Catalysis Letters

, Volume 146, Issue 4, pp 718–724 | Cite as

Direct Water Decomposition on Transition Metal Surfaces: Structural Dependence and Catalytic Screening

  • Charlie Tsai
  • Kyoungjin Lee
  • Jong Suk Yoo
  • Xinyan Liu
  • Hassan Aljama
  • Leanne D. Chen
  • Colin F. Dickens
  • Taylor S. Geisler
  • Chris J. Guido
  • Thomas M. Joseph
  • Charlotte S. Kirk
  • Allegra A. Latimer
  • Brandon Loong
  • Ryan J. McCarty
  • Joseph H. Montoya
  • Lasana Power
  • Aayush R. Singh
  • Joshua J. Willis
  • Martin M. Winterkorn
  • Mengyao Yuan
  • Zhi-Jian Zhao
  • Jennifer Wilcox
  • Jens K. Nørskov


Density functional theory calculations are used to investigate thermal water decomposition over the close-packed (111), stepped (211), and open (100) facets of transition metal surfaces. A descriptor-based approach is used to determine that the (211) facet leads to the highest possible rates. A range of 96 binary alloys were screened for their potential activity and a rate control analysis was performed to assess how the overall rate could be improved.

Graphical Abstract


Heterogeneous catalysis Kinetic modeling DFT 

1 Introduction

The dissociation of water is often considered for its importance in the industrial water gas shift reaction (WGS), CO + H2O → CO2 + H2, which is essential for the production of H2 via steam reforming of methane. H2 is a valuable feedstock for other industrial processes such as the Haber–Bosch process or for hydrogen fuels. Water can also be directly dissociated to form gaseous H2 and O2 without going through WGS [1]. This is typically considered in the context of the electrocatalytic oxygen evolution reaction [2], and in high temperature thermal water splitting [3]. Using a descriptor-based analysis [4, 5] the structural sensitivity of water decomposition and the requirements for an active catalyst can be mapped out. Descriptor-based approaches have been successfully used to gain mechanistic insight and in many cases, for screening new catalysts [4, 6, 7, 8, 9, 10]. This approach exploits the linear scaling relationships between adsorption energies of reaction intermediates [11, 12, 13] and between adsorption energies and transition state energies [14, 15, 16]. This allows for the energetics involved in a micro-kinetic model to be determined as a function of the adsorption energies of a few key intermediates. The requirements for an ideal catalyst are then identified in terms of the adsorption energies that yield the highest possible rate. High-throughput computational screening can then be performed by only calculating the descriptors on a range of new materials.

In this work we demonstrate the descriptor-based approach for catalytic thermal water decomposition. We find that the production rates on transition-metal catalysts are indeed on the low end. This is partly due to limitations in the catalysts, since higher rates cannot be achieved unless hydrogen binding can be strengthened relative to oxygen binding. The absolute rates depend on the surface termination and the under-coordinated step sites have the most activity. We explore different ways of achieving the theoretical optimal rate by performing a high-throughput screening of binary transition-metal alloys and using a degree of rate control analysis.

2 Methods

2.1 Calculation Details

Plane-wave density functional theory employing ultra-soft pseudopotentials [17] was carried out using the Quantum ESPRESSO calculator [18]. The Bayesian error estimation functional with van der Waals interactions [19] (BEEF-vdW) was used for describing the exchange–correlation energy. BEEF-vdW has been found to be accurate for both short-range chemisorption energies as well as for describing long-range physisorption. A plane-wave cutoff of 500 eV and a density cutoff of 5000 eV were used, where the convergence with respect to adsorption energies has been confirmed in previous works [9]. The Brillouin zones were sampled using a 4×4×1 Monkhorst and Pack [20] k-point grid. Only fcc crystal structures were considered in this study. The parameters used for calculations on each surface are summarized in Table 1. The bottom two layers were fixed while the top two layers were allowed to relax. At least 12 Å of vacuum in the z-direction was used to separate repeating slabs. Various possible adsorption sites were considered, and the adsorption energies used in this study corresponded to the most stable adsorption sites. Free energies of adsorption were determined according to ∆G = ∆E − TS + ∆ZPE as in previous studies, where the vibrational frequencies calculated on a Cu(111) surface were used to determined the entropies, which are assumed to not vary significantly between metal surfaces [21, 22]. Transition states were obtained using a “fixed-bond length” method [21], where the distance between atoms were incrementally decreased, fixed, and relaxed on the surface until a saddle point was reached. The climbing image nudged elastic band (CI-NEB) method [23] was used to confirm the transition state energies for a representative number of examples. The results were found to be in close agreement (typically within 0.1 eV).
Table 1

