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

mdtsakir
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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?
 
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