Active sites and mechanisms for H₂O₂ decomposition over Pd catalysts

Significance

The use of hydrogen peroxide (H₂O₂) for catalytic oxidations is limited by the energy-intensive and wasteful process by which H₂O₂ is currently produced—the anthraquinone process. The direct synthesis of H₂O₂ (DSHP) is a promising alternative process, yet catalysts active for this reaction (Pd being the most widely studied) are generally hindered by subsequent H₂O₂ decomposition. Through a combined theoretical and experimental approach, our work (i) provides an understanding of the nature of Pd active sites responsible for H₂O₂ decomposition and (ii) identifies a single type of elementary step that controls the rate. These structural and mechanistic insights are important for designing improved DSHP catalysts and for developing transition-metal–catalyzed oxidations that efficiently use H₂O₂.

Abstract

A combination of periodic, self-consistent density functional theory (DFT-GGA-PW91) calculations, reaction kinetics experiments on a SiO₂-supported Pd catalyst, and mean-field microkinetic modeling are used to probe key aspects of H₂O₂ decomposition on Pd in the absence of cofeeding H₂. We conclude that both Pd(111) and OH-partially covered Pd(100) surfaces represent the nature of the active site for H₂O₂ decomposition on the supported Pd catalyst reasonably well. Furthermore, all reaction flux in the closed catalytic cycle is predicted to flow through an O–O bond scission step in either H₂O₂ or OOH, followed by rapid H-transfer steps to produce the H₂O and O₂ products. The barrier for O–O bond scission is sensitive to Pd surface structure and is concluded to be the central parameter governing H₂O₂ decomposition activity.

Hydrogen peroxide (H₂O₂) is a desirable oxidant because the only by-product from its reduction is water (1). The largest demand for H₂O₂ is in the pulp and paper industry (2). In addition, there are applications for H₂O₂ in catalytic oxidations (3) such as the epoxidation of propene to propylene oxide (4). However, the current production process for H₂O₂, the anthraquinone process, is complex, energy intensive, and only economic for large-scale productions (5).

The direct synthesis of hydrogen peroxide (DSHP) from H₂ and O₂ is an appealing alternative that has the potential to enable small-scale integrated production of H₂O₂ (5). A commercial DSHP process has not yet been implemented, although Degussa/Headwaters announced the successful integration of a pilot plant for the DSHP and a pilot plant for the manufacture of propylene oxide in 2005 (6). García-Serna et al. (7) have discussed the economic viability of a DSHP process in comparison with the existing industrial-scale anthraquinone process.

The primary catalytic challenge for the DSHP is identifying catalysts that can maintain high selectivity for H₂O₂ at industrially relevant H₂O₂ concentrations. The complete reduction of O₂ to H₂O is more thermodynamically favorable than the partial reduction of O₂ to H₂O₂:

$${\text{H}}_2\left(\text{g}\right)+{\text{O}}_2\left(\text{g}\right)\to {\text{H}}_2{\text{O}}_2\left(1\right)\hspace{1em}\mathrm{\Delta }{G}_{298\text{K}}^{°}=-120.4\hspace{0.17em}\mathrm{k}\text{J}/\text{mol},$$ [Reaction 1],

$${\text{H}}_2\left(\text{g}\right)+{\text{O}}_2\left(\text{g}\right)\to {\text{H}}_2\text{O}\left(1\right)+\mathrm{½}{\text{O}}_2\left(\text{g}\right)\hspace{1em}\mathrm{\Delta }{G}_{298\text{K}}^{°}=\mathrm{-}237.1\hspace{0.17em}\mathrm{k}\text{J}/\text{mol},$$ [Reaction 2].

Consequently, H₂O₂ decomposition,

$${\text{H}}_2{\text{O}}_2\left(1\right)\to {\text{H}}_2\text{O}\left(1\right)+\mathrm{½}{\text{O}}_2\left(\text{g}\right)\hspace{1em}\mathrm{\Delta }{G}_{298\text{K}}^{°}=\mathrm{-}116.7\hspace{0.17em}\mathrm{k}\text{J}/\text{mol},$$ [Reaction 3],

and H₂O₂ hydrogenation by H₂,

$${\text{H}}_2{\text{O}}_2\left(1\right)+{\text{H}}_2\left(\text{g}\right)\to 2{\text{H}}_2\text{O}\left(1\right)\hspace{1em}\mathrm{\Delta }{G}_{298\text{K}}^{°}=\mathrm{-}353.8\hspace{0.17em}\text{kJ}/\text{mol},$$ [Reaction 4],

are also thermodynamically favorable reactions. The optimal DSHP catalyst must therefore selectively produce H₂O₂ at high rates and preserve H₂O₂ from decomposition.

Pd is widely recognized as the most effective transition metal for the DSHP; however, Pd generally exhibits poor selectivity in the absence of promoters and is highly active for the H₂O₂ decomposition reactions. Experimental strategies to improve selectivity of Pd-based catalysts include the following (8, 9): adding strongly coordinating anions (e.g., CN⁻, Cl⁻, Br⁻) and acids to the solvent; alloying Pd with other noble metals, namely Au or Pt; and controlling the nature of the catalyst support material. The performance of Pd-based catalysts has also been shown to strongly depend on the oxidation state of Pd (i.e., catalyst pretreatment conditions, O₂:H₂ feed ratio, etc.) (8).

A common goal in many of these modifications is the minimization of the H₂O₂ decomposition reactions (reactions 3 and 4) (10). Importantly, H₂O₂ has been identified as the primary product on Au-Pd catalysts at low H₂ conversion (11, 12), whereas the subsequent H₂O₂ decomposition reactions decrease overall yield as the reaction progresses. Experiments also suggest that the active sites for H₂O₂ synthesis (reaction 1) and decomposition on Pd-based catalysts may be different (12, 13). In particular, Hutchings and coworkers (14) demonstrated that the H₂O₂ decomposition reactions on a Au-Pd/C catalyst could be suppressed by pretreating the carbon support with HNO₃, and this resulted in a stable catalyst with >95% selectivity for H₂O₂ during the DSHP reaction. A detailed understanding of the active site(s) and elementary reaction mechanisms for these undesired reactions would benefit the identification of improved catalysts. Nonetheless, there is still much work to be performed to elucidate the optimal structure and composition of Pd-based catalysts for the DSHP; some recent important contributions on this front can be found in refs. 11 and 15–18.

This paper will focus on the mechanism and the nature of the dominant active site(s) responsible for H₂O₂ decomposition (reaction 3, with no H₂ present) under conditions relevant to the DSHP process. We highlight key factors that will aid in the identification of improved DSHP catalysts that exhibit minimal H₂O₂ decomposition activity. These findings are also relevant to transition-metal–catalyzed oxidation reactions that use H₂O₂—whether produced in situ or fed as reactant—but whose efficiency may be limited by catalytic H₂O₂ decomposition (19–22).

Materials and Methods

Density Functional Theory.

Periodic Pd(111) and Pd(100) slabs were chosen as representative models for the planar surfaces of the supported Pd nanoparticles used in the experiments. Pd(111) and Pd(100) have the lowest surface free energies among the clean Pd facets, and a truncated octahedron minimizes the total surface free energy for Pd particles >3–5 nm based on a Wulff construction (23, 24). Therefore, in the absence of strong particle-support interactions, both of these Pd surfaces are expected to be in high abundance.

All density functional theory (DFT) calculations were performed using the DACAPO total energy code (25, 26), using the self-consistent PW91 generalized gradient approximation (GGA-PW91) (27, 28) to describe the exchange correlation energy and potential, and ultrasoft pseudopotentials (29) to describe the ionic cores. Electron density was determined by iterative diagonalization of the Kohn–Sham Hamiltonian, Fermi population of the Kohn–Sham states (k_BT = 0.1 eV), and Pulay mixing of the resulting electron density (30). The total energy was then extrapolated to k_BT = 0 eV. The Kohn–Sham one-electron valence states were expanded using a plane wave basis with kinetic energy below 25 Ry.

The (111) and (100) metal surfaces were modeled using a slab geometry with a periodically repeated (2 × 2) unit cell and four atomic layers; this corresponds to 1/4 monolayer (ML) coverage of a single adsorbate placed in the unit cell. The surface Brillouin zone was sampled using 18 special Chadi–Cohen (31) k-points for the (111) slabs, and a (6 × 6 × 1) Monkhorst–Pack (32) k-point mesh for the (100) slabs. All slab layers were fixed for calculations on the (111) slabs [previous calculations show minimal effect of surface relaxation on the calculated energetics for a similar system (33)], whereas the top two metal layers were allowed to relax in the (100) slabs. A distance of 14 Å of vacuum separated successive slabs in the z direction, and adsorption was only permitted on one of the two available surfaces with the electrostatic potential adjusted accordingly (34, 35). The equilibrium PW91 bulk Pd lattice constant has been calculated previously (33) to be 3.99 Å [experimental value is 3.89 Å (36)]. Calculations involving O₂ were performed spin-polarized.

Binding energies (BEs) are reported based on the total energy of the metal slab with the adsorbate on it (E_ads) with respect to the total energies of the free gas-phase adsorbate (E_gas) and the clean slab (E_clean). All reported DFT results have been corrected for the zero-point energy (ZPE). The minimum energy paths for elementary steps were calculated using the climbing image–nudged elastic band method (37, 38) with at least seven intermediate images, and the transition state was verified by identification of a single imaginary frequency along the reaction coordinate. Vibrational frequencies were calculated by diagonalization of the mass-weighted Hessian matrix and using the harmonic oscillator approximation (39).

Experiments.

