ENCUT and k-point convergence for slab+molecule adsorption

[emilyherrmann]

Hello!

I am studying the adsorption energy of an organic semiconductor molecule (pentacene) on a metal (copper) surface and I have a few questions about ENCUT and k-point convergence.

I had previously done these convergences just for the unit Cu cell and was converging based on the E0 value. After reading further, I have learned that it is beneficial to converge based on the adsorption energy, because that is my property of interest. This means that I will need to collect the value of (E0 - KE correction term) for the surface on its own, then for the molecule on its own, then for the combined system.

1) I have read that when modelling a single molecule, you should always use just the Gamma point for your k-point mesh. I would assume, however, that you should use the same k-point mesh for all three sets of runs (surface, molecule, combined) of the process. Is this true? If that's the case, will you end up using a non-gamma point mesh for the molecule?

2) When I previously did k-point convergence for just the Cu unit cell, the intended process was: 1) Converge k-points for single unit cell 2) Do Cu layer convergence. Every time the size of the Cu cell doubles in the z direction, halve the number of k-points in the z direction. 4) Do vacuum convergence on the pentacene molecule to determine how far apart the molecules would need to be to avoid interaction. Make the Cu cell this size in the x and y directions, similarly decreasing the number of k-points as the cell increases in size. Should I instead not do any of this halving and just converge the k-points for my adsorbed system and use that value?

If it is easier for you to just explain the process of ENCUT and k-point convergence for an adsorbed system step by step instead of directly answering my questions, that is fine!

Thanks!
Emily

[christopher_sheldon1]

\(\)Dear Emily,

Thank you for your question. You are correct that, for modelling adsorption on a metal surface, it is important to converge the adsorption energy. More generally, we recommend converging with respect to your property of interest. Converge using the

Code: Select all

free  energy   TOTEN  =

found in the OUTCAR file, except for a few special cases (this is not one of them).

The adsorption energy \(\Delta E\_{ads}\) is the energy difference between the bare surface \( E\_{S}\), the molecule \( E\_{M}\), and the molecule on the surface \( E\_{M \cdot S}\):

\(\Delta E\_{ads} = E\_{M \cdot S} - E\_{S} - E\_{M} \)

1) You should use the same k-mesh for S and M · S. It is important to use only the Gamma-point on the molecule. This is because you do not want any periodic interactions. Instead, you want to eliminate these to obtain energies for a gas-phase molecule. If you use a k-mesh, then you include the periodic images of the molecule and so calculate the energy of a diffuse molecule crystal, not the gas phase.

TLDR: use only the Gamma point k-mesh for a gas-phase molecule

2) To converge with respect to k-points, use an NxNx1 mesh, where 1 is the direction with the vacuum. You need to converge the k-mesh separately for each cell that you are using. For example, you could start with a 2x2x1 k-mesh for a (2x2) cell, then increase to 4x4x1, 6x6x1, etc until you reach convergence. This needs to be done for both S and M · S. The energy is not variational with respect to k-points, so it is important to use an even set of meshes (i.e., 2x2x1, 4x4x1, 6x6x1) or and odd set (e.g., 3x3x1, 5x5x1, 7x7x1) but do not mix the two, as some of the special points in the Brillouin zone will not be in both, which introduces additional error.

TLDR:
Should I instead not do any of this halving and just converge the k-points for my adsorbed system and use that value?
Yes, converge your adsorption energy with respect to k-point mesh.

You should also perform similar convergence for the energy cutoff (ENCUT) and the vacuum. Converge each variable in turn, rather than doing all at once. I tend to do:

• Number of layers of atoms - I usually stick with 4 but this should be tested in principle

• Vacuum height - (surface - 14 A is usually sufficient but should be checked) + (molecule - i tend to use 20x20x20 A, for a molecule as large as pentacene, you may need something larger)

• ENCUT

• k-point mesh

I notice that you're also using pentacene on the metal surface. It's worth checking to see if van der Waals is important (IVDW), which can be tested by doing all the calculations with and without it. D3 is a reasonable first guess, dDsC or MBD perform better but can also come with some computational difficulties. I covered the convergence test for the adsorption energy of RPA in this paper (https://doi.org/10.1063/5.0071995) but the procedure stands true for any density functional.

