Binding Energies on Surfaces

DFT is routinely used to determine the adsorption energies of different atoms and molecules on metal surfaces. The adsorption energy is simply the change in energy when an atom or molecule is brought from (infinitely) far away from a surface to it’s equilibrium adsorption configuration.

In the case of a single atom X (of a diatomic molecule X2) adsorbing on a surface it is typical to evaluate the adsorption energy as [1]:

\begin{equation}E_{ads} = E_{surf+X} –  0.5E_{X_{2}}-E_{surf}\end{equation}

Adsorption Sites on FCC (111) Metal Surfaces

The (111) surface of FCC crystals (metals) have 4 unique adsorption sites. They are called the atop, fcc hollow, hcp hollow, and bridge site for the surface. They are pictured below convenience.

Atoms and molecules tend to preferentially bind to certain sites. This is something we would like to be able to determine. Luckily, (1) is valid for all of these binding sites so we can simply calculate the adsorption energies directly to determine what site an atom/molecule of interest may bind to.

Coverage Effects

When using plane-wave DFT codes, ones must always be aware of mirror images interacting. The distance between mirror images in such DFT calculations depends on the size of the supercell chosen as well as the number of adsorbates in the supercell.

It is common practice to place only 1 adsorbate within a supercell, meaning the supercell size determines the distance between mirror images. Below are figures showing how mirror images of adsorbates might “see” one another and how the distance between mirror images changes with supercell size.

The above figures help us infer that adsorption energies might decrease (adsorption more favorable) with increasing supercell size. This is consistent with the idea that most interactions between atoms fall off pretty rapidly with distance (e.g. vdW).

We investigate this by comparing the adsorption energies of an O atom adsorbed on the atop, fcc, hcp, and bridge sites of  Pt(111) using two different sized supercells, (2×2) and (3×3). These correspond to 1/4=0.25 ML coverage (O:Pt = 1:4) and 1/9 = 0.11 ML coverage (O:Pt = 1:9) respectively.

Calculation Details

All calculations were performed using the plane-wave Vienna Ab Initio Software Package (VASP) with the PBE exchange-correlation functional [1-4,7-8]. Core electrons were treated using the Projector Augmented Wave approach [5,6]. 1x1x1 Monkhorst-Pack mesh was used to sample k-space for the isolated O atom whereas 12x12x1 and 8x8x1 Monkhorst-Pack meshes were used to sample k-space for the 2×2 and 3×3 supercells, respectively. The plane wave cut-off energy was set to 550 eV and the structural optimizations considered complete when the magnitude of the forces on each atom was less than 0.02 eV. Dipole corrections were included in all surface calculations. Surface calculations used a 4-layer slab model wherein the bottom two layers were frozen during optimization. The lattice constants used was that determined using DFT instead of experiment; a = 2.78.

For discussions on convergence with respect to k-points and energy cut-off follow this link.

Results

Below are presented all energies calculated using VASP for the purposes of this exercise. First we present the energies of the bare surfaces as well as the isolated oxygen molecule followed by the calculated energies of the adsorbed oxygen at different binding sites.

System	Energy (eV/atom)
O2	-9.864
(2x2) Surf	-5.762
(3x3) Surf	-5.762

Table 1. Energies of Oxygen and Bare Surfaces

From the above results, particularly Fig.4 , a few observations can be made (elaboration to these observations is given in the following section):

1. At 0.25 ML coverage, the adsorption energies for O at the fcc and bridge sites are identical, and the lowest out of all sites (meaning O appears to preferentially bind to both the fcc and bridge sites at this coverage).
2. At 0.11 ML coverage the adsorption ebergies for O at the fcc and bridge sites are identical, and the lowest out of all sites (meaning O appears to preferentially bind to both the fcc and bridge sites at this coverage).
3. The difference in adsorption energies between 0.25 and 0.11 ML coverage is somewhat inconsistent: ignoring the bridge site calculations and comparing only hcp, fcc and atop sites, the adsorption energy is slightly lower for 0.25 ML in the case of  the fcc site while lower for 0.11 ML in the case of the hcp site and again lower for 0.11 ML in the case of the atop site.
4. Overall there is little difference in the magnitude of the adsorption energy between coverages for the same site.

Conclusions

We now try to reason reason with our results/observations from above.

In regards to point 1, a simple look at the optimized geometries reveals that initially placed bridge oxygen “fell” into the more stable fcc site. If one is careful about the choice in calculation parameters (specifically the maximum ionic displacement), it is possible to recover the actual bridge site adsorption energy. We leave this discussion here as it is theoretically and experimentally predicted that O will not bind to bridge sites, though calculating the bridge site adsoption energy would make a nice exercise in understanding how different calculation parameters affect one’s results. We can conclude that at 0.25 ML O adsorbs at the fcc site.

Point 2, similar to point 1, simply reveals that the 0.11 ML bridge site calculation “fell” to the more stable fcc, reinforcing the idea that the bridge site equilibrium geometry is sensitive to the calculation parameters. Regardless, the bridge sites for both 0.25 and 0.11 ML coverage failed to converge to the desired geometry and instead relaxed to other adsorption sites. From this we may conclude that the bridge site is not the preferred binding site of atomic oxygen on Pt(111).

Below we show the geometry of the system as built as well as after convergence for the bridge site calculation at 0.11 ML to show what we mean be the Oxygn “falling” into the more stable fcc adsorption site.

Comparing the two figures we can see the “guessed” (initial) position of the oxygen is rather close to both the equilibrium fcc and hcp sites. Due to this, during optimization when the atoms move, it is possible the O explores a region in space that is “too close” to the minimum associated with the fcc site. Since VASP is searching for a minimum and not a specific minimum, this means once the O explores regions of space that fall in the fcc minimum, the calculation will continue to allow the O atom to relax into the fcc site.

Moving to point 2 we may concisely conclude that at 0.11 ML O adsorbs at the fcc site.

Our last two observations are a little more nuanced. In this calculation scheme, we have chosen not to apply zero-point energy corrections, nor have we included any entropic effects. In this case, we might expect out entropic effects to be roughly the same since both the 0.25 and 0.11 ML cases have 1 O atom and the same number of metal atoms “before” and after “adsorption”. Zero-point energy corrections (ZPE) can be significant, at least relative the the energies we are considering.

Thus, for now, we can conclude that O binds to the fcc site of Pt(111) surfaces at 0.25 and 0.11 ML coverage and that without ZPE and entropy corrections, there is a negligible difference in adsorption energies with respect to the coverage.

While the effect of coverage is not clear using the methods outlines above, it is reassuring that our calculations predict O to preferentially bind to the fcc site at both 0.25 and 0.11 ML coverage, as is found in experiment and predicted by computation [9].

Future Work

Naturally one would like to see how the ZPE and entropy corrections influence the results. One would expect there to be some increase in the difference between adsorption energies at 0.25 and 0.11 ML coverage. On a similar note, in this work we have used an asymmetric slab model with 4 layers (as is common for efficiency). One may also consider a symmetric slab model or perhaps a 5 layer slab to see if there is any splitting between these two coverages. This will be explored in future posts.

References

 

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[9]     Chen, M., Bates, S. P., Santen, van, R. A., & Friend, C. M. (1997). The chemical nature of                    atomic oxygen adsorbed on Rh(111) and Pt(111): a density functional study. Journal of                  Physical Chemistry B, 101(48), 10051-10057.