Computational Oxygen Evolution Reaction

In an explicit thermochemical description of the OER, the overall rate depends on the free energy of the reaction steps involving catalyst bound intermediates.

Since energies of the reaction steps depend on the nature of the catalyst, it is important to develop a fundamental understanding of these reactions on different materials.¹⁷⁰Different surface structures, types of adsorbate and solvent effect can have a strong influence on the relative stability of the reaction intermediates.

Then, the potential-determining steps and viable reaction paths can vary from one surface to another.

1.5 - State of the Art: RuO₂for OER 35 DFT calculations have allowed an explicit description of OER activity in terms of calculated adsorption energies. Through theSabatier principle, it has been shown that OER activity is to a large extent determined by the binding strength of the reaction intermediates to the electrocatalyst surface. Depending on the number of different important surface intermediates many descriptors may be identified. For the OER at metal oxides surfaces the suggested intermediates are HO^∗, O^∗and HOO^∗.^171,172In the literature, it has been shown that the binding energies of these three intermediates are strongly correlated. In general, the binding energies of the intermediates which bind to a surface through the same kind of atoms are found to scale linearly with each other as the electrocatalyst material is varied. To this point, schematic scaling relations between the binding energies of the OER intermediates and∆GHO^∗ are presented. The slopes of these scaling relations are related to the number of bonds with the surface of each intermediate. For instance, the HO^∗ and HOO^∗ species both present a single oxygen bond to the surfaces and so, the slope of their scaling relation is one, while the slope of the scaling relation between the OH^∗and O^∗ binding energies is two, as the O^∗intermediate is bonded by a double bond to the surface.

Significantly, it has been found that∆GOH^∗ and∆GOOH^∗ are both related to each other by a constant of about 3.2 eV, Eq. 1.17.¹⁷³

∆GHOO^∗ = ∆GHO^∗+ 3.2eV (1.17) This relationship^173,174has been reported both for metals and for a wide range of oxide surfaces, which means that there is a general scaling relation between the HO^∗ and HOO^∗ intermediates regardless of the binding site. Taking this relationship in consideration, the energy of the second reaction step in the reaction pathway∆G2, has been proposed as a general chemical descriptor of oxygen evolving catalytic activity. It has been reported that the potential determining step (PDS) for the OER is the hydro-peroxide specie formation or the O-O bond formation step. Noting that the O^∗specie is enrolled in both steps, and taking into account the general scaling relation the equation (Eq. 1.18).

36 Chapter 1 - Introduction

∆G2= ∆GO^∗−∆GHO^∗ −qV (1.18)

It clearly contains the required chemical information on the binding energies for all three important OER intermediates. Indeed this chemical descriptor has been shown to be a good general parameter of the overpotential trends for a huge variety of oxides. In particular, allows for a comparison between different families of oxides using a single parameter.

Implications of these electrocatalyst optimization are significant. The ideal catalyst is defined by a free energy reaction diagram in which the four charge transfer steps have identical reaction free energies of 1.23 eV. This can only be achieved at a specific binding of all intermediates. However, due to scaling relations it is not possible to independently tune up the binding energy of each intermediate on a surface to get this optimal situation. Because, altering the binding energy of one intermediate will also change the binding energies of all other intermediates.

Regardless of the binding energy of the O^∗, there is a constant difference between the binding energies of these species of 3.2 eV. This is considerably higher than the optimal separation of 2.46 eV, which would be expected for the transfer of two electrons and two protons.

While the identification of descriptors has been widely used by the calculation of adsorption energies, it is important to understand the relationship between this adsorption behavior and the fundamental properties of the catalytic mate-rial. Since the activation energies for elementary surface reaction are strongly correlated with adsorption energies, a good knowledge of the catalyst ability to form bonds is essential. In principle, the catalytic properties of a material are completely determined by its electronic structure. In the case of pure transition metals, the d-band approach provides a useful account of the ability of surface atoms to form bonds to an adsorbate, the higher in energy the d-state are relative to the metal Fermi level, the stronger the interaction with the adsorbate.^175–178 Arising from this, the d-band center is widely used as a descriptor for the activity of transition metals and their alloys. In the case of transition metal oxides,

how-1.5 - State of the Art: RuO₂for OER 37 ever, it is unclear whether such an interpretation can be realistically applied. The complexities of the oxide surface such as the configuration of the metal atoms and their ligands, the oxidation state of the metal and the nature of the interaction between the active site and the adsorbates, can all influence the adsorption energies. This success of d-band theory, motivates a molecular understanding of OER activity using the concepts of orbital occupancy and electron counting.¹⁷⁹ The present thesis provides an exhaustive electronic study on the interaction of water molecules based on periodic boundary DFT calculations. We start from one molecule to a full monolayer coverage, on the main crystallographic orientations (110), (100), (011) and (001) of stoichiometric non-polar morphology.

Other surfaces arising from the different pH conditions and the application of external voltages could be envisaged.¹⁸⁰Moreover, Wulff construction approach has been used to build up RuO₂ stoichiometric nanoparticles to analyze how water adsorption is influenced by the nanoparticle shape and size. Results show that water coverage, surface morphology and temperature play an important role in the degree of water dissociation on the surface and nanoparticle shell, which is characterized by the formation of H₃O₂^– "water dimer" units. Finally, their performance in the oxygen evolution reaction (OER) will be discussed, both surface and nanoparticles as a function of water coverage, facet orientation and nanoparticle size.

38 Chapter 1 - Introduction