Definition for formation energy

Hi everyone. I’d like to find the exact definition of formation energy as intended in Materials Project, e.g., in “Explore Materials”.

How (if it does) the definition for formation energy differs from the definition of the cohesive energy of a compound Ecoh = E(AnBm) - nE(A) - mE(B)?

Many thanks.

The difference is the state of the references, which means how E(A) and E(B) are defined.

The cohesive energy is the energy of bringing each atom of A and B together from infinite distance. Experimentally the equivalent would be going from gas and crystallizing into that compound. Here E(A) and E(B) is the energy of a single atom of A and B in vacuum.

The formation energy is the energy of starting at the ground state of pure A and B. Here, E(A) and E(B) are the ground states from MP Phase diagrams of pure A and pure B. For instance, for Fe, that would be energy of BCC Fe: mp-13

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Thanks a lot. These are, indeed, the definitions for E_coh and E_form as commonly understood. A concrete question, though, let’s take Ta3N5; the formation energy as reported in materialsproject runs is calculated based on Tantalum (bulk metal) and N2 gas molecule, am I right?
Thanks again.

Yup, that is correct. The only reason for that is because the N2 entries in the MP phase diagram are corrected to be the gas phase energy.