I hope that this helps to answer your question.

Best wishes,

Chris

EDIT:
It's also important to check whether or not the dipole correction is important. This requires the DIPOL, IDIPOL, and LDIPOL tags; Exercise 5 of the surface tutorials goes through this (https://vasp.at/tutorials/latest/surfac ... urface-e05). Apply it to the surface and surface with molecule adsorbed. If you place the molecule at the centre of the cell

[emilyherrmann]

Hello,

Thank you for this amazing reply! This has been extremely helpful. Sorry for my slow response, I've been going through your reply and have some follow up questions but wanted to make sure I had my thoughts all together first. Thank you for the link to the DIPOL exercise; figuring out whether to use the dipole correction is something I'd been trying to figure out.

1) I've seen other forum replies (including to another post I made) that do suggest subtracting off the KE error term when doing ENCUT convergence. Can you summarize (or link to another resource that talks about) when subtracting off this KE error is important? I convinced myself it makes sense to subtract it out when doing ENCUT convergence, but would love to hear more about any guidelines for deciding when to use it.

2) I have been planning to use van der Waals corrections. Up until now, however, I have not been using the IVDW tag and instead have been using the INCAR tags from the nonlocal vdW functionals page https://vasp.at/wiki/Nonlocal_vdW-DF_functionals page.

This decision was made only because a colleague had used these settings previously on a similar project. I've read through the articles explaining their differences, but can't figure out good guidelines for knowing which method (IVDW vs nonlocal functional) is more appropriate. The articles seem to suggest that the fully nonlocal functionals are more computationally expensive, so using the IVDW tag is appealing to me because the supercell will be large.

Also, if I wanted to test if vdW is needed at all, I could do the ENCUT convergence with and without vdW enabled, and if the result is the same for both, is that sufficient to say it is not needed?

3) Assuming vdW is needed, I'm also not completely sure how to test which of the vdW methods is "best." I have read papers discussing which method is most accurate for predicting lattice constants of various types of metals compared to experiment, but I am not sure this still holds true when choosing the "best" one for the molecule interaction, since best for intra-copper results may not translate to best for molecule-on-copper. Is there a way to specifically test if, for example, if dDsC is giving better results than D3 or if they are just different?

My general plan is as follows:
- Volume relaxation of bulk fcc Cu to find lattice constant. Because I will (probably) use vdW in my final system, I will have vdW enabled here as well.
- Use this lattice constant to create a layered slab of Cu of sufficient thickness (~8 layers)
- Choose a partially charged hydrogen to passivate the surfaces of the Cu and relax it into place. For this step, use a sufficiently large ENCUT based on all atoms that will be in adsorption system.
- Remove the hydrogen from the top and create a supercell of sufficient size (~5 layers, 15-20A vacuum) and do ENCUT convergence based on adsorption energy. Use this ENCUT going forward.
- Fix the bottom couple layers and hydrogen and do layer convergence to determine how many layers of Cu I need. Use sufficiently fine k-point mesh (~14)
- Do vacuum convergence for pentacene to determine how much vacuum above I need as well as how big in x,y my Cu supercell needs to be.
- Do k-point convergence for both supercell and supercell + molecule to determine k-point mesh
- Likely do final recheck of ENCUT convergence using the other converged values to make sure it is still converged.

Thanks!
Emily

[emilyherrmann]

After thinking more, I don't think the passivation of the copper slab is necessary or correct and I plan to remove it. Previous work by a colleague used partially charged hydrogen for passivation, but that work involved a semiconductor surface, not a metal. Using the hydrogen to passivate dangling, directional bonds makes sense, but seems to not be relevant for a metal surface. Other papers involving adsorption (including your linked one) do not passivate the bottom of the slab, which leads me to believe this change is correct.

