Chemical potential of an atom in a compound that is not in equilibrium

[mdtsakir]

TL;DR

Can a single, well-defined elemental chemical potential be directly obtained from a compound DFT calculation in VASP?

While reading DFT literature, I often see the chemical potential of an element described as its reference energy, typically taken from a bulk phase. For example, in BCC Li metal containing 128 atoms, the chemical potential of Li is commonly taken as the total energy divided by 128, which corresponds to the Li-rich limit.

However, for multicomponent compounds such as LLZO (La₃Li₇Zr₂O₁₂), papers usually report a range of allowed chemical potentials for each element. These ranges are determined by thermodynamic stability constraints: the chemical potentials must sum to the total energy (or formation enthalpy) of LLZO and also satisfy phase stability conditions against competing compounds.

My question is more fundamental. In a single VASP calculation of a compound, does VASP internally assign an energy to each atom that sums to the total energy of the system? In other words, is there a way to directly extract a unique chemical potential for a specific element in a compound from one DFT calculation, without invoking rich/poor limits or stability ranges? In Li metal, we effectively obtain a single chemical potential because it serves as its own reservoir. Is there any analogous way to obtain a single-valued chemical potential for Li (or any element) inside a compound from DFT, so that I can use that single number in further analysis (for example, when discussing related properties such as Fermi level alignment), instead of working with a range?

 

[Astronuc]

TL;DR: Can a single, well-defined elemental chemical potential be directly obtained from a compound DFT calculation in VASP?

While reading DFT literature, I often see the chemical potential of an element described as its reference energy, typically taken from a bulk phase. For example, in BCC Li metal containing 128 atoms, the chemical potential of Li is commonly taken as the total energy divided by 128, which corresponds to the Li-rich limit.

That would seem to work for a metal, especially a pure metal of which one gives an example. It might work for a binary (2-element) compound, but it may not work for ternary, quaternary or higher order compounds.

I see LLZO also written as Li₇La₃Zr₂O₁₂, which is a complex system.

TL;DR: Can a single, well-defined elemental chemical potential be directly obtained from a compound DFT calculation in VASP?

papers usually report a range of allowed chemical potentials for each element. These ranges are determined by thermodynamic stability constraints: the chemical potentials must sum to the total energy (or formation enthalpy) of LLZO and also satisfy phase stability conditions against competing compounds.

Does one have examples of such papers? Does the range reflect uncertainties, or different exchange correlations? Or does the range of chemical potential values relate to polymorphs/polytypes? Stoichiometry is another possibility, as is the presence of impurities and imperfections.

Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree–Fock theory with the rest of the exchange–correlation energy from other sources (ab initio or empirical). The exact exchange energy functional is expressed in terms of the Kohn–Sham orbitals rather than the density, so is termed an implicit density functional. One of the most commonly used versions is B3LYP, which stands for "Becke, 3-parameter, Lee–Yang–Parr".

Ref: https://en.wikipedia.org/wiki/Hybrid_functionals

Principal component analysis enables the design of deep learning potential precisely capturing LLZO phase transitions
https://www.nature.com/articles/s41524-024-01240-7

In looking for examples in the literature that might partially answer one's question, I found the following:
Reproducibility in density-functional theory calculations of solids.
https://backend.orbit.dtu.dk/ws/fil..._functional_theory_calculations_of_solids.pdf

Elastic Properties of the Solid Electrolyte Li₇La₃Zr₂O₁₂ (LLZO)
https://pubs.acs.org/doi/10.1021/acs.chemmater.5b03854

Looking at the individual cations, Li, La, Zr, they prefer compounds with O: Li₂0, La₂O₃, ZrO₂, so there are possibly polytypes. With Li, Zr and O, one obtains lithium zirconate, Li₂ZrO₃ <=> Li₂O + ZrO₂. Similarly, for lithium pentaaluminate, LiAl₅O₈ <=> LiAlO₂ + 2 Al₂O₃.

This thesis might be of interest - https://web.ornl.gov/~kentpr/thesis/Thesis.html

I have not used VASP or performed DFT, but I have had colleagues do such calculations on different materials, and I am families with some issues. It is an area of interest from the standpoint of the influence of radiation (and ionization) on the chemical potential of solids.