# Formation energy from energy_per_atom

Hello. I’m searching for hydride datas from mp by mp-api.
But I found something awkward.
For La(mp-26), Ni(mp-23), LaNi5(mp-2317),
energy_per_atom is -29.745, -11.982, -5.9212.
And formation_energy_per_atom is 0, 0, -0.2817.
All units are eV/atom.

Simply I thought formation energy per atom of LaNi5 is
(6E_per_atom(LaNi5) - E_per_atom(La) - 5E_per_atom(Ni))/6
But this value is not matching with data from mp which is -0.2817.

Is there something I missed? I’ll glad to let me know.

Thanks a lot

Hey @cdwon7393,

The uncorrected r2SCAN energies per atom (eV/atom) for those materials are (check the `.uncorrected_energy_per_atom` tag of the `SummaryDoc`:
La: -29.744780205
Ni: -11.98171716
La Ni5 : -15.182276991666667

Your formula for the formation energy is correct - computing it with the uncorrected energies gives -0.240 eV/atom. Last, GGA / +U energies are admixed with r2SCAN energies to give the final formation energy per atom.

See here for a description of the corrections used by MP.

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@cdwon7393 I willl add on to Aaron’s answer that the particular -0.28 formation energy value can be solved for by using corrected GGA energies (in this case). As Aaron said, the formula you are using is correct but the La, Ni, and LaNi5 energies should be changed. I got these energies from the Phase Diagram app (they can also be queried from `mp-api`):

E_La = -4.94 eV/atom
E_Ni = -5.78 eV/atom
E_LaNi5 = -5.92 eV/atom

E_f = (6*(-5.92) - (-4.94) - 5*(-5.78))/6 = -0.28 eV/atom

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@Aaron_Kaplan @mattmcdermott Thank you so much for clear explanation. It was very helpful