Large deviations in single-atom total energy calculations

Hello all.

I am trying to calculate the vacancy formation energies in some alloys, and to do this I need to estimate the chemical potentials of the atoms of each individual elements. Accurately calculating these values is computationally expensive, so I would like to start with the total energy of the individual atoms of each element to get some rough preliminary results.

I do this by placing a single atom in the center of a large (acell 3*30) box and using the gamma point only to perform a basic GS run.

The problem is that the total energy I get by doing so differs greatly from what I see in relevant papers. For example, many of those papers state that the chemical potential of a Fe atom in a pure metal is about -8 eV, but the total_energy_eV for a single Fe atom in a large box that I got is about -3300. I have also tried using a denser k-mesh, a higher ecut, using the GGA-PBE pp or the PAW basis from Pseudo Dojo, and have gotten similar results.

Typically, the vacancy formation energy in these alloys is calculated using the total energy of the perfect supercell minus the total energy of the supercell containing the vacancy, plus the chemical potential of that atom corresponding to the vacancy. I did a rough calculation of the total energy of the two supercells mentioned above and noted that the difference between their total energy is indeed close to -3300 eV. What concerns me is that this value differs so much from other research (they’re like -8~9 eV) that it is hard to be sure that the resulting formation energy is reliable (in fact it also differs greatly from other similar research).

What I would like to know is whether I am correct in my calculation of the total energy of a single atom. Also, is the total energy that is usually used to approximate the chemical potential the same total energy that is obtained from the GS calculations?

These are the abi, abo & pp files I used (.psp8 and .xml pps are acquired from Pseudo Dojo, you may delete the .txt suffix to use them to reproduce my strange results):
Fe-psp.abi (978 Bytes)
Fe.psp8.txt (273.5 KB)
Fe-psp.abo (35.0 KB)
Fe-paw.abi (1006 Bytes)
Fe.xml.txt (896.5 KB)
Fe-paw.abo (34.8 KB)


Hi Iavas,
Your approach is correct. Note that the total energy of one particular system doesn’t have much physical meaning. What count are total energy differences, and when you compute those differences, you must make sure that the number of atoms balances out.
For example, if S denotes your supercell, V denotes your supercell with one atom removed, and A denotes the isolated atom, then the energy difference

E[V] + E[A] - E[S]

should correspond to the formation energy of the vacancy.

Hi Antonius.

Thank you for your reply! Another thing I’m not sure about is how the total energy of a single atom is properly obtained. Again, using iron as an example, the total energy of an iron atom I looked up in various literature and material databases (like the material project) was between 8 and 9 eV, but I got 3300+ eV from placing an iron atom directly in the middle of the big box, whether using norm-conserving pseudopotential or PAW.

Maybe I still need to use some kind of energy difference to calculate the energy of a single iron atom, perhaps? But I don’t know how to obtain the total energy of a single atom from any kind of energy difference. This total energy should be a direct result of the GS calculation, not derived from other values.

A value of 3300+ eV is perfectly reasonable (it sums the energy of all valence electrons), but it is arbitrary (the core / valence partitioning is arbitrary). When a paper reports a value between 8 and 9 eV for the chemical potential of a Fe atom, they mean the difference in energy with respect to the most stable structure, that is, the energy per atom of bcc iron.

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