A 0.09 wt% Pd/spSiO₂ (spSiO₂ denotes the spherical silica support) catalyst was prepared for reaction kinetics experiments. The spSiO₂ was synthesized by a modified Stöber process (40) described in a previous publication (41), resulting in spherical silica particles (∼100–200 nm in diameter) with no internal pore structure and a Brunauer–Emmett–Teller surface area of 21 m²/g (41). The Pd was loaded onto the spSiO₂ by vacuum evaporative impregnation (in a rotary evaporator) using a solution of Pd(II) acetate dissolved in dichloromethane. The dried material was reduced in a quartz cell following a procedure described in ref. 42 to promote formation of large Pd particles (average particle size of 5.6 ± 2.4 nm determined from scanning transmission electron microscopy images of the Pd/spSiO₂ catalyst) that better compare with the Pd(111) and Pd(100) DFT models. This heat treatment procedure involved a temperature ramp to 673 K (10 K/min) and 3-h hold at 673 K in flowing H₂ (30 mL/min), followed by cooling to room temperature under flow of Ar (30 mL/min) and passivation with 1% O₂ in Ar. The Pd surface site density was determined by irreversible CO uptake experiments at 300 K, using an apparatus and procedure described previously (43), and applying a surface stoichiometry of 2:3 for CO:surface Pd atom (42).

H₂O₂ decomposition experiments were performed in a 50-mL Parr Instrument Company Hastelloy C-276 autoclave containing an overhead magnetic stirrer (Magnetic Drive A1120HC6CH, Parr Instrument Company, Moline, IL), a fixed thermocouple, and a pressure gauge. A Teflon liner was used in all experiments to minimize contact of H₂O₂ with metallic components in the autoclave. Blank experiments were performed before each reaction to ensure negligible contributions to H₂O₂ decomposition from the stirrer/thermowell/liner; these wetted parts of the reactor were passivated using 25 vol% HNO₃ in cases where significant H₂O₂ decomposition was measured in the absence of catalyst. The bare spSiO₂ support (no Pd loaded) was shown to be inert toward H₂O₂ decomposition over all conditions studied.

In a typical reaction, the autoclave was loaded with catalyst, sealed, and purged with Ar. The autoclave was then pressurized to 450 psi with 4% H₂ in Ar (Airgas), and held at 323 K for 1 h to reduce the passivated Pd nanoparticles. After cooling to room temperature, the autoclave was again purged with Ar, pressurized to 115 psi with Ar, and cooled to the desired reaction temperature using a refrigerated bath circulator (ARCTIC A25; Thermo Scientific). The H₂O₂ feed solution (12.5 g of 0.08–0.60 M H₂O₂ in H₂O) was prepared by dilution of a nonstabilized 30 wt% H₂O₂ solution (<10 ppb Cl⁻; Gigabit; KMG) in ultrapure water (18 MΩ·cm), cooled to reaction temperature, and then charged into the autoclave using a HPLC pump (Chrom Tech Series 1). The resulting pressure in the autoclave before reaction was 150 psi. Stirring (1,200 rpm) was then started. Conversion of H₂O₂ was determined by titration of the final solution with 0.05 M Ce(SO₄)₂ using ferroin as indicator.

Initial reaction rates were calculated by fitting a line through a plot of the moles H₂O₂ consumed versus time for conversions under 15% and normalizing to the total number of Pd surface atoms determined by the CO uptake experiments; all conversion versus time data points were replicated at least two times. The apparent activation energy barrier was determined over a temperature range of ∼25 K, and the apparent reaction order with respect to H₂O₂ was determined by varying the feed concentration of H₂O₂ with all other reaction parameters constant. The apparent reaction order with respect to the O₂ product was determined by varying P_O2 in the gas phase using a 25% O₂ in Ar mixture, with all other conditions invariant. This mixture was introduced immediately after charging the autoclave with the H₂O₂ feed, before stirring.

Microkinetic Model.

A mean-field microkinetic model was developed to describe the experimentally measured reaction rates, reaction orders, and apparent activation barrier. The model parameters were defined using a procedure described in our previous work (44–46), using the ZPE-corrected BEs and activation energy barriers determined through DFT as initial guesses; preexponential factors and entropies were derived from the DFT-calculated vibrational frequencies. The maximum adsorbate coverage permitted was 1 ML, and adsorption/desorption steps were assumed to be quasiequilibrated. In the case that the microkinetic model-predicted adsorbate coverage exceeded the minimum adsorbate coverage in the context of the unit cell used in the DFT calculations (1/4 ML), the DFT calculations were repeated with the appropriate spectator species coadsorbed in the unit cell. Note that, although the experimental measurements were performed in a three-phase system using conditions relevant to a DSHP process, no corrections were made to the DFT calculations to reflect potential interaction with the liquid phase. Further details of the microkinetic model formulation and parameter sets are provided in Supporting Information.

Results

The decomposition of H₂O₂ has been studied both in the vapor phase (47) and aqueous phase (48) (thermal, noncatalyzed), and over a variety of materials including metal oxides (49–51) and metal ions in solution (52, 53). Based on these studies, we have compiled an encompassing network of 17 elementary reactions involving four closed-shell species (H₂O₂, H₂O, O₂, H₂) and four surface intermediates (O, H, OH, OOH), which are shown in Table 1. Elementary reactions are classified as follows: adsorption/desorption, O–O bond scission, dehydrogenation, and hydrogen transfer. Note that the majority of calculations presented below on Pd(111) are based on a previous publication (33), and these results will not be described in detail here aside from noting key differences between binding properties and reaction energetics on Pd(111) and Pd(100). Reference 54 also presents a subset of DFT results on Pd(100). The “*” appended to a species denotes adsorption at a single surface site, or an unoccupied surface site if the “*” stands alone.

Table 1.

Calculated BEs of adsorbed species, their preferred adsorption sites, and O–O bond lengths (d_O–O) on Pd(111) and Pd(100)

	Pd(111)†			Pd(100)
Species	Adsorption site	BE, eV	dO–O, Ň	Adsorption site	BE, eV	dO–O, Ň
H*	fcc	−2.70	N/A	Hollow	−2.74	N/A
O*	fcc	−3.64	N/A	Hollow	−3.90	N/A
OH*	Bridge-tilted	−2.03	N/A	Bridge-tilted	−2.43	N/A
OOH*	Bent-top	−0.94	1.46	Bent-bridge	−1.28	1.51
H2O*	Top	−0.22	N/A	Top	−0.30	N/A
H2O2*	Top	−0.32	1.48	Top	−0.36	1.49
O2*	Top-bridge	−0.50	1.35	Hollow	−1.27	1.41

Reference energy corresponds to the adsorbate in the gas phase far away from the metal surface. N/A, not applicable.

^†Data based on ref. 33.

^‡Calculated gas-phase d_O–O for O₂, OOH, and H₂O₂ are 1.24, 1.35, and 1.48 Å, respectively.

Thermochemistry and Binding Configurations of Reaction Intermediates on Clean Pd Surfaces.

Table 1 summarizes the most stable adsorption sites and binding energies for all surface species on Pd(111) and Pd(100). Images of the individual adsorbates in their preferred binding geometry on Pd(100) can be viewed in Fig. 1; refer to ref. 33 for the corresponding images on Pd(111). The Pd(100) facet is more open than the Pd(111) one and binds all intermediates more strongly.

Fig. 1.

(A–G) Side and top-down views of the preferred binding sites for all adsorbates on Pd(100). Blue spheres are hydrogen, red spheres are oxygen, and gray spheres are Pd atoms.

The BE of atomic hydrogen (H*) on Pd(100) is −2.74 eV, only 0.04 eV stronger than its BE on Pd(111). H* preferentially binds to the fcc site on Pd(111) and the hollow site on Pd(100). Furthermore, H* is expected to be mobile on Pd(100), as the BE of H* on a bridge site of Pd(100) is only 0.14 eV less stable than that on the hollow site. Similarly, on Pd(111), the BE of H* constrained to a bridge site is 0.14 eV less stable than that on the fcc site.

Atomic oxygen (O*) has the same site preferences as H* on both Pd(111) and Pd(100). The binding strength of O* on Pd(100) is −3.90 eV, which is 0.26 eV stronger than that on Pd(111). Moreover, O* has a strong preference for the hollow site on Pd(100), with the next best adsorption site (bridge) being less stable by 0.48 eV. On Pd(111), the next best adsorption site for O* is the hcp site, which is 0.15 eV less stable than O* binding to the fcc site.

Hydroxyl (OH*) is often proposed to be the initial intermediate generated during H₂O₂ decomposition, resulting from homolytic O–O bond cleavage in H₂O₂ (55). OH* binds most stably to the bridge site on both Pd(111) and Pd(100) with the O–H bond tilted away from the plane perpendicular to the surface. The BE of OH* on Pd(100) is −2.43 eV, which is 0.40 eV stronger than the BE on Pd(111). OH* binding at the hollow site of Pd(100) is only 0.05 eV weaker than on the bridge site, which is similar to the difference in energy between OH* binding at the fcc site and bridge site on Pd(111) (0.08 eV).

Hydroperoxyl (OOH*) is considered an important intermediate in the DSHP and was identified spectroscopically during the gas-phase reaction of H₂ and O₂ on Au/TiO₂ using inelastic neutron scattering (56). OOH* binds through its nonhydrogenated oxygen atom to a top site on Pd(111) with the hydroxyl group positioned over an adjacent bridge site and the O–H bond pointing away from the surface, whereas OOH* binds through its nonhydrogenated oxygen atom to a bridge site on Pd(100) with the hydroxyl group positioned over an adjacent hollow site and the O–H bond pointing away from the surface. The binding energy of OOH* on Pd(100) is −1.28 eV—stronger than its binding energy on Pd(111) by 0.34 eV. However, the site preference for OOH* on Pd(100) and Pd(111) is weak: on Pd(100), OOH* can also bind to top and hollow sites with less than 0.12 eV difference in binding energy from its most stable adsorption site; on Pd(111), OOH* can also bind through its nonhydrogenated oxygen atom to bridge sites with less than 0.03 eV difference in binding energy from its most stable adsorption site.

