Defect-engineered nonstoichiometric perovskite hosting high-activity PdO sites for enhanced hydrocarbon oxidation

Domain: biology
Published: 2026-04-02
Editorial outcome: minor_revision

Abstract
Supported noble metal catalysts are central to industrial, environmental, and energy applications, yet precisely constructing active sites with optimized geometry remains a formidable challenge beyond conventional particle size control. Here, we introduce a perovskite-based surface defect engineering strategy that enables atomic-level regulation of noble metal active sites. By tailoring La stoichiometry in La AlO , La AlO , and La AlO , we engineer three distinct surface morphologies (planar, stepped, and crater-like) that serve as templates for anchoring and replicating supported PdO nanoparticles. Among these, the step-rich PdO configuration on La AlO exhibits the highest methane oxidation activity, with a linear correlation between Pd step-site density and catalytic performance. The enhancement arises from low-coordination Pd atoms at step sites, which form stable Pd–C(CH ) covalent bonds and facilitate C–H bond activation, the rate-determining step in methane oxidation. This work establishes a generalizable approach to precisely tailor noble metal active sites through perovskite surface engineering, providing a robust framework for the rational design of efficient and durable oxidation catalysts.

Introduction
Supported noble metal catalysts are central to industrial manufacturing, environmental protection, and energy conversion because of their unique surface chemistry and electronic properties.1-3 Catalyst supports are generally classified as inert (e.g., SiO , Al O ) or redox-active (e.g., CeZrO , Fe O , and perovskite oxides). While inert supports primarily provide mechanical stability and high surface area, redox-active supports can also participate directly in catalytic processes by storing and releasing lattice oxygen or by facilitating electron exchange with the metal or reactants.4-8 For the noble metal active phase, particularly in structure-sensitive reactions, parameters such as particle size, oxidation state, surface orientation, defect structure, and metal–support interaction critically influence both catalytic performance and stability.9-11 This complexity underscores the challenge and necessity of achieving rational catalyst design through precise control of metal–support interfaces.

Recent advances in wet-chemical synthesis have enabled the fabrication of metal nanoparticles with precisely controlled sizes, shapes, and surface orientations.12,13 However, once these nanoparticles are supported on oxide substrates and the structure-stabilizing ligands are removed during thermal treatments, they often undergo severe structural destabilization. Metal–support interactions (MSI) offer a promising route to modulate active-site properties: they can regulate metal dispersion, suppress sintering, and tailor the electronic structure of noble metals to enhance both catalytic activity and durability.9,14-16 Surface defect engineering of supports is a commonly employed strategy for modulating MSI, introducing controlled defects can strengthen metal–support interactions and create opportunities for tailoring the geometric and electronic structure of supported noble metals.2,17-19 However, increasing surface defect density often comes at the cost of structural stability of the support.

Perovskite oxides (ABO ), which consist of a rigid three-dimensional network of corner-sharing BO octahedra, exhibit exceptional structural tolerance over a wide range of compositions and distortions owing to the Goldschmidt tolerance factor.20,21 This inherent structural robustness makes them an ideal platform for precisely regulating the surface active sites of supported noble metals while maintaining support integrity. Previous studies have demonstrated that perovskite oxides can modulate the particle size, the electronic structure and redox behavior of the supported metals through tuning A- or B-site cation compositions or introducing lattice defects.22-27 Whereas, these approaches often involve the simultaneous variation of multiple parameters, making precise single-variable control difficult and thereby preventing the decoupling of the individual contributions of each factor to the overall catalytic performance. More importantly, compared with macroscopic descriptors such as particle size and oxidation state, probing and deliberately tailoring the atomic-scale microstructure of supported noble metal particles remain far more challenging. These bottlenecks hinder the rational design of catalysts with predictable performance and obscure the establishment of unambiguous structure–activity relationships.

Here, we employ LaAlO perovskite as a support, PdO as the active phase, and low-temperature methane oxidation as the probe reaction to demonstrate that precise control of the support’s defect density enables atomic-level control over supported PdO nanoparticles. Both experimental and density functional theory (DFT) approaches are combined to elucidate this relationship. From a theoretical perspective, systematic tuning of A-site stoichiometry was used to introduce controlled defects, yielding over 800 distinct defect structures. These defects were found to serve as anchoring and restructuring centers for PdO nanoparticles. Guided by these predictions, we synthesized perovskite supports with well-defined defect types, which generate strong metal–support interactions that stabilize step-rich PdO configurations. This stabilization enables precise structural control of the supported PdO. Collectively, our results establish a surface-defect engineering strategy for perovskite oxides that allows atomic-level regulation of noble-metal active sites. This generalizable approach provides a new pathway for the rational design of highly efficient and durable catalysts for alkane oxidation and potentially a broad range of oxidation reactions.