Super-cell sizes and adsorption sites chosen for each type of surface termination





3 × 3 × 4

Top, bridge, hcp, fcc


2 × 2 × 4

Top, bridge, hollow


2 × 1 × 4

Top, bridge, threefold, fourfold

2.2 Microkinetic Model

A mean-field microkinetic model [24] was used to solve for the catalytic activity using the adsorption energies and activation energies. This was done under the steady-state assumption. We consider the following simple elementary steps in the direct dissociation of water:
$${\text{H}}_{2} {\text{O}}\,({\text{g}}) +\,\text{2}\,* \to \text{OH}\,* + \,\text{H}\,*$$
$$\text{OH}\,* \, + \,* \to \text{O}\,* \,+\, \text {H} \,*$$
$$2\text{O}\,* \to {\text{O}}_{2}\,({\text{g}}) + 2\,*$$
$$2\text{H}\,* \to {\text{H}}_{2}\,({\text{g}}) + 2\,*$$
where * represents an active site on the catalyst. Furthermore, surface-bound oxygen species have been shown to activate H2O, especially on noble-metal surfaces [25]. We include this pathway via the following step:
$${\text{H}}_{2} {\text{O}}\, ({\text{g}}) + \text{O}\,* + \,* \to 2\text{OH}\,*$$

Based on the linear scaling relations between adsorbates on transition metal surfaces, the energetics of all reaction steps can be determined as a function of a few adsorption energies, called the descriptors. In this work we use ∆E H, the adsorption energy of H*, and ∆E O, the adsorption energy of O* as the descriptors. Here, ∆E H is calculated relative to H2 gas while ∆E O is calculated relative to gaseous H2O.

In the mean-field approximation, rate expressions take the following form:
$$r_{i} = \left( {k_{f,i} \prod\limits_{{j \in p_{\text{IS}} }} {p_{j} \prod\limits_{{\theta \in \theta_{IS} }} {\theta_{j} } } } \right) - \left( {k_{r,i} \prod\limits_{{j \in P_{\text{FS}} }} {p_{j} } \prod\limits_{{\theta \in \theta_{FS} }} {\theta_{j} } } \right)$$
where r i is the rate of the ith elementary reaction step, and P j and θ j are the gaseous pressures and coverages of intermediates respectively, for the initial state (IS) or final state (FS). The coverages θ j were determined by solving the rate equations at steady state, with the sum of all coverages for each type of adsorption site set to 1. The reaction rate constants for the forward and reverse reactions can be calculated using transition state theory:
$$k_{f,i} = \frac{{k_{\text{B}} T}}{h}\exp \left( {\frac{{ - \Delta G_{a,i} }}{{k_{B} T}}} \right)$$
$$k_{r,i} = \frac{{k_{\text{B}} T}}{h}\exp \left( {\frac{{ - \left( {\Delta G_{a,i} - \Delta G_{{{\text{rxn,}}i}} } \right)}}{{k_{B} T}}} \right)$$
where k B is the Boltzmann constant, h is Planck’s constant, ∆G a,i is the activation free energy and ∆G rxn,i is the reaction free energy for step i. The rate equations were solved and determined as a function of the descriptors using the CatMAP micro-kinetic modeling module [5], a Python package for descriptor-based analyses.

3 Results and Discussion

The surface structures and adsorption sites for the (111), (100), and (211) surfaces are the same as in previous studies [21]. All energetics were determined for the most stable adsorption sites on each surface.