Molecular oxygen (O₂*) has the largest disparity in binding strength between Pd(111) and Pd(100); the BE on Pd(100) is −1.27 eV, which is 0.77 eV stronger than that on Pd(111). O₂* binds flat on Pd(100) centered over a hollow site, whereas on Pd(111) O₂* binds across a hcp site with one O atom at a bridge position and the other at a top position. Interestingly, Long et al. (57) used probe molecules and electron spin resonance spectroscopy to show that Pd(100) can more readily activate O₂ through excitation of ground-state triplet O₂ to reactive singlet O₂. This result is in agreement with our calculations; O₂* retains some of its magnetic moment on Pd(111) (33) but a negligible magnetic moment on Pd(100). The strong affinity of Pd(100) for O₂* and O* are reflected in the tendency to reconstruct to a kinetically stable (√5 × √5)R27° surface oxide phase under moderate chemical potentials of O₂ (58). The next best adsorption site for O₂ on Pd(100) is a top–top site with a binding energy of −0.85 eV.

The binding energies of H₂O* and H₂O₂* are weak (<0.4 eV) on both Pd(111) and Pd(100). H₂O* preferentially binds to top sites on both Pd(111) and Pd(100) with the O–H bonds parallel to the Pd surface. The binding energy of H₂O* on Pd(100) is −0.30 eV. H₂O₂* also preferentially binds to top sites and adopts the trans configuration on both Pd facets; one oxygen atom is bound to a top site with its hydrogen atom pointing slightly away from the surface plane, and the other oxygen atom is positioned over an adjacent (fcc or hollow) site with its hydrogen atom pointing toward the surface.

Other potential intermediates include aquoxyl (OOHH*, an isomer of H₂O₂* with both hydrogen atoms on the same oxygen atom) and trihydrogen peroxide (HOOHH*). Similar to our findings on Pd(111) (33), neither of these species is stable on Pd(100), i.e., adsorption of aquoxyl and trihydrogen peroxide structures on Pd(100) results in spontaneous decomposition to (O* + H₂O*) and (OH* + H₂O*), respectively.

Table 1 provides the calculated O–O bond lengths for the adsorbed dioxygen species (O₂*, OOH*, and H₂O₂*) and the corresponding values calculated in the gas phase. There is significant expansion of the O–O bond in both O₂* and OOH* upon adsorption, whereas the O–O bond length in H₂O₂* remains within 2% of its calculated gas-phase value. The larger O–O bond expansion on Pd(100) compared with Pd(111) suggests a weaker O–O bond strength on the more open surface for all of the dioxygen species.

Activation Energy Barriers of Elementary Steps.

The calculated activation energy barriers (E_a) and reaction energies (ΔE) are reported with respect to reactant and product states at infinite separation, unless stated otherwise. Table 2 summarizes the results for all elementary steps on Pd(111) and Pd(100). Transition-state geometries for the elementary steps are shown in Fig. 2.

Table 2.

Elementary steps considered for the decomposition of H₂O₂

No.	Elementary step	Pd(111)†		Pd(100)
		Ea, eV	ΔE, eV	Ea, eV	ΔE, eV
1	H2O2 + * ↔ H2O2*	—	−0.32	—	−0.36
2	H2O* ↔ H2O + *	—	0.22	—	0.30
3	O2* ↔ O2 + *	—	0.50	—	1.27
4	H* + H* ↔ H2 + 2*	—	1.11	—	1.19
5	H2O2* + * ↔ OH* + OH*	0.18	−1.53	0.05	−2.29
6	OOH* + * ↔ O* + OH*	0.08	−1.50	0.02	−1.83
7	O2* + * ↔ O* + O*	0.85	−1.23	0.30	−0.98
8	OH* + * ↔ O* + H*	1.02	0.07	1.03	0.17
9	H2O* + * ↔ OH* + H*	1.10	0.37	0.67	0.00
10	OOH* + * ↔ O2* + H*	0.59	−0.20	0.52	−0.67
11	H2O2* + * ↔ OOH* + H*	0.62	0.05	0.44	−0.29
12	H2O* + O* ↔ OH* + OH*	0.33	0.33	0.00	−0.51
13	H2O2* + O* ↔ OOH* + OH*	0.04‡	−0.44	0.14‡	−0.87
14	H2O2* + OH* ↔ OOH* + H2O*	0.00	−0.16	0.00	−0.17
15	OOH* + O* ↔ O2* + OH*	0.00	−0.27	0.02	−0.81
16	OOH* + OH* ↔ O2* + H2O*	0.00	−0.38	0.00	−0.13
17	H2O2* + O2* ↔ OOH* + OOH*	0.20	−0.02	0.00	0.00

Energetics are reported with respect to either reactants/products at infinite separation (steps 1–11) or coadsorbed for H-transfer reactions (steps 12–17) because these reactants/products are generally stabilized through hydrogen bonding. Elementary steps are classified as follows: adsorption/desorption (steps 1–4); O–O scission (steps 5–7); dehydrogenation (steps 8–11); and H transfer (steps 12–17). E_a and ΔE represent the calculated activation energy and reaction energy in the forward direction. —, no activation barriers are calculated for adsorption/desorption steps.

^†Data for steps 1–12 on Pd(111) are based on ref. 33.

^‡Activation energy corresponds to breaking Pd–O bonds to lift O* from its preferred binding site (fcc or fourfold hollow).

Fig. 2.

Side and top-down views of the transition-state geometries for O–O bond scission (A–C), dehydrogenation (D–G), and H-transfer (H–M) elementary steps on Pd(100). Blue spheres are hydrogen, red spheres are oxygen, and gray spheres are Pd atoms. Elementary step numbers are in reference to Table 2. Bond lengths (d_x-y, in Å) refer to the bond being broken in the forward reaction, as written. Note that in I, the transition state for step 13 involves breaking Pd–O bonds to lift O* from its preferred binding site, followed by spontaneous H transfer from H₂O₂* to O*.

O–O bond scission.

At least one type of O–O bond scission step can be involved in the decomposition mechanism of H₂O₂. OH* and/or O* fragments are the direct products of O–O bond scission. Both Pd(111) and Pd(100) can readily break the O–O bond in H₂O₂* and OOH*, but there is a significant difference in the ability of these facets to dissociate O₂*.

H₂O₂* + * → OH* + OH*.

H₂O₂* decomposes to two OH* on Pd(100) with a barrier of 0.05 eV and a reaction energy of −2.29 eV. The corresponding barrier and reaction energy on Pd(111) are 0.18 eV and −1.53 eV. This step occurs through a similar mechanism on both Pd(111) and Pd(100) whereby H₂O₂* rotates from its most stable position on a top site to the transition state at which the O–O bond is elongated and both OH groups are bound to adjacent Pd atoms across a bridge site. However, at the transition state, the O–H bonds are on the same side of H₂O₂ molecule on Pd(100), whereas they are on different sides of the molecule on Pd(111). Following O–O bond scission, the two OH* relax to bridge sites in their final coadsorbed state, stabilized through a hydrogen bond.

OOH* + * → O* + OH*.

OOH* decomposition to O* and OH* on Pd(100) is nearly spontaneous with a barrier of 0.02 eV and a reaction energy of −1.83 eV—similar to the energetics on Pd(111). The O–O bond scission occurs over a hollow site on Pd(100) and a hcp site on Pd(111).

O₂* + * → O* + O*.

The dissociation of O₂* on Pd(100) occurs over a hollow site, whereby the O–O bond stretches from 1.41 Å in the initial state to 1.90 Å in the transition state. The reaction energy is −0.98 eV and the barrier is 0.30 eV on Pd(100), which is 0.55 eV lower than the corresponding barrier on Pd(111).

The reverse of O₂* dissociation, O* recombination, represents a potential pathway for formation of the O₂ product; this step has been proposed in a number of papers (59–61). Our calculations show that O* recombination has prohibitively high barriers—and is thermodynamically unfavorable—on both Pd(111) and Pd(100); the activation barrier exceeds 2 eV on Pd(111) and 1 eV on Pd(100). These results are in agreement with temperature programmed desorption experiments for O₂ desorption from Pd(111) (62) and Pd(100) (63), in which the evolution of O₂ from these Pd single crystals after preadsorbing O* at near-ambient temperatures is only observed at temperatures exceeding 600 K. Furthermore, in the context of the DSHP, Lunsford (64) used a mixture of [¹⁸O₂ + ¹⁶O₂] with H₂ over a Pd/SiO₂ catalyst and observed that no H₂¹⁶O¹⁸O was formed, indicating that O*/OH* recombination reactions were not relevant to H₂O₂ formation.

Dehydrogenation.

Because in this study we are only investigating the decomposition of H₂O₂ (reaction 3) in the absence of H₂ as reactant, H* can only be derived from dehydrogenation of surface species through O–H bond scission. Barriers for O–H bond scission are generally lower on the more open Pd(100) facet compared with those on Pd(111).

H₂O₂* + * → OOH* + H* and OOH* + * → O₂* + H*.

The O–H bonds in H₂O₂* and OOH* are more difficult to break than the O–O bond, based on the activation barriers in Table 2. On Pd(100), the O–H bond in H₂O₂* that is pointing toward the surface is cleaved over a bridge site. The activation barrier is 0.44 eV, and the reaction energy is −0.29 eV.

For OOH* on Pd(100), the O–H bond is also broken over a bridge site. This breaking requires rotation of the O–H bond toward the surface, starting from the most stable OOH* geometry. The corresponding activation barrier and reaction energy for O–H bond cleavage in OOH* are 0.52 and −0.67 eV on Pd(100).

H₂O* + * → OH* + H* and OH* + * → O* + H*.

Dehydrogenations of H₂O* and OH* require a larger activation energy compared with H₂O₂* and OOH* dehydrogenations. On Pd(100), the barrier to break the O–H bond in H₂O* is 0.67 eV, and the reaction is thermoneutral. OH* dehydrogenation is more difficult and has a barrier of 1.03 eV on Pd(100), and the reaction is slightly endothermic. The transition state for O–H cleavage in both H₂O* and OH* occurs over a hollow site on Pd(100).

Hydrogen transfer.