[christopher_sheldon1]

Dear Emily,

I'm glad that it helped. I'll try to answer your points individually:

1) I am unsure about this. I have never done this myself but will ask in our meeting this week and check.

2/3) There is a certain amount of personal preference. There is no perfect van der Waals functional or dispersion correction.
TLDR: converge the adsorption energy or whatever your variable of interest is with respect to the dispersion correction/ vdW functional

I will include some images from my thesis that are not published elsewhere currently (https://edoc.hu-berlin.de/server/api/co ... 68/content):

For adsorption energies of (methane, ethane, propane, and n-butane on Pt(111) - C1-C4):

Screenshot 2026-09-22 163717.png

Screenshot 2026-09-22 163710.png

For the average height of the alkane chain above the Pt(111) surface:

Screenshot 2026-09-22 163702.png

Screenshot 2026-09-22 163453.png

PBE+D3 is a standard dispersion correction to use. It is okay for metals. PBE+D2 should never be used for adsorption on metal surfaces, unless you swap the C6 coefficients for those from the preceding noble gas. PBE+D3 overbinds a lot but is very easy to use. It gets too close to the surface, so the structure is not great. PBE+MBD and PBE+dDsC are both better for this; however, they are computationally trickier. MBD doesn't work for some highly polarisable atoms (https://vasp.at/wiki/Many-body_dispersion_energy), i.e., some metals, and dDsC (https://vasp.at/wiki/DDsC_dispersion_correction) can be difficult to converge the forces with, which brings problems with optimisation. They end up with similar results if all terms are considered. So, for the dispersion corrections, MBD and dDsC are your best bet energetically and structurally but more expensive and require more care than PBE+D3, which is simple and consistent, while overbinding energtically. The dispersion corrections are quick and cheap, which is their great strength, especially for long MD runs. Their accuracy is also reasonable.

For the vdW functionals, I don't know any individual one as well. You can see that the energies are pretty good (ignore the values for SCAN+rVV10 - this is a mistake that has subsequently been fixed. SCAN+rVV10 is about the same as the other functionals). The distances about the surface are reasonable. There is little between vdW-DF2, optPBE-vdW, and optB88-vdW. I wouldn't recommend one over the other. BEEF-vdW binds the energy very well but the structure is further from the surface. These vdW functionals are more expensive and don't offer much improvement compared to the dispersion corrections. I would test them, or perhaps a more modern one like r2SCAN+rVV10. They will be more expensive but quite reliable.

Ultimately, which dispersion correction of vdW-functional is best depends on your system and setup. I'd try a good vdW functional, and compare it to PBE+D3, PBE+MBD, and PBD+dDsC for example. You still need to do convergence tests for each of them but do it after the energetic convergence. The disadvantage of the vdW-functionals is that they are completely different functionals, so you need to converge the energetic part separately to the other three which are all PBE-based.

Your general plan is reasonable. Including vdW in the bulk calculation makes sense. Ideally it shouldn't make too much difference but it is more rigorous (I did not do this in my calculations). The most important thing is to consistently use the same lattice constants throughout. 8 layers is quite thick. I tend to use 4 but this is something to be tested. For DFT, the additional cost is not too much. Passivation I have no experience here, so cannot advise on this. Make sure to do the k-point/ layer convergence with respect to the adsorption energy or whatever property you are interested in. Likely you will not require such a dense k-mesh, which will save a lot of computational time. I'd do the k-mesh convergence before the vacuum, as it'll save you a lot of time in the vacuum convergence. With ENCUT, I'd use the largest ENMAX value for your POTCARs. Later, you can test to see if something larger is required. It most likely won't be but it is very important to check that the basis is converged.

I hope that you find this helpful.

Best wishes,

Chris