3.1 Scaling Relations

Since the rates are determined by the reaction energies and activation energies, an initial comparison can be made between the surfaces through their energetic scaling relations. All reaction steps directly involve either ∆E H, ∆E O, or ∆E OH, so the energetics of all reaction steps can be determined as a function of one of these adsorption energies [11, 15, 26]. In terms of adsorption energies, ∆E O scales linearly with ∆E OH, while ∆E H scales with neither (supplementary information), suggesting that ∆E H and one of ∆E O or ∆E OH are needed to describe all the energetics for this reaction. ∆E O and ∆E H were chosen, with ∆E O being used to determine ∆E OH. ∆E O is also used to scale the transition state energy of \(2 {\text{O}}\,* \to {\text{O}}_{ 2} \,\,\left( {\Delta E_{{{\text{O}}{-}{\text{O}}}} } \right),{\text{ H}}_{ 2} {\text{O}} + {\text{O}}\,* \to 2 {\text{OH}}\,* \,\, \left( {\Delta E_{{{\text{HO}}{-}{\text{H}}{-}{\text{O}}}} } \right),\) and ∆E H is used to scale the transition state energy for \(2 {\text{H}}\,* \to {\text{H}}_{ 2} \,\,\left( {\Delta E_{{{\text{H}}{-}{\text{H}}}} } \right),\) and ∆E O and ∆E H are both used to scale the transition state energies of \({\text{H}}_{ 2} {\text{O}} \to {\text{OH}}\,* + {\text{H}}\,* \,\, \left( {\Delta E_{{{\text{H}}{-}{\text{OH}}}} } \right){\text{ and OH}}\,* \to {\text{O}}\,* + {\text{H}}\,* \,\, \left( {\Delta E_{{{\text{O}}{-}{\text{H}}}} } \right).\) For the O* promoted H2O activation, the transition states were explicitly calculated for the (111) and (211) surfaces [25] whereas the transition state scaling relation was used to estimate the barriers for the (100) surface. Parity plots for all energetics determined using scaling relations on the (211) surface are shown as an example in Fig. 1 (all scaling relations used are summarized in the supporting information).
Fig. 1

Parity plots showing the calculated adsorption energies and transition state energies against their predicted values from using the scaling relations for the (211) surfaces. The linear fits are indicated in the axes labels. All units are in eV. The transition states are denoted by the bond “–” being broken

3.2 Catalytic Activity

The linear scaling relations between the descriptors and the reaction energetics allow for the total rates to be determined as a function of ∆E H and ∆E O. In Fig. 2, the activity map for direct water dissociation on the (111), (100), and (211) facets are shown. A temperature of 800 K and partial pressures of \(p_{{{\text{H}}_{ 2} {\text{O}}}} = 1. 9 7 \;{\text{bar}},{\text{ and}}\;p_{{{\text{O}}_{ 2} }} = p_{{{\text{H}}_{ 2} }} = 0.0\; {\text{bar}}\) were used. This condition was chosen so that the maximum rate on the volcanoes were within 1–10 s−1, which approaches industrially practical rates. The shapes are all similar, and the maximum possible rates in the descriptor space follow (211) > (100) > (111). The more under-coordinated surfaces lead to the highest possible rates. In all cases, the location of the volcano’s maximum is separated from the metal surfaces by approximately the same amount for all surface terminations. This is in good qualitative agreement with previous studies on the structural dependence of catalysts for NO decomposition [21], where the qualitative features and trends were consistent across a range of surface terminations. In all cases, the transition metals are at least 0.5 eV away from the optimum. Hydrogen adsorption needs to be strengthened relative to oxygen adsorption in order to reach the theoretical optimum.
Fig. 2

The production rate of H2 (turnover frequencies) as a function of the descriptors ∆E H and ∆E O at a temperature of 800 K and partial pressures of \(p_{{{\text{H}}_{ 2} {\text{O}}}} = 1. 9 7 \;{\text{bar }}\;{\text{and}}\;p_{{{\text{O}}_{ 2} }} = p_{{{\text{H}}_{ 2} }} = 0.0 {\text{bar}}\). All rates below 10−15 s−1 are indicated by the same color. The production rate of O2 is half that of H2

