Category Archives: Adsorption

Predicting the Preferred Binding Site of Atomic O on Pt (111)

By Nathan McKee

Introduction

This post examines the adsorption of atomic oxygen on the platinum (111) surface. Platinum has an fcc structure, so there are four high-symmetry adsorption sites on the (111) surface. These are the top, bridge, hcp hollow, and fcc hollow sites. DFT calculations were performed for atomic oxygen placed on a slab of platinum (111) in each of the high-symmetry sites, and their energies were compared to determine the preferred binding site. The DFT calculations were carried out with the plane-wave based code CASTEP. The GGA PBE functional was used1, as well as on-the-fly generated (OTFG) ultrasoft pseudopotentials2. These pseudopotentials include 6 valence electrons for oxygen in the 2s2 2p4 configuration with a cutoff radius of 0.58 Å, and for platinum they include 32 valence electrons in the 4f14 5s2 5p6 5d9 6s1 configuration with a cutoff radius of 1.27 Å. The convergence tolerance was set at 2.0*10-5 eV per atom.

Cell Construction

The unit cell used for the calculations was constructed to form a p(2 x 2) 0.25 monolayer (ML) surface coverage, as shown in figure 1. This means that the unit cell contains a 2 x 2 arrangement of Pt (111) unit cells with one oxygen atom on top. This results in having one oxygen atom adsorbed to the surface for every four platinum atoms on the surface of the slab. In other words, a quarter of a monolayer of oxygen covers the surface in an ordered pattern.

Figure 1: The p(2 x 2) 0.25 ML surface coverage is shown, with the supercell represented by the solid black line. Adapted from Sholl & Steckel3.

The thickness of the platinum slab was chosen to be 3 layers. While more layers would result in a more accurate calculation, three layers was estimated to be sufficient for identifying the preferred binding site of oxygen. In addition, including more than 3 layers became prohibitively expensive for the calculations.

The length of the vacuum in between slabs was chosen to be 10 Å. This distance was chosen to be sufficiently large to determine energies accurately enough to identify the preferred binding site. Larger vacuum gaps may provide more accurate calculations, but would require a larger cutoff energy and more computational time. It should also be noted that a self-consistent dipole correction in the z direction (normal to the slab) was implemented in the calculation to prevent different slabs from interacting with each other and altering the calculated energy.

Cutoff Energy and k Points

To ensure that the calculations converge properly, an analysis of the selection of k points and the cutoff energy was performed. The k points were chosen to be an NxNx1 Monkhorst-Pack grid4 of evenly spaced points in reciprocal space, as is conventional for slab models in which the “a” and “b” lattice constants are equal.

Figures 2 and 3 show how an energy calculation converges as the number of irreducible k points is increased and as the cutoff energy is raised. In both cases, an arbitrary constant (157046 eV) was added to the calculated energies so that the values would be close to zero and the convergence could be seen more easily. The calculations for k point convergence were performed with the oxygen on the top site, 2.01 Å away from the surface plane, with a cutoff energy of 650 eV. The calculations for the cutoff energy convergence were performed for the same site with a 6x6x1 k-point grid.

Figure 2: The energy calculation converges as the number of irreducible k points increases. The y axis has been shifted by +157046 eV to better show the differences. A 6x6x1 k point grid, with 18 irreducible k points, reproduces the results of a calculation with 41 irreducible k points within 0.01 eV.

Figure 3: The energy calculation converges as the cutoff energy increases. The y axis has been shifted by +157046 eV to better show the differences. A cutoff energy of 650 eV produces the same result as a cutoff energy of 750 eV, within 0.003 eV.

Using these graphs as a guide, a 6x6x1 k point grid was used in conjunction with a cutoff energy of 650 eV for further calculations. A variation of ~0.01 eV is sufficient for measuring energy differences between binding sites, which were later calculated to be on the order of ~0.5 eV.

Results

At first, calculations were made with a static slab, placing the oxygen atom on a particular site and manually setting the adsorbate’s distance from the surface. Energy calculations were made in this way, varying the vertical position of the adsorbate in order to minimize the energy. Thus an approximation of the minimum energy was made for each of the four high-symmetry binding sites. The results of these calculations are shown in figures 4-7. Note that all the y axes have been shifted by the same amount, allowing for easy comparisons of the energy. The results suggest that the fcc hollow site is the most preferred binding site, followed in order by the hcp hollow site, the bridge site, then the top site.

Figure 4: The equilibrium z-position of the oxygen atom on the top site is found through energy minimization. The y axis has been shifted by +157046 eV. A quadratic fit indicates a minimum energy of 2.21 eV.

Figure 5: The equilibrium z-position of the oxygen atom on the bridge site is found through energy minimization. The y axis has been shifted by +157046 eV. A quadratic fit indicates a minimum energy of 1.50 eV.

