# Binding energy calculation for Zn atom on armchair graphene slab?

I am trying to repeat the result of this paper for Zn absorbed on the armchair graphene slab.

The relaxed top and side structures are the following:  The relaxed structure is almost the same as the cited paper. Then the energy calculation based on this relaxed structure is listed below:

• E(slab+Zn)=-759.31696 (eV)
• E(slab)=-759.30724 (eV)

The energy of Zn is obtained from its bulk calculation:

• E(Zn)=-1.1078938 (eV)

Then the binding energy is estimated as:

• $$\Delta E$$=E(slab+Zn)-E(slab)-E(Zn)=1.0981738 (eV)

However, the result of the cited paper is -0.2 eV: What am I missing?

For completeness, I will give my input cards for relaxation and static calculations as follows:

 System=2D
ISTART=0        !startjob: 0-new 1-cont 2-samecut
ICHARG=2        !charge: 1-file 2-atom 10-const
ENCUT=500       !energy cutoff in eV
EDIFF=1E-6      !stopping-criterion for electronic upd.
NELM=300        !nr. of electronic steps
ISMEAR=0        !part. occupancies
SIGMA=0.05      !broadening in eV -4-tet -1-fermi 0-gaus
IALGO=38
LREAL=Auto
IVDW=11

#------------------
#ISPIN=2        !spin polarized calculation (2-yes 1-no)
#MAGMOM=128*0   !initial mag moment / atom
#LSORBIT=.TRUE. !if .TRUE. switches on spin-orbit coupling
#SAXIS= 0 0 1   !quantisation axis for spin
#ISYM=0         !symmetry: 0-nonsym 1-usesym

Dynamic:
ISIF=2
IBRION=2
NSW=300
EDIFFG=-0.005

Parallelization:
NPAR=8
#KPAR=4

Output:
LCHARG=.FALSE.
LWAVE=.FALSE.


=========================================

 System=2D
ISTART=0        !startjob: 0-new 1-cont 2-samecut
ICHARG=2        !charge: 1-file 2-atom 10-const
ENCUT=500       !energy cutoff in eV
EDIFF=1E-6      !stopping-criterion for electronic upd.
NELM=300        !nr. of electronic steps
ISMEAR=0        !part. occupancies
SIGMA=0.05      !broadening in eV -4-tet -1-fermi 0-gaus
IALGO=38
LREAL=Auto
IVDW=11

#------------------
#ISPIN=2        !spin polarized calculation (2-yes 1-no)
#MAGMOM=128*0   !initial mag moment / atom
#LSORBIT=.TRUE. !if .TRUE. switches on spin-orbit coupling
#SAXIS= 0 0 1   !quantisation axis for spin
#ISYM=0         !symmetry: 0-nonsym 1-usesym

Dynamic:
#ISIF=2
#IBRION=2
#NSW=300
#EDIFFG=-0.005

#Parallelization:
NPAR=8
#KPAR=4

Output:
#LCHARG=.FALSE.
#LWAVE=.FALSE.


For convenience, the computational details for the cited paper are put below: • Can you share your INCAR? Are you reproducing their exact theory? – Tristan Maxson Oct 13 '20 at 16:03
• The energy of Zn was obtained from bulk but is not the bulk energy right? – Camps Oct 13 '20 at 18:03
• @Camps I calculated from bulk because from this information: [The energy of the Zn atom was calculated using the metallic Zn configuration]. Am I wrong? How can estimate the energy of the single Zn atom? – Jack Oct 13 '20 at 21:16
• Yes, you should use the energy of a single atom, as it is a single atom interacting with your slab. – Camps Oct 14 '20 at 12:26
• Using the energy of a single atom can mean many things. It should be a single atom in its standard state (Zn metal) not a single atom in gas phase. Technically you could use a single atom in gas phase as the reference if you wanted to calculate a true "binding" energy but this sort of binding is unreasonable to look at. Using the metallic state you would get a formation energy. Maybe this is the confusion. – Tristan Maxson Oct 14 '20 at 15:06

## 1 Answer

As mentioned by @Camps in the comments, the Zn reference used in the paper is almost certainly that of an isolated Zn atom in the gas phase. If I understand correctly from briefly scanning the paper, the source of Zn in the device (as viewed from the graphene-coated separator) will be Zn2+ ions dissolved in the electrolyte - not quite the same thing as Zn in the gas phase, but certainly not Zn bulk.

In order to get an accurate result, take the cell you used for the slab+Zn calculation, delete the slab and recompute the total energy.

I agree that the description "metallic Zn configuration" in conjunction with individual Zn atoms is somewhat confusing; it may have been intended to indicate the (neutral) charge state or a specific magnetic configuration - I'm sure the authors would be happy to clarify!