The coverages of H*, O*, and OH* on all of the surfaces are shown in Fig. 3. The coverage of H* is negligible on all of the surfaces at ∆E H > −1.0 eV, whereas O* poisons the surface for most of the more reactive metals. Adsorbate–adsorbate interactions are not included in this work; however, the repulsion between poisoned O* is expected to weaken their binding to the surface and allow O2 to form more readily. This would increase the rates in the O* poisoned regions, though the total effect may be small [27]. The maximum possible rates roughly follow the coverage of OH*. The (211) surfaces are able to stabilize the OH* intermediate the most and have the highest OH* coverages. Among the transition metals, Pt(211) and Pt(100) have the most intermediate coverages for each species, meaning they are not poisoned by any intermediate, and thus also have the highest production rates. For all surface terminations, Pt and Pd have the highest reaction rates. Although the magnitudes at the peak of the volcano differ between the surface terminations, the trends are largely consistent. The most active transition metals predicted for one surface termination are also the most active for the other surface terminations.
Fig. 3

Coverages (θ in units of monolayers) of the surface intermediates H*, O*, and OH* as a function of ∆E H and ∆E O for all surface facets

3.3 High-Throughput Screening of Binary Transition-Metal Alloys

Having mapped out the production rates as a function of ∆E O and ∆E H, these descriptors can be used to screen for improved catalysts. The (211) facet was determined to have the highest possible production rates, so ∆E O and ∆E H were calculated on the (211) surfaces for a range of 96 different binary transition-metal alloys with the A3B stoichiometry, where A and B are distinct metals. The metals considered include: Ag, Al, As, Au, Bi, Cd, Co, Cr, Cu, Fe, Ga, Ge, Hf, In, Ir, La, Mn, Mo, Ni, Pd, Pt, Rh, Sb, Sc, Si, Sn, Ta, Ti, V, W, Y, Zn, and Zr. Due to strain and ligand effects [7, 28, 29, 30], the binding strengths of different intermediates could deviate from the pure transition metals. The most stable binding sites were chosen for the (211) surface of each A3B alloy. The predicted rates for the alloys are shown in Fig. 4. Although there is significantly more scatter in the points, they largely fall in the neighborhood of the pure transition-metal surfaces. The alloys closest to the peak of the volcano are still ~ 0.5 eV away, and have ∆E O and ∆E H that are similar to that of the pure Pt and Pd steps. Moreover, these alloys all contain either Pt or Pd as one of its constituent metals and none of them show markedly improved predicted activity. The Pt(211) is still the most active surface amongst all metal steps considered in this study. However, many of the constituent metals are considerably cheaper and more widely available than Pd or Pt, so they may still be relevant for reducing the overall cost of the process. Although alloying is an effective way to produce a wide range of adsorption energies, it appears insufficient for deviating from the pure transition metal catalysts and reaching the theoretical optimal rate (Table 2).
Fig. 4

High-throughput screening of the (211) surface on 96 binary transition-metal alloys. The production rates (turnover frequencies) of H2 and O2 as a function of the ∆E O and ∆E H descriptors. Both pure metals (filled circle) and binary alloys (filled triangle) are shown

Table 2

Descriptors and predicted rates for the metal and bimetallic alloy (211) steps


E H (eV)

E O (eV)

log(TOF) (s−1)





























































Only the most active pure metal steps and binary alloys are shown

3.4 Degree of Rate Control

In order to determine how the stabilities of the various intermediates and transition states affect the overall rate, the degree of rate control [31] can be used. This concept provides additional insight into how the rate can be improved beyond just using the two descriptors. The degree of rate control is defined as:
$${X_{{i_j}}} = \frac{{{\rm{d\,log(}}{r_i})}}{{{\rm d}\left( { - {G_j}/{k_B}T} \right)}}$$
for the production rate of product i and species j. A positive X ij indicates that making the species more stable (decreasing G j ) would increase the rate, whereas a negative X ij indicates the opposite. The degree of rate control as a function of the descriptors ∆E O and ∆E H and the transition state energies are shown for the (211) surfaces as an example (Fig. 5, the same plots for the other surfaces are in the supplementary information). As with the rate and coverage plots, the degree of rate control is qualitatively similar across all three surface terminations. Unsurprisingly, for the regions where the surface is O* or H* poisoned (Fig. 3), weakening those binding energies can significantly improve the rate. Similarly, for regions where oxygen binding is too weak, strengthening it would also improve the rate. In the region of the volcano’s peak (approximately ∆E O = 1.5 eV, ∆E H = –1 eV), the transition state energies for both the associative desorption energies of H2 (H–H*) and O2 (O–O*) need to be strengthened in order to improve the rate. The largest improvement in the theoretical optimum will thus be from lowering the transition state barriers for product desorption. Assuming that the transition state energies are constrained by the linear scaling relations with ∆E H and ∆E O, this cannot be achieved for any one of these surface terminations.
Fig. 5

