Author: Hoang (Bolton) Tran

Problem Statement [1]

In this study, the preferred hydroxyl (OH) adsorption configuration on Pt (111) surface was determined by using Density functional theory (DFT) [2].

Firstly, adsorption site was considered. The top mono-layer of Pt (111) had 4 distinct high symmetry adsorption sites, namely atop, bridge, hcp hollow and fcc hollow (Fig. 1). Secondly, the angle of O-H bond with respect to surface normal (z-axis) was optimized and analyzed for each adsorption site.

Figure 1. Visualization of OH adsorbed at each high symmetry sites. Blue is Platinum, red is Oxygen and white is Hydrogen. Cell size is extended for better visualization.

Methodology

Software:

DFT was implemented in CASTEP, a plane wave basis set software embedded inside BIOVIA Material Studio (MS). [3]

Calculation:

1. Calculation setting

• Exchange-Correlation Functional: Generalized Gradient approximations – Perdew-Burke-Ernzerhof (GGA-PBE) [4]
• Self-Consistent Field tolerance: 2E-06 eV
• Pseudo potential: On-the-fly Generated (OTFG) ultrasoft (Vanderbilt-type) [5].
  • Pt: Core radius: 2.4 a.u.. Core orbitals: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10. Atomic Pseudo Energy: -13042.3015 eV
  • O: Core radius: 1.1 a.u.. Core orbitals: 1s2. Atomic Pseudo Energy: -431.8855 eV
  • H: Core radius: 0.6 a.u.. Core orbitals: None. Atomic Pseudo Energy: -12.4592 eV
• Monkhost-Pack [6] grid size: 10x10x1 (50 irreducible kpoints)
• Plane-wave energy cutoff: 450 eV
• Self-consistent dipole correction in z-direction (normal to surface).
• Geometric Optimization parameter:
  • Convergence criteria: 1E-05 eV/atom energy | 0.03 eV/Å force |0.001 Å displacement.
  • No cell optimization.
  • BFGS algorithm [7]

2. Pt (111) slab adsorption:

A primitive cell of FCC Platinum was first optimized for lattice constants using DFT. The (111) slab was cleaved from the optimized cell with 4 layers thickness. A vacuum of 12Å was set between each periodic surface in the z direction (surface normal) . No supercell was created for this slab. This means that with one OH attached to any site inside the unit cell, the surface coverage is effectively 1 ML.

Firstly, the bare slab was geometrically optimized to determine its relaxed energy \(E_{slab}\). The bottom two layers of the slab was fixed in position, in order to simulate bulk behavior. Both Michaelides [8] and Seitsonen [9] performed almost identical study and reported that 3-layer-slab with only one free top layer is sufficient for convergence of adsorption energies.

Secondly, a OH radical was optimized alone to determine \(E_{OH}\). Although it might not be physical in term of having a OH radical in the gas/vacuum space, it was merely used as a reference energy to calculate the adsorption energy  \(E_{ad}\) (one could simulate dissociation of water with H co-adsorption or with dissociation energy instead).

Finally, the optimized OH was set on each of the 4 adsorption sites. Aside from the bottom 2 layers of the slab, the O atom was also constrained in space to avoid transitioning to other adsorption sites (although this was proven to not work as expected later on). The H atom was allowed to be relaxed in terms of position, which meant the O-H angle w.r.t surface normal \((\theta)\) would also be relaxed. Geometric optimization was carried out to calculate the energy of the OH/slab system \(E_{OH/slab}\).

The adsorption energy was calculated as

\begin{equation} E_{ad}=E_{OH/slab}-E_{OH}-E_{slab} \end{equation}

This geometric optimization would yield the local minimum of \(\theta\) and also the Pt-O bond length  \((L_{Pt/O})\), since surface Pt atom could still move. Therefore, initial values of \(\theta\)  and  \(L_{Pt/O}\) are important (Fig. 2).

Figure 2. Visualization of tilt angle \((\theta)\) and Pt-O bond length \((L_{Pt/O})\) of OH at atop site

• \(L_{Pt/O}\) obviously must not be too close to overestimate the energy due to repulsion (since O atom is fixed could not bounce off). However, it should be close enough to form a bond. It has been experimentally reported [8] that optimal Pt-O bond is around 2.11Å. Therefore, \(L_{Pt/O}\) was initially set to be around that value.
• \(\theta\) ranges from 0º to 90º. However, 0º was avoided since it is quite symmetric (not perfectly because the adjacent Pt sites are different) in the xy-plane, which means it maybe a local minimum and \(\theta\) may not change during optimization. To sample the angles and ensure that there is only one optimal \(\theta\) between 0º to 90º (though in theory, there should be only one), two initial \(\theta\) which are 30º and 60º, were used at each adsorption site.

