Dear Sir, 

Let us first discuss about Cohesive energy of Nitrogen doped Graphene, which can be obtained by, 

Ecoh = TOTAL E-n(single Carbon E)-y(single nitrogen atom E) 

where n = Total number of  C atoms in the unit cell

          y = Total number of N atoms in the unit cell

lly, In the N-doped graphene the formation energy can be calculate as 

Eform = TOTAL E- n(Binding energy per C atom in pure graphene sheet)-n(E(N2)/2) 

n, and y are same as above.

* in formation energy you should take the binding energy of constituent atoms in their native state

Also consider an important difference: do you need the formation energy of the doped crystal or the energy needed to dope it?

The cohesive energy of the crystal is defined as the energy (per unit cell) required to from the crystal starting from the elementary constituents. The latter, can be isolated atoms or molecules, depending on the system.

The doping energy, instead, is define as the energy needed to insert the dopant at some site in the crystal.

Aldo the choice of elementary constituents has to be carefully considered. For example, if you adsorbing and H atom on a surface, the energy of the "isolated" H atom is taken as half the total energy of the H2 molecule, because this is the most stable form of H. In this case you are considering that your system is in contact with a reservoir of H2 molecules. But if you are inserting a Si atom, you  might want to use the  cohesive energy per atom of bulk Si, because this is the usual stable form you encounter.

You can consider D'Amico, Nunzio Roberto, Giovanni Cantele, and Domenico Ninno. “First-Principles Calculations of Clean and Defected ZnO Surfaces.” Journal of Physical Chemistry C 116, no. 40 (October 11, 2012): 21391–400. doi:10.1021/jp306785z and, in particular, references 61-64 which quite clearly explain the concept of formation energy, surface energy, chemical potential of a given species, and so on.

Article First-Principles Calculations of Clean and Defected ZnO Surfaces

thanks for the help Dr Naga & Dr. Giovanni.

Hello,

I think you touch the question of the stability of a compount not only with respect to its structure but also to its composition.

Thereon we did some work in our series of calculations on "stability lines" in energy diagrams (I-III). I hope it can help.

F. Bachhuber, A. Krach, A. Furtner, T. Söhnel, J. Rothballer, R. Weihrich, Phase Stabilities of pyrite-related MTCh Compounds (M=Ni, Pd, Pt; T=Si, Ge, Sn, Pb; Ch=S, Se, Te): A systematic DFT study, J. Solid State Chem. 2015; 226, 29-35.

F. Bachhuber, J. Rothballer, T. Söhnel, R. Weihrich,

Phase stabilities at a glance: Stability diagrams of nickel dipnictides

J. Chem.Phys. 2013, 139, 214705

F. Bachhuber, J. Rothballer, T. Söhnel, R. Weihrich, Energy diagrams II – ternary pyrites, Comput. Mater. Sci. 2014, 89, 114-121

https://www.researchgate.net/publication/272182027_Phase_Stabilities_of_pyrite-related_MTCh_Compounds_%28MNi_Pd_pt_TSi_Ge_Sn_pb_ChS_Se_Te%29_A_systematic_DFT_study?ev=prf_pub

Best wishes,

Richard

Article Phase stabilities of pyrite-related MTCh compounds (M=Ni, Pd...

using 09 gaussian software u easily find out the formation energy or minimum energy

Thanks Prof Kuppu & Prof. Weihrich 

You can calculate formation energy by using CASTEP code

Using gaussian or hyper chem software, you can calculate formation energy

By using gaussian you easily solve formulation energy

how to calculate formation energy by using wien2k code?