Formation and cleavage of O–H bonds in which the Pd surface is directly involved have significant activation barriers (>0.4 eV). Alternatively, the Pd surface can mediate H transfer between oxygenated intermediates—without involving an explicit H* species. These elementary steps involve nearly spontaneous H transfer in the exothermic direction on both Pd(111) and Pd(100) (Table 2). The activation energy barriers and reaction energies in this section are reported with respect to coadsorbed reactant and product states, because these states are generally stabilized through hydrogen bonding (∼0.1–0.4 eV per hydrogen bond) with respect to the infinitely separated reactants and products.

The hydrogen atom is always transferred between O atoms involved in hydrogen bonding in the most stable coadsorbed configuration. Importantly, the H-transfer steps represent potential pathways for formation of both the H₂O (H transfers to O*/OH*) and O₂ (H transfers from H₂O₂*/OOH*, retaining the O–O bond) products of H₂O₂ decomposition.

H transfer to O.

H₂O₂*, OOH*, and H₂O* can all directly transfer a H atom to O*; the activation energy barriers for these steps are 0.04, 0.00, and 0.33 eV on Pd(111), with reaction energies of −0.44, −0.27, and 0.33 eV. The corresponding activation energy barriers on Pd(100) are 0.14, 0.02, and 0.00 eV with significantly more exothermic reaction energies of −0.87, −0.81, and −0.51 eV.

H transfer to OH.

H₂O₂* and OOH* can also directly transfer a H atom to OH*. We calculate that these steps proceed with nearly zero activation energy barrier on Pd(111) and Pd(100). The reaction energy for H transfer from H₂O₂* to OH* is weakly exothermic [−0.16 eV on Pd(111) and −0.17 eV on Pd(100)]. The reaction energy for H transfer from OOH* to OH* is more exothermic on Pd(111) (−0.38 eV) than that on Pd(100) (−0.13 eV).

An additional H-transfer step that was explored is H transfer from H₂O₂* to O₂*. This reaction is nearly thermoneutral on Pd(111), with a reaction energy of −0.02 eV and an activation energy barrier of 0.20 eV. On Pd(100), the reaction is thermoneutral with negligible barrier.

Catalytic Cycles and Potential Energy Surfaces.

Based on the elementary steps above, several mechanisms are available to complete the catalytic cycle on clean Pd facets, as summarized in Fig. 3: “O*-assisted,” “OH*-assisted,” “O*+O*-recombination,” and “direct dehydrogenation.” A complete mechanism for direct dehydrogenation is not shown for simplicity, as both the DFT calculations and microkinetic modeling results suggest that direct dehydrogenation steps are characterized by much higher barriers and therefore not relevant under the reaction conditions explored in this study. The first step in all other pathways is H₂O₂ adsorption followed by homolytic O–O bond cleavage to form two OH* species. The second H₂O₂* species can also adsorb and directly decompose to two OH*; these OH* species can then disproportionate to form H₂O* and O*—necessitating the recombination of two O* to form O₂* (O*+O*-recombination mechanism). Alternatively, two channels exist that bypass the thermodynamically unfavorable and highly activated O* recombination step; both involve consecutive H-transfer steps from the second H₂O₂ molecule to the O*/OH* fragments with retention of the original O–O bond in H₂O₂ (O*-assisted and OH*-assisted mechanisms).

Fig. 3.

Schematic representation of reaction pathways for H₂O₂ decomposition on clean surfaces. The numbers by the black arrows correspond to the elementary steps from Table 2. The overall reaction for each of the three complete mechanisms described in this figure is as follows: 2 H₂O₂ → 2 H₂O + O₂.

The potential energy surfaces for all pathways are displayed in Fig. 4 for both Pd(111) and Pd(100). Based on the DFT calculations alone, the O*-assisted and OH*-assisted pathways not only provide the most energetically efficient route to form the products, but are also mutually competitive on both Pd(111) and Pd(100). However, the deep potential wells associated with the strongly bound O*/OH* fragments indicate that there is a strong thermodynamic driving force to populate the surfaces with O*/OH*—especially Pd(100). Therefore, the active surface under reaction conditions may be partially covered by O*/OH*.

Fig. 4.

Potential energy surfaces (thermochemistry only) for reaction pathways from Fig. 3 on clean Pd(111) and Pd(100) based on the DFT-derived energetics. Energies are referenced to two H₂O₂ molecules in the gas phase. The “|” separating two adsorbates denotes infinite separation from each other. The “(g)” denotes a gas-phase species. Insets compare O–H and O–O bond scission barriers in H₂O₂. “TS” denotes transition state.

Note that on O*/OH*-modified surfaces, there is an increased probability of H transfer from H₂O₂* before O–O bond scission; the required O–O bond scission step may then occur in OOH* rather than in H₂O₂*, slightly altering the succession of elementary steps proposed in Fig. 3.

Kinetics Experiments and Microkinetic Modeling.

The results from our kinetics experiments are shown in Tables 3 and 4. The experimentally determined activation energy barrier of 53.3 ± 3.0 kJ/mol indicates that there is a significant variation in H₂O₂ decomposition rate with reaction temperature under conditions relevant to the DSHP. The nearly first-order dependence on concentration of H₂O₂ is in agreement with other experimental studies of H₂O₂ decomposition on Pd under similar conditions of temperature and H₂O₂ concentration (13, 65). We also observed that the addition of O₂ to the gas phase did not significantly affect the decomposition rate of H₂O₂ up to O₂ partial pressures of at least 37 psi, indicating negligible product inhibition over the conditions studied. This finding is in agreement with the result of Choudhary and Samanta (66), who observed only a minor difference in the reaction rate for H₂O₂ decomposition over Pd/Al₂O₃ (in the absence of H₂) in a semibatch reactor when flowing either O₂ or N₂ through the liquid phase.

Table 3.

Reaction rates obtained from the kinetics experiments on Pd/spSiO₂

Run†	Temperature, K	y(O2)	x(H2O2)	Experimental rate, mol⋅molPds−1⋅s−1
1	307	0.00	0.60	71.8
2	307	0.00	0.30	31.5
3	307	0.00	0.15	17.1
4	307	0.00	0.08	10.5
5	297	0.00	0.15	7.9
6	285	0.00	0.15	3.4
7	307	0.25	0.15	16.7
8	307	0.13	0.15	16.2
9	307	0.06	0.15	16.9

^†y denotes mole fraction in the gas phase (balance Ar), and x denotes molarity (moles per liter) in the liquid phase at the start of reaction. Pd_s denotes surface Pd atoms determined by CO uptake. Total pressure was 150 psi, and the stir rate was 1,200 rpm for all experiments. Reaction rates reported here correspond to the initial rates measured from conversion versus time data at <15% conversion, which was approximately linear in this regime. Each reported rate represents the average from at least two repeated sets of conversion versus time data.

Table 4.

Experimental and microkinetic model-predicted reaction orders and apparent activation energy barriers (E_app)

Species	Experiment†	O*-coverage solution	OH*-coverage solution
H2O2	0.92 ± 0.08	1.00	0.97
O2	−0.01 ± 0.03	−0.01	0.00
Eapp, kJ/mol	53.3 ± 3.0	53.1	56.6

Reported experimental error is the SE from linear regression.

^†Subsequent catalyst batches yielded reaction orders and an apparent barrier within ∼15% of the values reported here.

Initial estimates for microkinetic model rate parameters are derived from the DFT-calculated energetics. The reactor is simulated as a continuous stirred tank reactor. The turnover frequencies for H₂O₂ decomposition obtained from this model (i.e., the rate of H₂O₂ converted per surface site) are used to calculate reaction orders and apparent activation barrier for comparison with the experimental data.

The rates, reaction orders, and apparent activation barriers predicted by the microkinetic model were initially in poor agreement with the experimental data when using purely DFT-derived parameters from Pd(111) or Pd(100). We subsequently used sensitivity analysis to identify the sensitive DFT-derived BEs of surface species and transition-state energies. We then fit model-predicted reaction rates to experimental rates (such that the residual error is less than 20%) by modifying sensitive parameters, constraining the adjustment of parameters such that (i) the deviation between DFT-derived BEs and activation barriers on a given Pd facet and the corresponding values from the microkinetic model should be within the ∼0.1- to 0.2-eV error bars generally attributed to DFT calculations (67), and (ii) the adsorbate coverage used in the DFT calculations should be consistent with the coverage predicted by the microkinetic model (that is, the solution should be self-consistent with respect to coverage).

Next, we present the results from two model solutions that satisfy the above criteria, but differ in both the coverage and identity of the most abundant surface intermediate, and are denoted as the “O*-coverage solution” and the “OH*-coverage solution.”

O*-coverage solution.

Fig. 5A shows a parity plot comparing the experimental H₂O₂ decomposition rates with the microkinetic model predictions for the O*-coverage solution [initial estimates of parameters are derived from DFT calculations on clean Pd(111), and Supporting Information provides details of the parameter adjustments used to obtain this solution]. There is good agreement between model-predicted and experimental reaction rates, and the microkinetic model is able to accurately reproduce the experimental activation barrier and reaction orders (Table 4).

Fig. 5.

(A and C) Parity plots of experimental and model-predicted reaction rates for H₂O₂ decomposition. Refer to Table 3 for reaction conditions at each of the points in A and C. Pd_s denotes surface Pd atoms determined by CO uptake. Red points are varying temperature; blue points are varying O₂ partial pressure; black points are varying feed concentration of H₂O₂. (B and D) Microkinetic model-predicted surface coverages of the most abundant surface intermediates (0.15 M H₂O₂ in H₂O feed with 150 psi Ar in gas phase). Plots on the Left refer to the O*-coverage solution, and plots on the Right refer to the OH*-coverage solution obtained from the microkinetic model. Insets in B and D provide graphical representations of the nature of the active sites as concluded through this study [nearly clean Pd(111) and OH*-modified Pd(100)]. Blue spheres are hydrogen, red spheres are oxygen, and gray spheres are Pd atoms.