Results
Morphology tailoring of PdO on La-deficient LaAlO : DFT studies. A defect-engineering strategy was developed to control perovskite surface reconstructions and dictate the morphology of supported PdO clusters. To guide the subsequent catalyst synthesis, this strategy was first examined through DFT calculations. Previous studies have shown that in the LaAlO system (denoted La Al), the most stable exposed surface is the LaAlO (001) surface, with the LaO-terminated configuration exhibiting the highest stability (Supplementary Fig. 1).28

In this work, we constructed La-deficient LaAlO (001) surface models via theoretical calculations to generate La Al O (La AlO , denoted La Al) and La Al O (La AlO , denoted La Al) structures with controlled La deficiencies. Given the structural complexity of defective LaAlO surfaces, a genetic algorithm (GA)–assisted DFT approach was employed to identify thermodynamically favorable configurations. During the global structural optimization, formal oxidation states of +3, +3, and −2 were assigned to La, Al, and O, respectively. To improve computational efficiency, a La Al O slab was used as the substrate. For the La Al model, an overlayer of La Al O was introduced to enable full surface relaxation, while the La Al model employed a La Al O overlayer.

Based on the initial surface models, metastable and globally stable configurations of both La Al and La Al systems were explored using the Universal Structure Predictor: Evolutionary Xtallography (USPEX) code.29-31 This search generated approximately 800 candidate structures, providing insight into the structural evolution of La-deficient LaAlO surfaces. The ten most stable configurations were subsequently refined through high-accuracy DFT calculations (Fig. 1a).

The stoichiometric LaAlO (001) surface exhibits a smooth topology with stable LaO terminations. As the La content decreases from 1.0 to 0.8, progressive surface reconstructions emerge (Supplementary Figs. 2–3): the La Al surface relaxes across two atomic layers, forming a stepped morphology, while the La Al surface undergoes a deeper four-layer reconstruction that produces a pronounced crater-like topology. These results demonstrate that controlled La deficiency drives distinct surface reconstructions, which can then serve as structural templates for tailoring the morphology of supported metal nanoparticles during catalyst synthesis.

To verify this hypothesis, a three-layer PdO thin film was deposited on the La Al surfaces to emulate supported PdO clusters. The calculated results reveal that the PdO films adopt morphologies that closely mirror those of their underlying supports (Figs. 1b–d). On the stoichiometric La Al surface, PdO retains a nearly flat and ordered configuration (denoted Pd/La Al), exposing three-coordinated Pd (Pd ) and O (O ) sites. In contrast, PdO supported on La-deficient surfaces undergoes substantial reconstruction: on La Al, PdO forms a stepped morphology exposing Pd , Pd , O , and O sites, whereas on La Al, it develops a crater-like topology dominated by Pd , Pd , and O terminations.

These distinct coordination environments are expected to strongly influence the activity and selectivity of structure-sensitive alkane oxidation reactions. Furthermore, charge-density difference analysis (Supplementary Fig. 4) indicates progressively decreased electron transfer from the support to PdO with increasing La deficiency. In general, these findings demonstrate that defect engineering of La-deficient LaAlO surfaces provides a powerful strategy to tailor PdO cluster morphology, thereby establishing a robust theoretical foundation for the rational design of next-generation oxidation catalysts. In later sections, CH activation on these model surfaces will be further probed via DFT.

Defect-engineered Pd/La Al: Experimental investigations. Guided by the theoretical predictions, a series of La Al perovskite materials with varying La deficiencies were synthesized by precisely controlling the La content. X-ray diffraction (XRD) patterns (Supplementary Fig. 5) confirm the formation of the perovskite phase for all compositions.25,32 With increasing La deficiency, the diffraction peaks gradually decrease in intensity and shift toward lower 2θ angles, suggesting a reduction in crystallinity and lattice expansion associated with defect incorporation.26 All samples exhibit comparable specific surface areas (12–15 m2·g−1, Supplementary Table 1), indicating that the introduction of La vacancies exerts minimal influence on the overall textural properties. To determine the distribution of La defects, ICP and XPS were used to analyze the bulk and surface La and Al contents of the La Al support (Supplementary Table 2). The ICP results reveal that the overall La/Al ratios are consistent with the theoretical values, while the surface La/Al ratios measured by XPS are lower, suggesting that La defects are mainly concentrated on the surface of La Al. CO -TPD and NH -TPD measurements (Supplementary Fig. 6) further verify invariant acid-base characteristics of these perovskites, despite the presence of surface defects. Together, these results confirm that the La Al perovskites maintain comparable physicochemical characteristics, thereby providing an ideal platform to precisely tailor the architecture of supported Pd species and to systematically isolate the influence of Pd surface structure on catalytic behavior.

