# How to reconcile API and manual calculation of energy above hull for triclinic VFeO4

Background: I am a geochemist by training. I am trying to solidify my understanding of the methods used for calculating the energy above the the convex hull. I am using triclinic VFeO4 as an example.

Question: What is the reason for the difference between the energy above the hull for VFeO4 (mp-504509) returned by the API (0.414647 eV/atom) and the energy manually calculated from the formation energies for each of the species in the decomposition reaction (0.413269 eV/atom)?

API value: I used the code at Plotting and analyzing a phase diagram using the materials api and modified it to change the Ca-C-O system to V-Fe-O. This is the result for mp-504509:

``````>>> print(df.loc[df['Materials ID'] == "mp-504509"])
Materials ID Composition     Ehull                   Decomposition
156    mp-504509       VFeO4  0.414647  0.79 V16 Fe8 O52 + 0.21 Fe4 O6
``````

The energy above the hull from the API agrees with the value on the web page for mp-504509 (0.415 eV/atom).

Manual calculation: According to the web page for triclinic VFeO4 (mp-504509), it decomposes to V4Fe2O13 (mp-558525) and Fe2O3 (mp-19770). I used the Materials API to retrieve the `formation_energy_per_atom` property for each of these materials, then multiplied by the number of atoms to get the formation energy per formula unit:

• VFeO4 (mp-504509): -1.756109 * 6 = -10.536654
• V4Fe2O13 (mp-558525): -2.238331 * 19 = -42.528289
• Fe2O3 (mp-19770): -1.907358 * 5 = -9.536790

The balanced decomposition reaction is VFeO4 = 0.25 V4Fe2O13 + 0.25 Fe2O3. (The coefficients here represent mole numbers, not mass fractions.) This has a reaction energy ΔEdecomp = 0.25 EV4Fe2O13 + 0.25 EFe2O3 - EVFeO4 . This gives ΔEdecomp = -2.47961575 eV per formula unit. Dividing by 6 atoms in VFeO4, the result is -0.413269 eV/atom.

I verified with the API that mp-558525 and mp-19770 are predicted stable materials (they both have zero energy above the hull). As far as I understand, the energy of the decomposition reaction to form stable products is the opposite of the energy above the hull, i.e. Ehull = -ΔEdecomp = 0.413269 eV/atom. How can this value be reconciled with the API value for Ehull (0.414647 eV/atom)?

Updates to the formation energies in the materials database appear to have fixed this issue. With formation energies obtained from the Materials API, the calculated energy above the hull for VFeO4 is now equal to the API value for Ehull.

@jedick, I’m glad to hear the recent update fixed your issue. My apologies you didn’t get a reply last time, we did discuss internally but didn’t reach a resolution and I intended to come back to it.