The microkinetic model predictions for the surface coverage for the most abundant intermediate, O*, range from 0.13 to 0.16 ML (Fig. 5B), with the remaining sites being vacant. Marginal changes to the clean surface energetics are expected from adsorbate–adsorbate interactions at such low O* coverage (68), and furthermore this adjusted parameter set compares well with the DFT-derived parameters on clean Pd(111); the maximum deviation in binding energy or activation barrier is a 0.24 eV destabilization of the binding energy of O₂* on Pd(111). Therefore, a partially O*-covered Pd(111) surface is a plausible representation of the active site for H₂O₂ decomposition.

On the other hand, DFT-derived parameters on Pd(100) deviate significantly (>0.35 eV for OH*, OOH*, and O₂*) from this O*-coverage solution parameter set. Pd(100) binds intermediates too strongly, and the low predicted O* coverage is not expected to destabilize intermediates on Pd(100) sufficiently for consistency with the O*-coverage solution parameters.

The O*-coverage solution predicts that the dominant reaction pathway is the O*-assisted pathway shown in Fig. 3 (sequence of elementary steps from Table 2: 1, 5, −12, 2, 1, 13, 16, 2, 3), with some reaction flux through the parallel OH*-assisted pathway (sequence of elementary steps from Table 2: 1, 5, 1, 14, 2, 16, 2, 3). The rate of O* recombination to form O₂* is negligible, and dehydrogenation reactions are also inactive (atomic H is only transferred between surface intermediates). The kinetic relevance of each elementary step was also analyzed using Campbell’s degree of rate control (69, 70):

$$X_{RC,i}=\frac{k_i}{r}{\left(\frac{\partial r}{\partial k_i}\right)}_{K_{i,\mathrm{eq}},k_j},$$

where k_i and K_i,eq are the rate constant and equilibrium constant for step i, and r is the overall reaction rate. O–O bond scission in H₂O₂* (step 5 of Table 2) carries the highest degree of rate control over the reaction conditions examined, shown in Table 5; the remaining rate control is distributed between the subsequent H-transfer reactions.

Table 5.

Degree of rate control (X_RC) calculated for kinetically relevant reaction steps for reaction condition 3 of Table 3

No.	Elementary step	XRC, O*-coverage solution	XRC, OH*-coverage solution
5	H2O2* + * ↔ OH* + OH*	0.59	0.00
6	OOH* + * ↔ O* + OH*	0.02	0.55
13–16	(H transfers)	0.40	0.43

X_RC is given for both the O*-coverage solution and the OH*-coverage solution at this experimental condition. Elementary step numbers (No.) are in reference to Table 2. X_RC for the H transfers is the sum over all steps listed.

OH*-coverage solution.

Using the DFT calculations on clean Pd(100) to derive initial estimates of parameters, a second solution was identified that also gave agreement with the experimental data set (Fig. 5C and Table 4). In this case, the model-predicted surface coverage is ∼0.5 ML of OH* (Fig. 5D) and is therefore not self-consistent with the clean Pd(111) and Pd(100) surface models used in the DFT calculations. To ensure a solution self-consistent in coverage, we recalculated the binding energies of surface intermediates and the activation energy barriers for steps carrying significant reaction flux (as predicted by the OH*-coverage solution) in the presence of 0.5 ML of OH* spectators, i.e., two OH* were added to the unit cell and allowed to relax in the DFT calculations.

The DFT-derived parameter set for the OH*-modified Pd(100) surface is found to be in close agreement with the adjusted parameter set from the OH*-coverage solution (BEs shown in Table 6, with further details in Supporting Information). The DFT calculations show that 0.5 ML of OH* destabilizes most intermediates and transition states investigated on Pd(100) relative to the clean Pd(100) calculations. The binding energies of O*, OH*, O₂*, and OOH* are weakened by >0.5 eV, whereas the binding energies of H*, H₂O*, and H₂O₂* are not significantly affected. In addition, the activation energy barriers for O–O bond breaking in OOH* and H₂O₂* increase by 0.39 and 0.56 eV, respectively. Activation energy barriers for H transfer from H₂O₂* or OOH* to OH* or O* remain small (<0.2 eV). The maximum deviation in binding energy or activation barrier between the OH*-coverage solution and DFT calculations on OH*-modified Pd(100) is a 0.18-eV decrease in the activation barrier for O–O breaking in OOH*. Therefore, OH*-modified Pd(100) also appears to be a feasible representation of the active site for H₂O₂ decomposition on Pd.

Table 6.

DFT-calculated BEs of adsorbed species on Pd(100) in the presence of 0.5 ML of OH*, and comparison with the BEs in the OH*-coverage solution

	Pd(100) + 0.5 ML OH*		OH*-coverage solution
Species	Adsorption site	BE, DFT, eV	BE, eV
H*	Hollow	−2.56	−2.56
O*	Hollow	−3.16	−2.99
OH*	Top-tilted	−1.68	−1.83
OOH*	Hollow-upright	−0.61	−0.51
H2O*	Top	−0.26	−0.32
H2O2*	Top	−0.36	−0.46
O2*	Hollow	−0.14	−0.14

The dominant reaction pathways predicted for the OH*-coverage solution are shown in Fig. 6. At high OH* coverage, immediate H transfer from H₂O₂* to OH* is predicted to be nearly quasiequilibrated (step 14 of Table 2). The O–O bond breaks in OOH*, and this step carries the highest degree of rate control (Table 5). Hydrogen transfers from OOH* to OH* (step 16 of Table 2) and from OOH* to O* (step 15 of Table 2) carry the remaining reaction flux to form O₂* and H₂O*; hydrogen transfer from H₂O* to O* (step 12 of Table 2) is also nearly quasiequilibrated.

Fig. 6.

Dominant reaction pathways predicted by the microkinetic model for the OH*-coverage solution. The numbers by the black arrows correspond to the elementary steps numbers given in Table 2.

Discussion

The microkinetic modeling results suggest that both the close-packed Pd(111) and more open Pd(100) facets can contribute to the total H₂O₂ decomposition activity. Furthermore, on both Pd facets, all reaction flux is predicted to go through an O–O bond breaking step (in either H₂O₂* or OOH*), followed by successive H-transfer steps to O*/OH* adsorbates. The relevant surface coverage of O*/OH* is then a function of the ability of the Pd surfaces to generate the O*/OH* fragments through O–O bond breaking [which can vary strongly with surface coverage, as seen from calculations on the OH*-modified Pd(100)], and the availability of H-donating species (H₂O₂* and OOH*) to reduce O*/OH* to H₂O* through the rapid H-transfer reactions. This mechanism is comparable to the redox mechanism discussed in refs. 65 and 71. The direct dehydrogenation and O*+O*-recombination pathways (Fig. 3) are predicted to be inactive over all experimental conditions examined.

Although H-transfer steps carry some degree of rate control in the microkinetic model solutions, the DFT calculations show that the activation barriers for these steps are nearly insensitive to the surface structure of the Pd substrate. Interestingly, experimentally measured activation energy barriers for the gas-phase H-transfer reactions of H₂O₂ or OOH• to OH• or O• radicals are also readily accessible (<0.2 eV) around room temperature (72). The action of the metal substrate is then to generate the O*/OH* species through O–O bond breaking, and localize the H-transfer event to the surface. H₂O₂*, OOH*, and H₂O* are mobile on both Pd(111) and Pd(100) based on the small differences in binding energies among the available binding sites and therefore can diffuse across the Pd surface to find—and react with—the O*/OH* fragments. Additionally, we note that O* strongly prefers the threefold and fourfold hollow sites on Pd(111) and Pd(100), respectively; and O* must be lifted slightly from its preferred binding site to accept a H atom. This behavior is reflected in the low activation energy barrier generally calculated for H transfers to O*, compared with the virtually zero barrier calculated for H transfers to OH*—which is more accessible at its most favorable binding site (bridge site) on Pd(111) and Pd(100).

Breaking of the O–O bond in either H₂O₂* or OOH* carries the majority of rate control, suggesting that strategies to reduce H₂O₂ decomposition activity must focus on tuning surface reactivity toward the O–O bond. Retention of the O–O bond in dioxygen species is generally acknowledged to be a key factor in the selective synthesis of H₂O₂ by the DSHP both in theoretical (33, 73, 74) and experimental literature (8, 12, 64, 75), and our results here quantitatively highlight this as the central parameter governing the subsequent H₂O₂ decomposition activity on the Pd surface.

In view of the aforementioned findings, reduced Pd nanoparticles would be expected to be an ineffective catalyst for the DSHP due to high activity of Pd for O–O bond breaking [0.18-eV and 0.05-eV barrier to break O–O bond in H₂O₂ on clean Pd(111) and Pd(100), respectively]. Extensive surface poisoning may be necessary to inhibit H₂O₂ decomposition on Pd, which our results suggest can readily occur on surface facets of supported Pd nanoparticles that are generally in high abundance [the (111) and (100) facets]. Indeed, the experimentally measured H₂O₂ decomposition activity of supported Pd nanoparticles can be effectively quenched upon adding halides (along with acids, whose role may partly be to facilitate halide adsorption) to the reaction medium, often at Pd:halide atomic ratios close to or exceeding 1:1 (66, 75–78). Unfortunately, there are limited fundamental studies that examine the halide coverage necessary to achieve this effect.

Some of the most successful experimental catalysts to-date for the DSHP are based on alloys of Pd with Au, on which the subsequent decomposition reactions of H₂O₂ are partially or completely inhibited. DFT calculations indicate that dilution of Pd surfaces with Au significantly increases barriers for O–O bond scission (79). However, experiments demonstrate that Au itself is generally an ineffective catalyst for the DSHP and gives slow rates (14, 80), likely due to the significant activation energy barrier required to dissociate H₂ on Au (81) and weak adsorption of O₂ (33). Promising search directions for improved DSHP catalysts may include bimetallic systems in which an active component (e.g., Pd) is effectively isolated in a relatively inert component (e.g., Au) resulting in reduced O–O bond breaking capacity but retention of H₂ dissociation (82) capacity; similar catalysts have proven very effective for the electrocatalytic synthesis of H₂O₂ (83, 84).