All energy was calculated as cohesive energy, which is the total 0 K energy given in CASTEP subtracted by the total pseudo-potential energy.

Results and discussion

The cohesive energy of Pt(111) bare slab was -33.35 eV and that of bare OH radical was -7.32 eV. The results are presented in Table 1 below.

Table 1. Adsorption energy, tilt angle and Pt/O bond length at different adsorption sites

Adsorption Sites	Initial \(\theta\)	Adsorption Energy (eV)	Optimized \(\theta\)	Optimized \(L_{Pt/O}\) (Angstrom)	Stable site?
Atop	30\(^o\)	-3.02	73.4\(^o\)	1.975	Yes
	60\(^o\)	-3.02	73.5\(^o\)	1.975	Yes
Bridge	30\(^o\)	-2.14	68.3\(^o\)	2.210	Yes
	60\(^o\)	-2.14	68.7\(^o\)	2.210	Yes
FCC Hollow*	30\(^o\)	-1.09	45.6\(^o\)	-	No
	60\(^o\)	-1.09	45.2\(^o\)	-	No
HCP Hollow**	30\(^o\)	-1.20	56.3\(^o\)	-	No
	60\(^o\)	-1.20	56.9\(^o\)	-	No

*FCC Hollow site has 3 \(L_{Pt/O}\) between O and 3 surrounding Pt fixed at 2.140, 2.134 and 2.133 Å

**HCP Hollow site has 3  \(L_{Pt/O}\) between O and 3 surrounding Pt fixed at 2.244, 2.240 and 2.272 Å

For the two hollow adsorption sites, attempts to geometrically optimize actually resulted in Pt surface atoms shifting and create a bridge adsorption site. Therefore the hollow sites are not stable. To really simulate the hollow configurations then, both O atom and the three adjacent surface Pt were fixed, effectively creating fixed bonds. Therefore optimization for the hollow configuration was solely in terms of angle \(\theta\).

Above point brings up a potential pitfall from fixing Oxygen atom in all 3 directions. Surface Pt atoms were still allowed to relaxed and might protrude upward spuriously. However, optimized \(L_{Pt/O}\) showed that the distance that Pt moved was within 0.1 Å which is considered to be normal for surface relaxation [1]. Retrospectively, it is clear that Oxygen atom should be fixed in only the x and y direction and allowed to move in the z-direction to avoid this pitfall.

The atop site, with lowest adsorption energy, is the predicted preferred adsorption site for OH. This preferred atop site for 1 ML coverage is supported by Michaelides [8] through DFT calculation and Seitsonen [9] through both DFT calculations and experimental LEED measurements.

For adsorption energy, Michaelides reported value of -2.5 eV. For \(L_{Pt/O}\), Michaelides reported 1.99 Å while Seitsonen reported 2.03 Å through DFT calculations (2.11 Å from experiment). For \(\theta\),  Michaelides reported \(73^o\) while Seitsonen reported \(75.8^o\). The literature values are in decent agreement with this study (-3.02 eV, 1.98 Å , \(73.5^o\)). The discrepancy can be attributed to different irreducible kpoints, energy cutoff, slab layers and relax-able layers used in the two papers. Fixing oxygen atom in all 3 directions in this study may also contribute to this discrepancy.

There are two interesting points of discussion from this result:

1. Pt-O bond and O hybridization:

In atop configuration, the O atom is sharing electrons with H atom and only 1 Pt atom. This fact, together with \(\theta\) being very similar to that of water (Pt-O-H of \(104^o\)), suggest that oxygen atoms are in sp3 hybridization state while being adsorbed.

At bridge site, \(\theta\) is different, but the Pt-O-H angle is still roughly \(104^o\) (Fig. 3), suggesting that oxygen also forms sp3 hybridization here.

At both the hollow sites, however, one would expect \(\theta\) to be 0 in order to form 4 bonds (with H and with 3 surrounding Pt) as is characteristic of sp3. Results clearly shows that \(\theta\) is not 0 (though it may stay at 0 if initially built that way), because H wants to form hydrogen bonds with neighboring O. That may suggests the reason why OH does not adsorb favorably on hollow sites, because it cannot both form sp3-type bonds and have non-zero (\theta\) at the same time.

