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.