Last, the presence of H₂ in the reactor feed (not considered in the present work) has been shown to enhance the overall H₂O₂ decomposition activity over Pd-based catalysts (66, 85). Choudhary and Samanta (66) observed that, on unmodified Pd, H₂ both increases the H₂O₂ decomposition rate and consumes H₂O₂ through complete hydrogenation to H₂O (reaction 4). Moreover, although adding chloride or bromide to an acidified reaction medium can quench H₂O₂ decomposition on Pd, H₂O₂ hydrogenation activity remains (66); this observation may indicate significant differences in the active site(s) and rate-controlling step(s) responsible for H₂O₂ decomposition versus H₂O₂ hydrogenation—although O–O bond breaking is required in both reactions. Tentative explanations addressing the role of H₂ have been proposed, such as maintaining the Pd surface in the reduced state (59) for facile O–O bond breaking. Additionally, direct hydrogenation of H₂O₂ was shown to be a highly activated step using DFT calculations (86). The influence of subsurface hydrogen or even Pd-hydrides may also be relevant (87). The next stage of this work is to investigate the mechanistic role of H₂ in accelerating H₂O₂ decomposition on Pd, in addition to probing the nature of the active site(s) in the presence of H₂.

Conclusions

Both the close-packed (111) and more open (100) facets can represent the active site for SiO₂-supported Pd nanoparticles. The DFT results show that O–O bond scission is facile on both Pd facets, such that O* and OH* intermediates are readily produced. Furthermore, H₂O₂* and OOH* can reduce O* and OH* to H₂O through thermodynamically driven H-transfer reactions, liberating O₂. The alternative step to produce O₂ (recombination of O*) is both thermodynamically and kinetically unfavorable. In addition, steps involving dehydrogenation through direct O–H bond cleavage over Pd are less favored than the H-transfer steps.

Microkinetic models based on two parameter sets are able to describe the experimental data for a SiO₂-supported Pd catalyst: the first set corresponds to a Pd surface partially covered in <0.2 ML of O*, and these adjusted parameters are consistent with the DFT-derived parameters on clean Pd(111); the second set corresponds to a Pd surface covered in ∼0.5 ML of OH*, and these adjusted parameters are consistent with the DFT-derived parameters on a Pd(100) surface with OH* spectators. Therefore, the microkinetic model suggests that both Pd(111) and Pd(100) can contribute to H₂O₂ decomposition activity. Experimental identification of dominant surface species during H₂O₂ decomposition on Pd might be realized by in situ X-ray photoelectron spectroscopy measurements in a similar manner to work performed on Pt for the oxygen reduction reaction (88).

Consistent with the insights from DFT calculations, the dominant reaction pathways involve O–O bond breaking in either H₂O₂* or OOH* followed by H-transfer reactions between various reaction intermediates. Breaking of the O–O bond is identified as the key parameter governing H₂O₂ decomposition activity, because this step carries the highest degree of rate control.

Microkinetic Model Formulation

In the microkinetic model simulation, the reactor is operated as a transient continuous stirred tank reactor (CSTR) and evolved to steady state as described in ref. 89. The CSTR model provides a good approximation to the experimental setup (a constant volume batch reactor) at low reactant conversion (H₂O₂ conversion was kept below 15% for all experimental rate measurements) and negligible product inhibition (apparent reaction order with respect to P_O2 was ∼0 over the range of conditions studied; Table 4 of the main text).

The proposed elementary steps (Table 2 of the main text) correspond to a Langmuir–Hinshelwood process. The adsorption/desorption steps are assumed to be quasiequilibrated. An aqueous H₂O₂ solution is used in the experiments, and the following procedure is implemented to reflect adsorption from the aqueous H₂O₂ solutions at each feed condition: (i) an experimentally derived Henry’s law constant (90) for dilute aqueous H₂O₂ solutions (obtained at similar temperature/concentration conditions to our experimental conditions) is used to calculate the equilibrium vapor pressure of H₂O₂; (ii) an ideal mixture is assumed to be formed between H₂O₂ and H₂O (Raoult’s law holds), and using Antoine equation parameters for H₂O taken from the National Institute of Standards and Technology (NIST) (webbook.nist.gov), the equilibrium vapor pressure of H₂O is calculated; and (iii) the DFT-derived gas-phase adsorption equilibrium constants for H₂O₂ and H₂O are used to determine their respective Pd surface concentrations. Note that, because no corrections are made to the energetics of the surface-bound species to reflect potential interactions at the liquid–solid interface, this treatment only considers the aqueous phase as a reservoir for H₂O₂ and H₂O.

The initial estimates of parameters for the O*-coverage solution are derived from the DFT calculations on clean Pd(111). Activation barriers are constrained (≥0) for exothermic steps and (greater than or equal to reaction energy) for endothermic steps in the microkinetic model. Preexponential factors for elementary steps are calculated from transition-state theory (44); a preexponential factor of k_BT/h is assumed for steps in which no transition state is identified in the DFT calculations. The Shomate parameters are calculated from the DFT-derived vibrational frequencies on Pd(111) (45) to describe the temperature dependence of entropies and enthalpies for surface species and transition states; these values are presented in Table S1. The final Shomate parameter values corresponding to the O*-coverage solution are obtained by adjusting only the Shomate parameter F (adjusting F corresponds directly to adjusting binding energies and transition-state energies).

Table S1.

Shomate parameters (A to G) for T = 100–400 K on clean Pd(111), where the Shomate parameter H has been set to the reference enthalpy H°_T0

Species	A	B	C	D	E	F	G	F (O*-coverage solution)
Individual surface species
H*	−1.2379	−31.0614	274.9744	−301.1067	0.0230	−1,572.20	0.1131	−1,572.20
O*	3.5819	40.1962	156.2183	−376.4105	−0.0709	−42,077.10	0.7089	−42,079.50
OH*	4.8344	121.4179	−60.9688	−136.1449	−0.0267	−43,653.89	8.8485	−43,653.89
OOH*	13.8608	172.3887	−231.4055	107.4082	−0.0458	−85,580.19	28.9736	−85,570.09
H2O*	13.0211	157.7417	−338.6789	278.7604	−0.0575	−45,267.04	25.9167	−45,267.04
H2O2*	26.5334	173.8183	−326.9946	307.0207	−0.0798	−87,162.06	63.5197	−87,167.26
O2*	12.3129	170.8770	−350.4969	286.8124	−0.0532	−84,026.41	36.2718	−84,002.91
Coadsorbed surface species
[H2O2* + O*]	−10.00	528.76	−1,147.58	1,000.37	−0.0689	−129,243.19	−63.32	−129,239.19
[H2O2* + OH*]	18.78	201.08	−131.12	19.37	−0.0901	−130,887.40	35.79	−130,887.40
[OOH* + OH*]	16.93	212.17	−126.11	−63.43	−0.1282	−129,291.72	23.32	−129,291.72
[O2* + H2O*]	3.59	406.90	−737.38	545.40	−0.0667	−129,322.19	−16.70	−129,298.69
[OOH* + H2O*]	11.49	329.61	−418.95	203.31	−0.0705	−130,900.76	10.82	−130,890.76
[OH* + OH*]	−10.73	355.60	−531.46	283.50	−0.0238	−87,315.31	−52.20	−87,315.31
[H2O* + O*]	−14.32	521.47	−1,229.11	1,089.45	−0.0533	−87,350.36	−74.03	−87,350.36
[H2O2* + O2*]	16.70	369.93	−571.72	388.33	−0.1296	−171,223.92	16.16	−171,200.42
[OOH* + OOH*]	−1.04	400.60	−555.99	379.77	−0.0611	−171,219.15	−29.52	−171,214.15
Transition states
(5) H2O2* + * ↔ [OH* + OH*]	19.1038	217.2597	−433.2384	374.5711	−0.0718	−87,143.93	42.1829	−87,138.13
(6) OOH* + * ↔ O* + OH*	10.2082	157.9428	−118.689	−94.1579	−0.0886	−85,576.35	11.2061	−85,551.35
(7) O2* + * ↔ O* + O*	−11.4069	327.403	−796.6204	705.6756	−0.016	−83,940.97	−50.7924	−83,917.47
(8) OH* + * ↔ O* + H*	3.3211	104.2105	−1.4067	−190.3628	−0.0481	−43,557.19	0.4708	−43,557.19
(9) H2O* + * ↔ OH* + H*	6.4144	107.4376	28.2296	−186.3454	−0.0378	−45,159.27	11.5313	−45,159.27
(10) OOH* + * ↔ O2* + H*	11.3126	145.9346	−50.2891	−141.1647	−0.0687	−85,525.28	18.297	−85,515.18
(11) H2O2* + * ↔ OOH* + H*	14.9553	176.278	−148.4772	6.5883	−0.0585	−87,099.96	30.1399	−87,104.96
(12) [H2O* + O*] ↔ [OH* + OH*]	Nearly spontaneous, transition state could not be isolated within the accuracy of the DFT parameters. (33)
(13) [ H2O2* + O*] ↔ [OOH* + OH*]	14.2811	285.1948	−435.9657	307.4847	−0.095	−129,242.16	18.8832	−129,222.26
(14) [H2O2* + OH*] ↔ [OOH* + H2O*]	Nearly spontaneous, transition state could not be isolated within the accuracy of the DFT parameters.
(15) OOH* + O* ↔ O2* + OH*	17.1135	202.604	−304.3029	233.8313	−0.0931	−127,649.63	34.4015	−127,633.63
(16) [OOH* + OH*] ↔ [O2* + H2O*]	13.1863	198.5609	−22.739	−224.1188	−0.091	−129,295.76	18.5607	−129,295.76
(17) [H2O2* + O2*] ↔ [OOH* + OOH*]	17.0212	279.2991	−275.2226	107.3011	−0.0951	−171,201.20	27.3271	−171,177.70
Gas-phase species
H2(g)	28.60	4.79	−16.29	18.74	0.00185	−3,041.56	168.41
O2(g)	28.93	2.86	−20.27	50.84	0.00040	−83,972.46	235.00
H2O(g)	33.75	−3.43	1.06	26.34	−0.00204	−45,239.60	236.46
H2O2(g)	31.01	36.28	53.24	−75.24	−0.00409	−87,123.43	259.82

