# How to calculate E_TM in the formation energy formulas?

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?

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

– Jack
Mar 18, 2021 at 10:36
• Its is done brother. Mar 18, 2021 at 12:34
• From the paper: "Here, Etotal, Edefect, and ETM represent...and the energy of the TM element".
– Camps
Mar 18, 2021 at 14:49

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.

• I have understand your point but when I have read the answer provided here : physics.stackexchange.com/questions/43935/…. I think E_TM is the energy of the atoms in bulk state as mentioned in link above. I am a little bit confused between the definition of formation and cohesive energy. Mar 18, 2021 at 21:19
• The formation energy is obtained from the system that will form the final compound. In this case, you have a crystal, and an atom. The example in the link, have two bulk systems (solid aluminum and O2) which is different from your.
– Camps
Mar 19, 2021 at 13:21
• will there be a big difference between the energy of bulk and of isolated state ? Mar 19, 2021 at 18:42
• Sure. But it is possible to calculate the energy of bulk crystal per atom, too. But I am not sure if this is correct.
– Camps
Mar 19, 2021 at 18:44