Recently, it has been seen in many article, dealing with ab-initio calculation, that energy of formation for a compound AxBy is expressed as below -
DelE (in eV) = E(AxBy) - xE(A) - yE(B)
Where, E(AxBy) is the energy of formation of the compound and E(A) and E(B) is energy of A and B in their respective stable state. At the outset it looks perfect, but problem starts if someone use a supercell (SC) with AnxBny where n is the multiplicity of the unit cell in the SC. In such cases the energy calculated from the above equation will be multiplied by n!!
Since, the energy/mol must be a constant value for a given compound and to compare energy of formation among different compounds the above equation should be modified as -
DelE (per mol) = c/(nx+ny) [E(AnxBny) - nxE(A) -nyE(B)]
where, c is the conversion factor from eV/atom to kJ/mol
Energy of formation normally is referred to the change in the energy for cleavage and formation of bonds. In the case of using SC, in adition to the bonds the neighboring interactions from periodic images are also included ( which in reality would affect the reaction energies, similar to including solvents).
One suggestion that I can make here is to determine the neighboring interactions by evaluation of energies in SC's with different sizes or comparing the energies at the same size under priodic and non-priodic conditions
Theoretically that is correct, however, we are interested in bulk material. For that one has to take periodic boundary condition in consideration. However, in that case the result should be independent of the SC size. But the question remains as to how the equation should be written. Alireza Asiaee
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