The Pd/La Al catalysts were prepared by incipient wetness impregnation of the La Al supports with an aqueous Pd(NO ) solution to achieve a nominal Pd loading of 1.0 wt.%, followed by calcination in air. Under these conditions, Pd is present predominantly as PdO nanoparticles. Inductively coupled plasma (ICP) analysis confirms an actual Pd loading of approximately 0.94 wt.% (Supplementary Table 1). Compared with the corresponding supports, the catalysts exhibit a slight reduction in specific surface area to approximately 10 m2·g−1 (Supplementary Table 1). Step-scan XRD patterns (Supplementary Fig. 7) reveal that all catalysts retained the characteristic diffraction features of the La Al supports, with no detectable PdO reflections, indicating that PdO species are highly dispersed on the support surface.

High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was used to characterize the dispersion and particle size of PdO nanoparticles (Figs. 2a–c), complemented by energy-dispersive X-ray spectroscopy (EDS) elemental mapping for accurate particle-size evaluation.33 The analyses reveal that PdO nanoparticles are uniformly distributed across all La Al supports, with sizes ranging from 4 to 12 nm and average diameters of 7.3, 7.1, and 7.0 nm for Pd/La Al, Pd/La Al, and Pd/La Al, respectively (Supplementary Fig. 8). The comparable particle sizes among these samples indicate that La stoichiometry exerts negligible influence on Pd nanoparticle growth under the applied synthesis conditions.

Aberration-corrected high-resolution scanning transmission electron microscopy (AC-STEM) provided direct visualization of the surface structures of PdO nanoparticles (Figs. 2d–f and Supplementary Figs. 9–11). In the Pd/La Al and Pd/La Al catalysts, most PdO particles displayed distinct lattice fringes corresponding to the PdO(101) and PdO(110) surfaces. PdO particles on La Al exhibited well-defined surface morphologies, consistent with growth governed by the Wulff construction.34,35 Those on La Al showed 1–2 atomic-layer steps, indicative of slight structural distortion. In contrast, PdO particles on La Al formed hemispherical aggregates with blurred lattice fringes, signifying reduced crystallinity.

These observations demonstrate that decreasing La stoichiometry progressively destabilizes the PdO lattice, thereby increasing surface disorder. Such disorder likely alters the distribution of edge and corner sites — structural motifs widely recognized as highly active for oxidation reactions. It is noteworthy that, although the experimentally observed PdO particles are significantly thicker than the three-layer PdO thin films modeled theoretically (Figs. 1b–d), the influence of support morphology remains remarkably consistent.

Following visualization of the PdO structural evolution, in situ CO-DRIFTS measurements were performed to obtain complementary insights into Pd surface structures (Figs. 2g–i). Prior to measurement, the catalysts were reduced in 5 vol.% H /N at a mild reduction temperature of 150 °C to preserve the morphological differences upon conversion to metallic Pd. Three characteristic CO adsorption regions were identified: linear CO at 2100–2050 cm−1 corresponding to Pd corner sites, bridging CO at 2000–1950 cm−1 associated with step sites, and threefold-hollow CO at 1950–1800 cm−1 attributed to Pd(111) terraces.36-38 Band integration (Supplementary Table 3) revealed that decreasing the La content from 1.0 to 0.8 led to a steady increase in linearly adsorbed CO and a decrease in threefold-hollow CO, indicating a higher proportion of corner sites and fewer extended Pd(111) terraces.

Under conventional particle-size effects, such trends are typically accompanied by a monotonic increase in bridging CO intensity due to a higher density of step edges.39,40 Unexpectedly, the bridging CO band here followed a volcano-type trend, peaking for Pd/La Al. This anomaly suggests that particle size alone cannot account for the observed Pd surface evolution. Instead, interactions between Pd species and the La-deficient perovskite support likely alter the electronic and geometric environments of surface Pd atoms, thereby regulating the balance among corner, step, and terrace sites. It should be noted, however, that the morphology of metallic Pd does not precisely replicate that of PdO, and thus the CO-DRIFTS results should be interpreted with this distinction in mind.

X-ray photoelectron spectroscopy (XPS) was used to determine the surface chemical state of Pd (Fig. 2j). The Pd 3d binding energy at 336.5–336.9 eV is characteristic of +2 oxidation state.41,42 The absence of signals below 336.0 eV indicates that metallic Pd is not present, confirming that Pd exists predominantly as PdO. The Pd K-edge XANES spectra (Fig. 2k) further support this assignment, although the white-line intensity in all catalysts is slightly weaker than that of bulk PdO.43,44 This attenuation is attributed to interfacial charge transfer between Pd and the La Al support, consistent with the theoretically predicted electronic redistribution at the Pd/La Al interface (Supplementary Fig. 4).