Coadsorbed reactants/products that can be stabilized through hydrogen bonding are treated as separate species in the microkinetic model that form from the infinitely separated reactants with no activation barrier and react through the H-transfer steps (e.g., the two steps for formation and reaction of coadsorbed hydrogen peroxide and atomic oxygen: H₂O₂* + O* → [H₂O₂* + O*], followed by H-transfer reaction [H₂O₂* + O*] → [OOH* + OH*]. The “[ ]” in this table denotes the coadsorbed species, which occupy two surface sites). Any contributions to rate control from the coadsorbate formation steps has been included in the sum over H-transfer steps in Table 5 of the main text. Both coadsorbed species [OOH* + O*] and [O₂* + OH*] are found to have a destabilizing interaction with respect to infinite separation based on DFT calculations on both clean Pd(111) and Pd(100), and are therefore not included as coadsorbed species in the microkinetic model. Only the Shomate parameter F is adjustable in the microkinetic model because this corresponds directly to adjusting binding energies and transition-state energies. The final adjusted value of F corresponding to the O*-coverage solution is provided in the last column. The ∼0.13–0.16 ML of atomic oxygen coverage predicted in the O*-coverage solution refers to the individual O* surface species.

Shomate equation according to NIST (webbook.nist.gov) is as follows:

$$\text{t}=\text{T}\left[\text{K}\right]/\mathrm{1,000}$$

$${\mathrm{C}}_{\text{p}}^{°}\left[\text{J}/\text{(}\mathrm{mol\; K}\text{)}\right]=\text{A}+\mathrm{B}\text{t}+{\text{Ct}}^2+{\text{Dt}}^2+\text{E}/{\text{t}}^2$$

$$\text{H}°-{\text{H}}_{\text{T}0}^{°}\left[\text{kJ}/\text{mol}\right]=\text{At}+\text{B}{\text{t}}^2/2+{\text{Ct}}^3/3+{\text{Dt}}^4/4-\text{E}/\mathrm{t}+\mathrm{F}-\mathrm{H}$$

$$\text{S}°\left[\text{J}/\text{(}\mathrm{mol\; K}\text{)}\right]=\text{Aln}\left(\text{t}\right)+\text{Bt}+{\text{Ct}}^2/2+{\text{Dt}}^3/3-\text{E}/\left(2{\text{t}}^2\right)+\mathrm{G}\text{.}$$

Analogously, the initial estimates of parameters for the OH*-coverage solution are derived from the DFT calculations on clean Pd(100). The Shomate parameters are calculated from the DFT-derived vibrational frequencies on clean Pd(100) (45) to describe the temperature dependence of entropies and enthalpies; these values are presented in Table S2. The final Shomate parameter values corresponding to the OH*-coverage solution are obtained by adjusting only the Shomate parameter F (adjusting F corresponds directly to adjusting binding energies and transition-state energies).

Table S2.

Shomate parameters (A to G) for T = 100–400 K on clean Pd(100), where the Shomate parameter H has been set to the reference enthalpy H°_T0

Species	A	B	C	D	E	F	G	F (OH*-coverage solution)
Individual surface species
H*	2.4742	78.1496	−29.9400	−119.8483	−0.0583	−1,584.14	−3.4570	−1,567.14
O*	7.1819	94.1544	−171.5667	89.7288	−0.0814	−42,102.80	6.2529	−42,014.80
OH*	2.5023	102.0164	55.4286	−293.2032	−0.0424	−43,693.80	−2.0461	−43,635.71
OOH*	16.1481	186.9070	−287.8807	153.4456	−0.1135	−85,619.16	23.6466	−85,545.13
H2O*	14.1861	209.8581	−497.7306	456.2954	−0.0045	−45,268.60	50.6399	−45,270.60
H2O2*	19.1131	199.2745	−325.1658	243.3293	−0.1187	−87,169.72	31.2071	−87,179.32
O2*	−17.8817	366.1298	−814.9159	680.9070	−0.0067	−84,094.93	−70.4549	−83,985.93
Coadsorbed surface species†
[H2O2* + O*]	9.71	393.72	−810.69	702.04	−0.103	−129,265.65	−2.74	−129,200.65
[H2O2* + OH*]	14.85	297.49	−393.35	258.50	−0.112	−130,907.08	15.55	−130,827.08
[OOH* + OH*]	0.35	357.22	−601.84	468.72	−0.067	−129,345.95	−19.13	−129,204.95
[O2* + H2O*]	−5.50	558.20	−1,316.93	1,175.29	−0.062	−129,358.13	−44.30	−129,258.13
[OOH* + H2O*]	−0.10	459.54	−836.91	646.44	−0.060	−130,917.92	−27.76	−130,836.92
[OH* + OH*]	9.33	148.28	102.13	−367.59	−0.092	−87,420.45	8.56	−87,332.07
[H2O* + O*]	−19.09	528.39	−1,224.49	1,080.39	−0.044	−87,365.85	−86.87	−87,315.85
[H2O2* + O2*]	−11.80	552.31	−1,129.58	1,011.99	−0.070	−171,283.27	−68.30	−171,213.27
[OOH* + OOH*]	−14.91	570.57	−1,181.29	1,067.56	−0.070	−171,283.08	−79.10	−171,098.08
Transition states
(5) H2O2* + * ↔ [OH* + OH*]	15.8130	182.5407	−253.3928	149.6250	−0.0630	−87,159.17	32.2389	−87,118.17
(6) OOH* + * ↔ O* + OH*	−7.1496	351.0642	−810.0315	711.7780	−0.0499	−85,610.65	−43.9678	−85,516.70
(7) O2* + * ↔ O* + O*	5.8195	69.2012	243.6839	−597.6716	−0.1060	−84,076.08	1.8144	−83,931.08
(8) OH* + * ↔ O* + H*	−0.6430	54.3148	216.6492	−426.8104	−0.0269	−43,592.42	−7.7810	−43,512.42
(9) H2O* + * ↔ OH* + H*	−27.6558	435.1438	−919.8486	737.9061	0.0165	−45,201.22	−99.2842	−45,201.22
(10) OOH* + * ↔ O2* + H*	10.3419	130.5716	−63.5579	−69.7197	−0.0917	−85,567.26	12.2305	−85,487.26
(11) H2O2* + * ↔ OOH* + H*	12.0433	165.3644	−11.8770	−220.3537	−0.0918	−87,124.60	14.9198	−87,124.60
(12) [H2O* + O*] ↔ [OH* + OH*]	−22.7796	423.6000	−820.7693	652.6636	0.0086	−87,366.18	−85.3674	−87,281.18
(13) [ H2O2* + O*] ↔ [OOH* + OH*]	−3.0431	373.9495	−677.1616	525.9745	−0.0446	−129,246.02	−31.9938	−129,170.02
(14) [H2O2* + OH*] ↔ [OOH* + H2O*]	17.4539	229.3678	−137.8705	−45.9880	−0.0810	−130,910.53	33.0865	−130,822.53
(15) OOH* + O* ↔ O2* + OH*	−2.0505	346.9272	−671.5379	564.6279	−0.0671	−127,672.98	−30.9511	−127,672.98
(16) [OOH* + OH*] ↔ [O2* + H2O*]	−6.9963	372.1790	−577.7797	389.5662	−0.0170	−129,348.30	−29.3073	−129,348.30
(17) [H2O2* + O2*] ↔ [OOH* + OOH*]	−21.6571	572.7990	−1,126.8435	965.9686	−0.0254	−171,284.89	−91.5796	−171,284.89

Coadsorbed reactants/products that can be stabilized through hydrogen bonding are treated as separate species in the microkinetic model that form from the infinitely separated reactants with no activation barrier and react through the H-transfer steps (e.g., the two steps for formation and reaction of coadsorbed hydrogen peroxide and atomic oxygen: H₂O₂* + O* → [H₂O₂* + O*], followed by H-transfer reaction [H₂O₂* + O*] → [OOH* + OH*]. The “[ ]” in this table denotes the coadsorbed species, which occupy two surface sites). Any contributions to rate control from the coadsorbate formation steps has been included in the sum over H-transfer steps in Table 5 of the main text. Both coadsorbed species [OOH* + O*] and [O₂* + OH*] are found to have a destabilizing interaction with respect to infinite separation based on DFT calculations on both clean Pd(111) and Pd(100), and are therefore not included as coadsorbed species in the microkinetic model. Only the Shomate parameter F is adjustable in the microkinetic model because this corresponds directly to adjusting binding energies and transition-state energies. The final adjusted value of F corresponding to the OH*-coverage solution is provided in the last column. The ∼0.5 ML of hydroxyl coverage predicted in the OH*-coverage solution refers to the coadsorbed surface species [OH* + OH*], which occupies two surface sites (i.e., 0.5 ML of total hydroxyl coverage is 0.25 ML of [OH* + OH*]).

^†Coadsorbed surface species in the OH*-coverage solution of the microkinetic model were permitted to be stabilized by up to two hydrogen bonds (∼0.6 eV) with respect to separation of the constituent surface species.

Microkinetic Model Limitations

Solvation Effects.