Another interesting comparison can be made with the adsorption of a bare O atom. Without having to share an electron with H atom, the bare O atom actually prefers to form bonds with 3 other Pt atoms (hollow sites) [see Angela’s post].

2. Hydrogen bond network:

In any configuration, H atom wants to form hydrogen bonds with other neighboring O atoms. It wants to move down in z-direction (let’s call it “nodding”) and effectively, lower \(\theta\) because it gives the shortest distance with respect to neighboring O atoms (illustrated in fig. 3). Ideally, it would want to be perfectly parallel to the surface \((\theta=90^o)\) to form the strongest hydrogen bonds it could.

However, back to table 1, it can be seen that \(\theta\) is biggest in the atop site, but not quite 90º. This again goes back to sp3 hybridization of oxygen, due to steric hindrance of Oxygen’s electron pairs, it wants to maintain about \(104^o\) between each pair (i.e. the Pt-O-H angle), so it cannot “nod” all the way down.

Figure 3. Visualization of the hydrogen bonds (dotted red lines) between H atom and neighboring O atoms at optimized atop site (top) and bridge site (bottom). In both cases, Pt-O-H angle is roughly \(104^o\) indicating sp3 hybridization.

In conclusion, it is suggested that OH prefers to be on the atop site because it can form the strongest hydrogen bond network (highest \(\theta\)) without breaking its sp3 hybridization.

Limitations

There are many limitations to the scope of this study in terms of how “real” the system is as compared to the many interesting electrochemical or heterocatalytic systems.

1. This system modeled the adsorption energy based on the adsorption of a OH radical from gas phase, which was clearly not very realistic. As mentioned, a more realistic approach would be to consider the dissociation of water which leads to co-adsorption of both H and OH. The adsorption of both OH and water molecule is also possible [8,9].
2.  The environment of the slab was greatly oversimplified. There was no acidic/alkaline solvent (i.e. solvation effects) or applied surface electrostatic potential being considered, which would potentially change the preferred adsorption site of OH [10].
3. Being a DFT calculation, thermal effect and entropy are often neglected. Adsorption normally leads to negative changes in entropy, which are more significant at high temperature (\(T\Delta S\)). That leads to weaker adsorption at higher temperature.
4. 1 ML coverage may not be very probable in real system. Lower coverage would lead to different hydrogen bond effect and consequently different adsorption preferences [8,9].

Future study (3rd post)

Possible ideas that could be explored using DFT in later post:

• Measure frequency of O-H bond stretching at different \(\theta\) and use it to quantify the strength of hydrogen bonds.
• Lower surface coverage (0.25 ML) to observe its effect on hydrogen bond strength, \(\theta\) and energetic.
• Float a few water molecules/cluster above the adsorbed OH and observe its effects on hydrogen bond strength, \(\theta\) and energetic.

References

[1] Sholl, D., Steckel, J., & Sholl. (2011). Density Functional Theory (p. 46). Somerset: Wiley.

[2] R.O Jones (2015), Density functional theory: Its origins, rise to prominence, and future, Rev. Mod. Phys. 87, 897.

[3] “First principles methods using CASTEP”, Zeitschrift fuer Kristallographie 220(5-6) pp. 567-570 (2005) S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, M. C. Payne

[4] J. P. Perdew, K. Burke, M. Enzerhof (1996). Generalized Gradient Approximation Made Simple, Phys, Rev. Lett., 77, 3865.

[5] D. Vanderbilt (1990), Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41 (11), 7892-7895.

[6] H. J. Monkhorst and J. D. Pack (1976), Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188.

[7] J. D. Head and M. C. Zerner (1985), A Broyden-Fletcher-Goldfarb-Shanno optimization procedure for molecular geometries, Chem. Phys. Letters, 122 (3), 264-270.

[8] A. Michaelides and P. Hu (2001), A density functional theory study of hydroxyl and the intermediate in the water formation reaction on Pt, J. Chem. Phys. 144, 513.

[9] A. P. Seitsonen, Y. Zhu, K.Bedurftig and H. Over (2001), Bond mechanism and atomic geometry of an ordered hydroxyl overlayer on Pt(111), J. Am. Chem. Soc. 123, 7347 – 7351.

[10] D. Strmcnik, M. Uchimura, C. Wang, R. Subbaraman, N. Danilovic, D. Vlilet, A.P. Paulikas, V.R. Stamenkovic and N.M. Markovic (2013), Improving the hydrogen oxidation reaction rate by promotion of hydroxyl adsorption, Nature Chem. 5, 300 – 306.