Figure 6: The equilibrium z-position of the oxygen atom on the hcp hollow site is found through energy minimization. The y axis has been shifted by +157046 eV. A quadratic fit indicates a minimum energy of 1.40 eV.

Figure 7: The equilibrium z-position of the oxygen atom on the fcc hollow site is found through energy minimization. The y axis has been shifted by +157046 eV. A quadratic fit indicates a minimum energy of 0.93 eV.

To follow up on these estimations, two full geometry optimizations were performed. These calculations allow the oxygen atom to move around, and allow the top layer of the platinum slab to deform. The previous calculations were used to place the oxygen atom at a z-position close to the energy minima to ensure that the geometry optimizations converged correctly. The first optimization started with the adsorbate close to the hcp hollow site, and the second optimization began with the adsorbate close to the fcc hollow site. These sites were chosen because they had the two lowest energies from the first round of estimates. In each case, the oxygen atom was placed about 0.1 Å away (horizontally) from the site. This practice breaks the symmetry in the ab plane to test whether the site is a local minimum. In both cases tested, the adsorbate returned to the high-symmetry site being tested, indicating that the hcp hollow and fcc hollow sites are both local minima.

For the geometry optimization of the hcp hollow site, the calculated energy minimum was -157044.86 eV. For the fcc hollow site, it was -157045.47 eV. The fcc hollow site energy is lower by a margin of ~0.61 eV, indicating that atomic O prefers to bind to the fcc hollow site instead of the hcp hollow site. This is in agreement with the estimates obtained manually, but this result is more definitive because the calculations include deformations of the top layer of the platinum slab.

Note that both energies obtained through geometry optimization are lower than the energies obtained by manually adjusting the adsorbate position. This is expected, as the geometry optimization allows for surface relaxation on the top layer of the platinum slab.

Conclusion

These results indicate that atomic oxygen prefers to bind on the fcc hollow site of the Pt (111) surface. This is in agreement with previous results5, which also use DFT to identify the fcc hollow site as the preferred binding site.

References

  1. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
  2. Gonze, X. & Finocchi, F. Pseudopotentials Plane Waves–Projector Augmented Waves: A Primer. Phys. Scr. 2004, 40 (2004).
  3. Sholl, David S. & Steckel, Janice A. Density Functional Theory: A Practical Introduction. John Wiley & Sons, Inc. (2009).
  4. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).
  5. Gu, Z. and P.B. Balbuena, Absorption of Atomic Oxygen into Subsurfaces of Pt(100) and Pt(111):  Density Functional Theory Study. The Journal of Physical Chemistry C, 2007. 111(27): p. 9877-9883.

Effect of Coverage on Adsorption Energies

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.

Fig. 1 Adsorption sites on Pt(111); (left to right) bare surface, atop, fcc, hcp, bridge).

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.

Fig 2. Two 2×2 supercells of an O atom adsorbed on Pt(111). (The indicated distance is in Angstrom)

Fig 3. Two 3×3 supercells of an O atom adsorbed on Pt(111). (The indicated distance is in Angstrom).

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.

SystemEnergy (eV/atom)
O2-9.864
(2x2) Surf-5.762
(3x3) Surf-5.762
Table 1. Energies of Oxygen and Bare Surfaces

Fig. 4 Adsorption energies of atomic Oxygen on Pt(111) at 0.25 and 0.11 ML.

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.

Fig. 5 0.11 ML bridge site geometry as built (left) and after convergence (right).

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

 

[1]     G. Kresse and J. Hafner. Ab initio molecular dynamics for liquid metals. Phys. Rev. B,                      47:558, 1993.

[2]     G. Kresse and J. Hafner. Ab initio molecular-dynamics simulation of the liquid-metal-                      amorphous-semiconductor transition in germanium. Phys. Rev. B, 49:14251, 1994.

[3]     G. Kresse and J. Furthmüller. Efficiency of ab-initio total energy calculations for metals and            semiconductors using a plane-wave basis set. Comput. Mat. Sci., 6:15, 1996.

[4]     G. Kresse and J. Furthmüller. Efficient iterative schemes for ab initio total-energy                            calculations using a plane-wave basis set. Phys. Rev. B, 54:11169, 1996.

[5]     D. Vanderbilt. Soft self-consistent pseudopotentials in a generalized eigenvalue                              formalism. Phys. Rev. B, 41:7892, 1990.

[6]      G. Kresse and J. Hafner. Norm-conserving and ultrasoft pseudopotentials for first-row                   and transition-elements. J. Phys.: Condens. Matter, 6:8245, 1994.

[7]      J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized gradient approximation made                      simple. Phys. Rev. Lett., 77:3865, 1996.

[8]     J. P. Perdew, K. Burke, and M. Ernzerhof. Erratum: Generalized gradient approximation                 made simple. Phys. Rev. Lett., 78:1396, 1997

[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.