Work function of functionalized graphene

[GJK]

Hi,

Request the procedure for computing the work function of functionalized graphene nanoribbon..For silver we have but what are the parameters to be fixed if we are to compute workfunction of GNR.A detailed procedure could help us in this regard

Already we are calculating chemical potential during optimization process.Can we use that result as work function or not???

[Petr Khomyakov]

I do not see much of a difference when computing work function
 of functionalized vs. pristine graphene sheet, see the following tutorial for work function calculations,  https://docs.quantumatk.com/tutorials/work_function_ag_100/work_function_ag_100.html.

[GJK]

Hi,

I have read this tutorial.For graphene nanoribbon. We  are already defining the structure for GNR as described by QUANTUMATK.

In the tutorial for Ag work function there are parameters for vacuum padding ,thickness  etc.
How to fix ghost atoms in GNR?? Do we need to perform surface cleave as said for Silver in your tutorial???

We are already calculating chemical potentail for our functionalized system.Can we take that as work function?? If not then how to fix the ghost atom and is surface cleave parameters necessary for GNR???

[Petr Khomyakov]

If you already have a graphene sheet, you do not need to cleave it from the graphite crystal. In fact, you do not need to do it in any way, because a single graphene monolayer can be built by just increasing the out-of-plane lattice parameter of graphite to add a sufficiently-thick vacuum padding in-between the graphite monolayers.

Setting ghost atoms is more tricky. If you use plane-wave DFT calculator of QuantumATK, you actually do not need to use any ghost atoms. Otherwise, for LCAO-DFT it involves some experimenting. You  may first start doing these calculations without ghost atoms.   

[GJK]

Hi,

In the calculator we have option ATK_DFT and we use LDA.PZ single zeta polarized for our functionalized GNR structure and optimized the same. In result we obtained the chemical potential.can we consider chemical potential to be the work function???

Because we did optimization of the structure as a whole.Do we need to include ghost atoms or can we consider the chemical potential as work function???

[Petr Khomyakov]

Do we need to include ghost atoms or can we consider the chemical potential as work function???

That are two completely different things. Work function is in the energy required to remove an electron from the Fermi level and move it far from the surface to the vacuum level. If the vacuum level energy coincides with zero energy (which can be checked by computing the effective potential or Hartree difference potential), then work function is absolute value of the chemical potential. Otherwise, you have to measure the energy between the Fermi energy (chemical potential) and the vacuum level energy as given by the effective or Hartree difference potential.

Using ghost atoms might be required for more accurate description of wave function tails in the vacuum region, i.e., relatively-far from the surface, when using an LCAO basis set, because of the localized nature of the numerical atomic orbitals.

[GJK]

How to calculate the workfunction for the functionalized graphene nanoribbon which is given in the attachment???

[GJK]

Herby I have attached the effective potential for ZGNR. How to find the value of effective potential inorder to calculate the vacuum  level energy. Since, we are getting a 3-dimensional cube file.

[GJK]

Also we have attached the Hartree difference potential calculated for ZGNR.
The formula for work function is W= -e(phi)-EF

1.Should we multiply the Hartree difference potential by e???
2.As you advised, we computed both Effective potential and Hartree difference potential but we are getting two different values as reflected by colour coding. What potential value we should subtract from Fermi Level(Chemical Potential)

Because Effective potential is showing -52 eV whereas Hartree Difference Potential is showing +0.14 eV which value we should take for vacuum energy level???

[Petr Khomyakov]

- Hartree difference potential [eV] = - |e| Electrostatic difference potential [Volt]

- The vacuum level is well-defined in the vacuum region infinitely-far from the nanoribbon. So, one should therefore use thick-enough vacuum padding around the nanoribbon when computing the work function, as well as non-periodic boundary conditions at the simulation cell boundaries. In this case, the effective potential and Hartree difference potential should approach the same value in the vacuum far from the nanoribbon. As a matter of fact, your simulation cell must be much larger than an effective width of your nanoribbon with or without functionalization.

I still do not fully understand what you are trying to achieve in this calculation. Work function is a solid-state concept for infinite surfaces, whereas your system looks more like an infinitely-long molecule. In this case, it seems to make more sense to talk about ionization potential. Is it what you are trying to compute?

[GJK]

First of all we sincerely thank you.

How to fix ghost atoms and boundary conditions for the functionalized ZGNR structure which is already given in as image file in attachment???

We want to compute the workfunction of functionalized ZGNR.

We have tutorial only for Silver work function.

Do we need to include ghost atoms or can we consider the chemical potential as work function???

That are two completely different things. Work function is in the energy required to remove an electron from the Fermi level and move it far from the surface to the vacuum level. If the vacuum level energy coincides with zero energy (which can be checked by computing the effective potential or Hartree difference potential), then work function is absolute value of the chemical potential. Otherwise, you have to measure the energy between the Fermi energy (chemical potential) and the vacuum level energy as given by the effective or Hartree difference potential.

Using ghost atoms might be required for more accurate description of wave function tails in the vacuum region, i.e., relatively-far from the surface, when using an LCAO basis set, because of the localized nature of the numerical atomic orbitals.

As per this reply we calculated the Hartree Difference potential and effective potential of ZGNR and functionalized ZGNR and obtained + 0.14 eV and -0.71 eV respectively.Whereas the effective potential came as -52 eV and -53 eV respectively.But we calculated without inclusion of ghost atoms.We took difference between this Hartree difference potential and Chemical potential which is the work function and obtained 5.24 eV for ZGNR.But the maximum reported value in litreature for graphene is 4.9 eV.

How and where to include the ghost atoms???
What should be the maximum vacuum padding to be fixed???
What boundary conditions to be employed for this kind of structure???

[Petr Khomyakov]

But we calculated without inclusion of ghost atoms.We took difference between this Hartree difference potential and Chemical potential which is the work function and obtained 5.24 eV for ZGNR.But the maximum reported value in litreature for graphene is 4.9 eV.

I am not sure I understand your argument regarding "maximum reported value".  Moreover, comparing work function of pristine graphene sheet with that of a narrow graphene nanoribbon (with or without functionalization) does not make much sense, at least to me.

How and where to include the ghost atoms???
What should be the maximum vacuum padding to be fixed???
What boundary conditions to be employed for this kind of structure???

I guess one would have to do actual calculations to answer all these questions. To avoid using ghost atoms, which is very tricky within the LCAO approach for such open structures as yours (compared to closed-packed structures such as Ag metal used in the work function tutorial), one could try using plane-wave basis set to do these calculations. The plane-wave approach is available in recent versions of QuantumATK.