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
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.