The experimental measurements were performed in a three-phase system (gaseous product, liquid reactant and product, and solid catalyst) using conditions relevant to a DSHP process. Water has been shown to interact weakly with noble metal surfaces (91) but can potentially solvate adsorbates and transition states (92). The influence of solvation is expected to be most pronounced for weakly bound adsorbates, whose chemisorption energies are comparable to the intermolecular interactions in water. Such effects are challenging to account for in DFT calculations for a number of reasons, including the following: the structure of water at metal interfaces remains a subject of intense study (93); there are inadequacies in the DFT description of liquids (94); and it is computationally expensive to explicitly treat solvent models in DFT calculations. As a first approximation to the H₂O₂ decomposition chemistry, experimentally carried out in the aqueous phase over a supported Pd catalyst, we neglect solvent effects in the DFT calculations. The validity of this approximation will depend on the degree of solvation of surface species in the kinetically significant steps.

pH Effects.

The solution pH has also been shown to significantly affect the rate of Pd-catalyzed H₂O₂ decomposition (8). One beneficial role of protons (for inhibiting H₂O₂ decomposition) has been proposed to be through decreasing adsorption of H₂O₂ onto the catalyst (10). In the absence of any direct role of protons in the reaction mechanism, the influence of pH could then potentially be incorporated in the adsorption equilibrium constant for H₂O₂. In addition, the counter anion strongly influences the H₂O₂ decomposition rate; coordinating anions like Cl⁻ and Br⁻ were shown to be effective inhibitors of H₂O₂ decomposition in the presence of acids (which, in part, may act to facilitate anion adsorption on Pd), whereas oxyacids like sulfuric and acetic acid are less effective (10). However, the effect of pH and other additives was not investigated in this work. All H₂O₂ feed solutions in our experiments were prepared using ultrapure water.

Comparison of Binding Energies and Activation Barriers from the O*-Coverage Solution and OH*-Coverage Solution with the DFT-Derived Values at 0 K

The adjustments (“Δ”) to the DFT-calculated binding energies and activation barriers on Pd(111) needed to obtain the O*-coverage solution are shown in Table S3. The Δ value for the binding energy of a surface species is equivalent to the difference between the DFT-derived Shomate parameter F for that species and its F parameter corresponding to the O*-coverage solution (Table S1). The Δ for the activation barrier of an elementary step is equivalent to the difference between the DFT-derived Shomate parameter F for that transition state and its F parameter corresponding to the O*-coverage solution, subtracting the change in the F parameter for the initial state of the elementary step (Table S1); for example, for step 5, there is a 0.06-eV increase in the transition-state F parameter for the O*-coverage solution with respect to the F parameter on clean Pd(111), and a 0.05-eV decrease in the F parameter for the initial state H₂O₂*—resulting in an overall adjustment in the activation barrier for step (5) of [+0.06 – (−0.05) = +0.11] eV.

Table S3.

Adjustments (“Δ”) to the DFT-calculated binding energies (BEs) and activation barriers (E_a) on clean Pd(111) needed to obtain the O*-coverage solution

Parameter	Pd(111), DFT, eV	O*-coverage solution, eV	Δ, eV
BE, H*	−2.70	−2.70	0.00
BE, O*	−3.64	−3.66	−0.02
BE, OH*	−2.03	−2.03	0.00
BE, OOH*	−0.94	−0.84	+0.10
BE, H2O*	−0.22	−0.22	0.00
BE, H2O2*	−0.32	−0.37	−0.05
BE, O2*	−0.50	−0.26	+0.24
Ea (5), H2O2* + * ↔ OH* + OH*	0.18	0.29	+0.11
Ea (6), OOH* + * ↔ O* + OH*	0.08	0.23	+0.15
Ea (7), O2* + * ↔ O* + O*	0.85	0.85	0.00
Ea (8), OH* + * ↔ O* + H*	1.02	1.02	0.00
Ea (9), H2O* + * ↔ OH* + H*	1.10	1.10	0.00
Ea (10), OOH* + * ↔ O2* + H*	0.59	0.59	0.00
Ea (11), H2O2* + * ↔ OOH* + H*	0.62	0.62	0.00
Ea (12), H2O* + O* ↔ OH* + OH*	0.33	0.33	0.00
Ea (13), H2O2* + O* ↔ OOH* + OH*	0.04	0.20	+0.16
Ea (14), H2O2* + OH* ↔ OOH* + H2O*	0.00	0.00	0.00
Ea (15), OOH* + O* ↔ O2* + OH*	0.00	0.17	+0.17†
Ea (16), OOH* + OH* ↔ O2* + H2O*	0.00	0.00	0.00
Ea (17), H2O2* + O2* ↔ OOH* + OOH*	0.20	0.20	0.00

Elementary step numbers (no.) are in reference to Table 2 of the main text. Activation barriers for steps 5–11 are with respect to infinitely separated reactants, whereas activation barriers for H-transfer steps 12–17 are in reference to the coadsorbed reactants. Boldface type indicates the BEs and E_a that needed adjustment from the clean Pd(111) DFT-calculated values to obtain the O*-coverage solution.

^†The adjustment Δ reported here only includes the change in transition-state energy for this step between the clean Pd(111) value and that for the O*-coverage solution, as the initial state of OOH* + O* was not treated as a separate coadsorbed state in the microkinetic model (described in caption of Table S1).

The maximum adjustment Δ of binding energies and activation barriers in Table S3 is a 0.24-eV destabilization of the binding energy of O₂* on Pd(111).

The adjustments (“Δ”) to the clean Pd(100) DFT-calculated binding energies and activation barriers (for elementary steps that carry the majority of reaction flux, as predicted by the OH*-coverage solution) needed to obtain the OH*-coverage solution are shown in Table S4. The Δ for the binding energy of a surface species is equivalent to the difference between the DFT-derived Shomate parameter F for that species and its F parameter corresponding to the OH*-coverage solution (Table S2). The Δ for the activation barrier of an elementary step is equivalent to the difference between the DFT-derived Shomate parameter F for that transition state and its F parameter corresponding to the OH*-coverage solution, subtracting the change in the F parameter for the initial state of the elementary step (Table S2); for example, for step 6, there is a 0.974-eV increase in the transition-state F parameter for the OH*-coverage solution with respect to the F parameter on clean Pd(100), and a 0.767-eV increase in the F parameter for the initial state OOH*—resulting in an overall adjustment in the activation barrier for step 6 of [+0.974 – (+0.767) = +0.21] eV from its value on clean Pd(100).

Table S4.

Adjustments (“Δ”) to the DFT-calculated binding energies (BEs) and activation barriers (E_a) on clean Pd(100) needed to obtain the OH*-coverage solution

Parameter	Clean Pd(100), DFT, eV	OH*-coverage solution, eV	Δ, eV	OH-modified Pd(100), DFT, eV
BE, H*	−2.74	−2.56	+0.18	−2.56
BE, O*	−3.90	−2.99	+0.91	−3.16
BE, OH*	−2.43	−1.83	+0.60	−1.68
BE, OOH*	−1.28	−0.51	+0.77	−0.61
BE, H2O*	−0.30	−0.32	−0.02	−0.26
BE, H2O2*	−0.36	−0.46	−0.10	−0.36
BE, O2*	−1.27	−0.14	+1.13	−0.14
Ea (6), OOH* + * ↔ O* + OH*	0.02	0.23	+0.21	0.41
Ea (12), H2O* + O* ↔ OH* + OH*	0.00	0.36	+0.36	0.41
Ea (14), H2O2* + OH* ↔ OOH* + H2O*	0.00	0.08	+0.08	0.00
Ea (15), OOH* + O* ↔ O2* + OH*	0.02	0.02	0.00†	0.00‡
Ea (16), OOH* + OH* ↔ O2* + H2O*	0.00	0.00	0.00	0.00

Only the steps that carry the majority of the reaction flux are shown, as predicted by the OH*-coverage solution. The last column shows the DFT values for the binding energies and activation barriers recalculated on Pd(100) modified with 0.5 ML of OH* spectators. Elementary step numbers (no.) are in reference to Table 2 of the main text. Activation barriers for H-transfer steps are in reference to the coadsorbed reactants.

^†The adjustment Δ reported here only includes the change in transition-state energy for this step between the clean Pd(111) value and that for the OH*-coverage solution, as the initial state of OOH* + O* was not treated as a separate coadsorbed state in the microkinetic model (described in caption of Table S2).

^‡Spontaneous in forward direction; transition state could not be isolated within the accuracy of our DFT parameters.

Adjustments Δ of binding energies on clean Pd(100) and those corresponding to the OH*-coverage solution are large (>0.5 eV for the binding energies of O*, OH*, O₂*, and OOH*). However, the OH*-coverage solution predicts a surface covered in 0.44–0.51 ML of hydroxyl over the range of experimental conditions studied, with the remainder of the surface essentially vacant (the next highest adsorbate coverage is <0.01 ML). Therefore, we recalculated these binding energies and activation barriers using DFT by including two OH* in the (2 × 2) unit cell for Pd(100) and allowing these OH* spectators to relax during calculations. The resulting binding energies and activation barriers are in agreement with the values from the OH*-coverage solution, as shown in Table S4 (maximum deviation is a 0.18-eV decrease in the activation barrier for O–O scission in OOH*).

Analysis of the Model-Predicted Apparent Activation Barrier

The contributions to the apparent activation barrier for the O*-coverage solution, which predicts a mostly vacant surface, can be extracted from the enthalpy surface in Fig. S1.

Fig. S1.

Enthalpy surface for adsorption and O–O bond scission in H₂O₂ corresponding to the O*-coverage solution parameters. The reference state is aqueous H₂O₂. The “|” separating two adsorbates denotes infinite separation from each other, “(g)” denotes a gas-phase species, “*” denotes a surface-adsorbed species, and “TS” denotes a transition state.

The van’t Hoff equation was used to estimate the enthalpy of H₂O₂ dissolution (−65.9 kJ/mol) from the experimental Henry’s law constant (90). The apparent activation barrier calculated in the microkinetic model can therefore be approximated by the sum of (i) the energy required to remove H₂O₂ from its aqueous solvation shell and bind it to the Pd surface; and (ii) the activation energy barrier for O–O bond scission in H₂O₂. Accordingly, the microkinetic model predicts that the activation barrier for O–O bond scission carries the highest degree of rate control compared with subsequent steps.