How to calculate E_TM in the formation energy formulas?

Question

I found in the literature that the formation energy of doped supercell (e.g.: 4x4x1 supercell with one dopant atom) has many formulas, and the most common one is :

$$E_{\textrm{form}}=E_{\textrm{total}}-E_{\textrm{defect}}-E_{\textrm{TM}}\tag{1}$$

1. What do they mean by $E_{\textrm{TM}}$? is it the energy of the dopant in its bulk stable phase ? or the energy of the dopant in isolated form?
2. How to calculate the energy of the Mn element in its bulk stable phase in VASP?
3. How to simulate and calculate the energy of an isolated atom in VASP?

Thanks in advance.

Reference paper : https://doi.org/10.1016/j.apsusc.2019.144367

Answer 1

What do they mean by ETM? is it the energy of the dopant in its bulk stable phase ? or the energy of the dopant in isolated form?

It is the energy of the transition metal element in its isolate form. A similar problem can be seen here. The energetic calculations can be seen here and here.

How to calculate the energy of the Mn element in its bulk stable phase in VASP?

You need the CIF (crystallographic Information File) with details of the crystal structure for $\ce{Mn}$ (you can obtain it from the Materials Project site). Then, you create the POSCAR input file where you add the calculation info (energy/mesh cutoff, exchange correlation functional, etc.)

How to simulate and calculate the energy of an isolated atom in VASP?

You can create an input file with only one atom (without crystal information) or create a (fake) crystal with only one atom in its center.