces the experimental values [E] much better as if I take the MP value of -2.733 eV:

FeO: -1.4097 [E], -1.4350 [A], -1.669 [MP]
Fe2O3: -1.7111 [E], -1.6986 [A], -1.886 [MP]
Fe3O4: -1.6596 [E], -1.6353 [A], -1.836 [MP]

All values are given in eV/atom. As said before, I only took MP total energies and applied the procedure of Jain (2011). So my question is whether I did a mistake here or the MP correction value for Fe is wrong, or if anything else was taken into account by MP which is not explained in the stated paper.

A reply would be highly appreciated.

Hi Daniel, thanks for the detailed post. I’ve suspected there might be an issue with this for a little while, but didn’t have a hard example (or a potential cause) other than what I’d seen with some of the non-corrected compounds (e. g. RuO2 is also pretty far off). Unfortunately, most of the experts in the correction scheme aren’t frequent forum users. I think we might get better mileage consulting the pymatgen google group. Is it okay if I post your message there? Alternatively, you’re welcome to do it:!forum/pymatgen

Also, for anyone reading this thread, we’ll follow up here with any results we find.

hi @danielr I am also trying to reproduce the correction value for Fe.
I want to make sure that I am doing correctly as in the paper Jain (2011).
Fe2O3: -1.7112 (exp), -1.8862 (theo_MP), 0.175 (exp-theo_MP), 0.4 (fraction of Fe in Fe2O3)
Fe3O4: -1.659571429 (exp), -1.84 (theo_MP), 0.180428571 (exp-theo_MP), 0.428571429 (fraction of Fe in Fe3O4)
FeO: -1.4097 (exp), -1.669 (theo_MP), 0.2593 (exp-theo_MP), 0.5 (fraction of Fe in FeO)
All energies are in eV/atom. Then I have used Linear-trendline to get the slope (by fixing intercept= 0). But I am not getting -2.27 or -2.733. The slope I am getting is 0.446!!
Can you please tell where I am doing the mistake?

Hi @Ami245. Unfortunately our historical correction values are not as well-documented as we would like. We will actually be releasing an updated and better-documented set of corrections in the very near future that I hope will clarify the procedure. In the mean time, I’ll do my best to explain why you are getting such a different number than what is currently used in MP.

First, the formation energies listed in the MP database are already corrected, so to re-fit the corrections yourself, you need to make sure to use the uncorrected energies. These can be found under “Final Energy/Atom” on any material page. In our case, -6.716 eV/atom for Fe2O3 and -6.659 eV/atom for FeO. Let’s disregard Fe3O4 for now because the MPCompatibility.yaml file indicates it was not used in the MP fitted correction.

Next, we need to calculate the reaction energy of

Fe + O -> FeO
2Fe + 3 O -> Fe2O3

Again we need to use the uncorrected energies. Looking at mp-13 for Fe and mp-12957 for Fe and O2, I get -8.46 and -4.936 eV/atom, respectively. However, the Oxygen energy needs to be adjusted by 0.702 eV/atom (the Wang et al. value cited in the Jain 2011 paper).

Putting the above energies together gives us the computed reaction energies, e.g. for Fe2O3:

( 5 * -6.716 - 2 * -8.46 - 3 * (-4.936 + 0.702) ) / 5 = -0.792 eV/atom

For the FeO reaction, I get -0.311 eV/atom.

Now, we can compute the difference between the computed reaction energies and the experimental values from the Kubaschewski tables (-1.363 and -1.707 eV/atom for FeO and Fe2O3).

FeO: delta E = -1.363 - -0.311 = -1.05 eV/atom
Fe2O3: delta E = -1.707 - -0.792 = -0.91 eV/atom

When I fit these values against the fractional compositions (0.4, 0.5) as you did, I get an energy correction of -2.17 eV/atom, which is similar to what the original poster had.

I hope this clarifies the procedure a bit. As I said above, we will soon release an updated set of corrections that will be better documented and hopefully easier to follow. Please watch for that, and post any further questions in the meantime!

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Hi all,

I just want to weigh in a bit here. I quickly checked what formation enthalpies we are getting on the Reaction Calculator App ( for:

Fe + O --> FeO
Fe + O --> Fe2O3

In both cases, our current settings overstabilize the compound by about 0.5 eV/Fe as compared to experiments, which would indicate that @danielr is fitting things correctly.

But, it is important to make sure the calculations were on the same systems as in the paper. IIRC, I used structures based on Table 1 in the paper below:

Thus, for FeO I would have used the Fm-3m structure with AFM ordering, whereas Materials Project would go with C2/m structure at FM ordering. A different FeO structure / magnetic ordering could lead to a different energy and different fit.

For Fe2O3, however, things should be comparable. I would have used R-3c structure at AFM ordering; in MP, this structure is basically stable and so this would essentially be the same. Thus, the best fit for Fe2O3 considered alone (and not fit together with FeO) should be essentially the value that @danielr reports.

To really check into this, someone would need to calculate FeO in Fm-3m structure with AFM ordering. Unfortunately, I don’t have any of those previous calculations when we re-fit all the GGA+U mixing parameters for Materials Project; that would probably have been done sometime ~2011, and I’m not sure even if I was the one that did the re-fit or not. It’s possible that whomever did that re-fit messed things up, as the procedure from @rkingsbury shows that there is a bunch to keep track of to do the procedure correctly. My guess is that the Fe correction currently being used is too aggressive and overstabilizes the Fe compounds - MP should look into it.