Hello everyone,
I’m new to DFT (Wien2k) and currently trying to calculate surface energies. For that, I need to determine the chemical potential of an element in its bulk form (e.g., Ni or P in my case).
I’ve searched online, but I couldn’t find a clear answer. Some sources suggest using the total energy per atom from a bulk calculation, but I want to confirm if that approach is valid.
Could someone please clarify:
- How do we correctly calculate the chemical potential of a pure element (like Ni) in DFT?
- Is it acceptable to take the total energy per atom of the bulk unit cell directly as the chemical potential?
- Are there any important corrections needed in this case?
Thank you in advance!
For your case (pure bulk solid), the total energy per atom of the bulk unit cell is often used directly as the chemical potential. If I recall correctly, that’s what I did in this paper: 10.1021/acs.jpcc.6b03371 .
In general, one thing you should make sure you’re clear on is whether you want the surface energy (usually just subtracting the electronic energies, and is essentially a surface enthalpy) or the surface free energy (usually involves some thermodynamic corrections). Depending on the specific conditions/material, if you truly want the chemical potential you may want to do some thermodynamic corrections, but in most cases for a bulk solid these are small and people just use the total energy straight from DFT.
Hey Barani Kumar
In fact, the chemical potential (mu) of a pure element is the Gibbs free energy per atom (mu = G/N) at 0 K and zero pressure, which happens to be the typical DFT conditions i.e., EDFT ~ U ~ G. EDFT doesn't consider vibrational contributions, so ZPE correction is needed for light elements, which is not the case for Ni. For light elements, include ZPE correction, so mu = (EDFT + EZPE)/N. If your system is under pressure, consider adding PV correction, mu = (EDFT + EZPE +PV)/N.
Now if you want to compare with experiments at non-zero temperatures, G ~ U - TS, i.e., entropy kicks in (normal pressure conditions). Overall, under standard DFT conditions, mu = G/N is good enough, but apply corrections for the cases above if needed.
Best,
Gabriel Vinicius
No, the total energy per atom is not an authentic representation of the chemical potential in DFT. Chemical potential is formally defined as the partial derivative of the total energy with respect to particle number, reflecting the energy change associated with adding or removing atoms or electrons. In contrast, total energy per atom is an average quantity and lacks the rigorous thermodynamic meaning required to describe chemical potential accurately.
Thank you for your valuable answers!
Prakash Yadav Gabriel Vinicius Matthew M. Montemore
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