Author: Sharad Maheshwari
Introduction
In the following work, we aim to use plane wave Density Functional Theory (DFT) calculations to identify the preferred adsorption site for atomic H on (111) crystal surface of Platinum. We further seek to examine how the adsorption preferences change as the coverage of atomic H changes on the surface.
Adsorption sites on Pt (111)
Adsorption on (111) crystal surface of FCC metals can take place on 4 different sites with metal coordination as indicated in the parentheses, namely: atop (1), bridge (2), fcc (3) and hcp (3). The fcc and hcp site differ in the sub-surface stacking of the metal atoms. Figure 1 below illustrates all these binding sites with an H atom on these sites.
Figure 1. Different adsorption sites on Pt (111) crystal surface illustrated with H atom1. a) Atop b) Bridge c) FCC d) HCP. The white ball is H atom. Yellow balls indicate metal atoms in the first layer. Dark green balls are the metal atoms in the second layer. On FCC site, there is no metal atom in the second layer right below the site, whereas for HCP site, one can see a metal atom in the second layer exactly below the H atom.
Adsorption Energy
To estimate the strength of binding between adsorbate and the surface, we can evaluate the adsorption energy of the species on the surface. For a reaction
A + * → A*
where, A is the adsorbate in the reference state, * indicates the surface and A* indicates the adsorbate bound on the surface, adsorption energy is can be given as
Eads = EA* – EA – E* (1)
where Eads is the adsorption energy, EA* is the DFT energy of the adsorbate A bound to the surface, EA is the DFT energy of free A and E* is the bare surface DFT energy It makes practical sense, however, to evaluate the adsorption energy with reference to a physically stable state of A. For diatomic molecule ( as in our case, H2), we can evaluate the reaction as
½ A2 + * → A*
and thus the corresponding adsorption energy is given as:
Eads = EA* – 0.5EA2 – E* (2)
Coverage Effects
To evaluate the effect of surface coverage on the adsorption energy and preference to the adsorption site, we evaluate the adsorption energy per atom for different coverage. We define the coverage of adsorbate in terms of number of adsorbate atoms with respect to the number of metal atoms on the surface. For e.g., 1/9 ML represents the 1 adsorbate atom per 9 surface metal atoms. The adsorption energy per metal atom is now evaluated as shown in eq. 3:
Eads = (EnA* – n/2EA2 – E*)/n (3)
where n is the number of adsorbate atoms on the metal surface. We will use eq. 3 to report all the adsorption energies.
Calculation Details
Electronic structure calculations were performed using the Vienna Ab initio Simulation Package (VASP)[1,2] a plane wave basis set pseudo-potential code. We used the projector augmented wave (PAW)[3] method for core-valence treatment. The exchange and correlation energies were calculated using the Perdew, Burke, and Ernzerhof (PBE)[4] functional described within the generalized gradient approximation (GGA)[5]. A plane-wave basis set cutoff energy of 450 eV was used. The calculations were considered optimized when the force on every relaxed atom ( ionic convergence limit) was less than 0.02 eV Å-1. The electron densities were self consistently solved for the energy with the convergence limit (electronic convergence) set to 10-5 eV.
A 3 x 3 surface slab model was used to construct periodic surfaces of Pt (111) using an experimental bulk lattice constant of 2.775 Å. The slab models were comprised of 4 layers of metal atoms. The top two layers of the slab were allowed to relax until convergence while the bottom two layers were kept fixed to imitate their bulk arrangement. A vacuum region of 10 Å was inserted in the models to exclude periodic interaction between the slabs. Dipole corrections were also added in the direction normal to the surface.
The sampling of the Brillouin zone for all 3 x 3 surface cells was conducted with a k-point mesh of 5 x5 x 1 generated automatically using the Monkhorst Pack method [6]. K-point mesh of 1x1x1 was used for the isolated H2 molecule
Results
Figure 2 illustrates the low coverage (1/9 ML) adsorption energies for all different sites. At very low coverage limit, the fcc site is the most preferred site, followed by the atop site. The preference for hcp and bridge site is almost the same at low coverages. These results match well with the previously reported results.. [7]
Figure 2. Adsorption energy of atomic H on different binding sites on Pt (111).
To evaluate the coverage effect, we evaluate the adsorption energy per H atom for 1/9 ML, 2/9 ML, 3/9 ML and 1 ML on fcc, hcp and atop sites (Figure 3).
Figure 3. 2/9 ML, 3/9 ML and 1ML of H on a)atop b) FCC c) HCP site of Pt(111).
For higher coverages (2/9 ML, 3/9ML, 1ML), when the calculations were initiated from the bridge site, the H atoms moved to the fcc site during optimizations. Even after several tries, the optimized geometry for the adsorption on the bridge site at higher coverages could not be found. Figure 4 shows the calculated adsorption energies per H atom for different coverages on atop, fcc and hcp sites.
Figure 4. Adsorption energy per H atom at 4 different coverages on atop, FCC and HCP sites on Pt (111).
As the coverage increases on the metal surface, we see that the adsorption energy per atom of adsorbate decreases. This is expected because as the coverage increases, it results in the repulsive interaction between the adsorbed species. We also see that as the coverage increases the preference for fcc and atop site becomes very similar. This trend is found to be true in the literature as well. However, the adsorption energies differ slightly as the energies reported in the literature are ZPVE (zero-point vibration energy) corrected whereas the numbers reported in this work do not correct for them [8,9].
References
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