Degree of rate control for H2 production for all the adsorption energies and transition state energies on the (211) surfaces (indicated by the bonds “–” being formed or broken)

4 Conclusions

In this work, we have examined the structural dependence of direct water dissociation over transition-metal catalysts using a descriptor based micro-kinetic analysis. Based on the hydrogen and oxygen binding energies on the surfaces, the maximum possible rates can be determined in a volcano relation for each type of surface. The activity of the surface facets followed (211) > (100) > (111) with the most under-coordinated surfaces having the most activity and the most close-packed surfaces having the least. While the absolute rates depend on the surface termination, the qualitative trends are relatively insensitive to the surface structure. Using the (211) volcano relation, we performed a high-throughput screening of binary A3B transition-metal alloys and identified several candidates that could show improved activity over most of the pure transition metals. However, their similarities to the pure transition metals also mean that they are insufficient for reaching the theoretical optimal rates. Detailed requirements for improving the rates were further revealed by the degree of rate control analysis. In both cases, the rates are unlikely to be significantly improved using transition-metal catalysts. Catalytic materials that display adsorption behavior that is distinct from the transition metals may be needed.



The authors thank the US Department of Energy, Office of Basic Energy Sciences.

Author contributions

This Project was carried out as part of the course “Electronic Structure Theory and Applications to Chemical Kinetics” (CHEMENG 444/ENERGY 256) from the Department of Chemical Engineering and the Department of Energy Resources Engineering at Stanford University. CT, KL, JW, and JKN designed the project. CT, KL, JSY, HA, LDC, CD, TG, CG, TJ, CK, AL, XL, BL, RM, JHM, LP, AS, JW, MW, MY, ZJZ carried out the calculations and performed the analysis.

Supplementary material

10562_2016_1708_MOESM1_ESM.pdf (3.2 mb)
Supplementary material 1 (PDF 3311 kb)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Charlie Tsai
    • 1
    • 2
  • Kyoungjin Lee
    • 3
  • Jong Suk Yoo
    • 1
    • 2
  • Xinyan Liu
    • 1
    • 2
  • Hassan Aljama
    • 1
    • 2
  • Leanne D. Chen
    • 2
    • 4
  • Colin F. Dickens
    • 1
    • 2
  • Taylor S. Geisler
    • 1
  • Chris J. Guido
    • 1
  • Thomas M. Joseph
    • 1
  • Charlotte S. Kirk
    • 1
    • 2
  • Allegra A. Latimer
    • 1
    • 2
  • Brandon Loong
    • 1
  • Ryan J. McCarty
    • 1
    • 5
  • Joseph H. Montoya
    • 1
    • 2
  • Lasana Power
    • 1
    • 6
  • Aayush R. Singh
    • 1
    • 2
  • Joshua J. Willis
    • 1
  • Martin M. Winterkorn
    • 7
  • Mengyao Yuan
    • 3
  • Zhi-Jian Zhao
    • 1
    • 2
    • 8
    • 9
  • Jennifer Wilcox
    • 3
  • Jens K. Nørskov
    • 1
    • 2
  1. 1.Department of Chemical EngineeringStanford UniversityStanfordUSA
  2. 2.SUNCAT Center for Interface Science and CatalysisSLAC National Accelerator LaboratoryMenlo ParkUSA
  3. 3.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  4. 4.Department of ChemistryStanford UniversityStanfordUSA
  5. 5.Department of Geological SciencesStanfordUSA
  6. 6.Department of Civil and Environmental EngineeringStanfordUSA
  7. 7.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  8. 8.Key Laboratory for Green Chemical Technology of Ministry of Education, School of Chemical Engineering and TechnologyTianjin UniversityTianjinChina
  9. 9.Collaborative Innovation Center of Chemical Science and EngineeringTianjinChina

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