# Inconsistent data of chemical potential from different papers

I am looking for chemical potential from literature.$$^{1,2}$$ I compared the method and data they provided. They use the Fitted Elemental Reference Energy method via GGA+U on VASP employing PAW. U values in these paper are a little different. As far as I understand from the papers, the chemical potential is equal to total energy of an isolated atom in a box (for example, 10x10x10). Am I right? Then I think it should be similar. However, found that the data are somehow inconsistent. For example:

Element Paper 2 (Table 1) Paper 1 (Table V: Appendix)
Fe 2.200 -6.15
Mn 1.987 -7.00
Co 1.987 -4.75

Can anyone help me to explain?

1. Stevanović, V., Lany, S., Zhang, X., and Zunger, A. Correcting density functional theory for accurate predictions of compound enthalpies of formation: Fitted elemental-phase reference energies Phys. Rev. B 85, 115104 https://doi.org/10.1103/PhysRevB.85.115104
2. Kirklin, S., Saal, J., Meredig, B. et al. The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies. npj Comput Mater 1, 15010 (2015). https://doi.org/10.1038/npjcompumats.2015.10
• Are these papers using different codes / levels of theory? Total energies are often arbitrary and only differences can be looked at. – Tristan Maxson Sep 20 '20 at 11:32
• I think chemical potential (reference) is not the isolated atoms in a box but from the elemental ground states, for example, metallic Fe for Fe. Note that the absolute value of chemical potential in DFT is only meaningful with respect to a particular set of pseudopotentials (just like the actual values of the energy themselves). – bzbzbz Sep 20 '20 at 11:42
• @TristanMaxson as I understand from these papers, they both used VASP with same method. – Binh Thien Sep 20 '20 at 14:47
• @Binh Thien yes, in theory, you are free to choose which phase to use but bear in mind that the experimental data are sometimes only available to some of the phases. The convention would be to use the one that is stable at "standard conditions". – bzbzbz Sep 21 '20 at 10:42
• It would be helpful if you explained why you need the chemical potentials. The chemical potential is the energy of an atom in a reference configuration, usually the elemental material (e.g. FM bcc for iron); since there is an arbitrary "zero" of energy, the absolute value of this number is meaningless, its usefulness comes from its value relative to that in other environments. A chemical potential computed in a plane-wave DFT package such as VASP would be expected to depend strongly on the pseudopotential and XC functional, but the relative values would be much more consistent. – Phil Hasnip Nov 12 '20 at 1:48