Extended X-ray absorption fine structure (EXAFS) analysis (Fig. 2l) revealed distinct Pd–O and Pd–Pd scattering paths, characteristic of PdO. Fitting of the coordination numbers (Supplementary Figs. 12–13 and Supplementary Table 4) showed a gradual decrease in the first-shell Pd–O coordination number (CN) with increasing La deficiency (CN = 3.9, 3.7, and 3.6, respectively, for x = 1.0, 0.9, and 0.8). This trend indicates slight destabilization of Pd–O bonding as defects accumulate and implies a stronger interfacial interaction between PdO and the defective La Al surfaces.

Low-temperature methane combustion over Pd/La Al catalysts. Methane combustion over supported PdO is a structure-sensitive reaction, in which activity strongly depends on the particle size and surface orientations of PdO.45,46 In the current work, the surface structure of PdO was tuned by varying the stoichiometry of the La Al supports, which is expected to directly influence the catalytic performance of Pd/ La Al catalysts. As shown in Fig. 3a, the light-off curves indeed reveal a pronounced dependence of catalytic activity on La stoichiometry. Among the three catalysts, Pd/La Al exhibited the highest activity, achieving 90% CH conversion (T ) at 365 °C, followed by Pd/La Al (T = 400 °C) and Pd/La Al (T = 420 °C). Kinetic measurements (inset of Fig. 3a and Supplementary Table 5) further confirmed this activity trend. The Pd/La Al catalyst showed the lowest apparent activation energy (E = 66.9 kJ·mol−1), indicating that CH activation and oxidation are energetically most favorable.47 Correspondingly, Pd/La Al exhibited the highest reaction rates and turnover frequencies (TOFs) for methane combustion at 300 °C (Supplementary Table 5). The enhanced activity of Pd/La Al persisted regardless of reductive pretreatment (5 vol.% H /N , 150 °C, 30 min) or variation of the CH /O ratio (1 vol.% CH , 2 vol.% O ; Supplementary Fig. 14). To contextualize its performance, the activity of Pd/La Al was compared with recently reported Pd-based catalysts using T and TOF as key metrics (Supplementary Table 6). Although direct comparison is complicated by differences in reaction conditions and experimental setups, Pd/La Al exhibits one of the most competitive catalytic activity among the evaluated catalysts.

The catalytic stability of the Pd/La Al catalysts, including durability in cyclic light-off tests and water tolerance, was systematically evaluated. During cyclic tests up to 500 °C (Supplementary Fig. 15a), Pd/La Al and Pd/La Al exhibited significant deactivation after the second cycle, with increases in T (the temperature for 50% CH conversion) of 33 °C and 23 °C, respectively, before stabilizing in the third cycle. In contrast, Pd/La Al showed only a modest 6 °C increase in T during the second cycle, and no significant decrease in activity was observed over the subsequent 10-cycle test (Supplementary Fig. 15b), indicating substantially enhanced durability.

The water tolerance of the catalysts was assessed by introducing 5 vol.% H O into the reaction stream (denoted Pd/La Al–W). Under these wet conditions (Supplementary Fig. 16), all catalysts experienced very clear H O inhibition, reflected by approximately 50 °C increases in their T values. This behavior is consistent with the well-known sensitivity of surface PdO species to water vapor.48-50

Stability tests at 380 °C (Fig. 3b) revealed that CH conversion remained nearly constant for Pd/La Al over the first 30 h, whereas Pd/La Al and Pd/La Al declined from 61% to 54%, 72% to 67%, respectively. Upon the addition of 5 vol.% H O, CH conversion for all catalysts decreased by approximately 25%, which is attributed to H O inhibition, and possible PdO deactivation, e.g., hydroxylation of the PdO surface.48,50 After returning to dry conditions, Pd/La Al rapidly recovered its initial conversion indicating H O inhibition alone; in contrast, the CH conversion for Pd/La Al and Pd/La Al only restored to 45% and 60%, respectively, suggesting combined H O inhibition and H O-induced PdO deactivation. Over the total reaction time of 100 h, Pd/La Al showed only a 5% loss in activity, confirming its high catalytic stability and enhanced resistance to H O.

To further evaluate the thermal durability of the catalysts, the fresh Pd/La Al catalysts were thermally aged at 600 °C and 700 °C for 2 h (Supplementary Fig. 17). After aging at 600 °C, the T values of Pd/La Al and Pd/La Al increased by only 8 °C and 6 °C, respectively, indicating largely preserved catalytic performance. In contrast, Pd/La Al showed a pronounced activity loss, with T increasing by 23 °C. When the aging temperature was raised to 700 °C, the T increases for Pd/La Al, Pd/La Al, and Pd/La Al were 25, 18, and 45 °C, respectively, reflecting more severe deactivation. Notably, Pd/La Al still exhibited the smallest T increase among the three catalysts at both aging temperatures. These findings confirm that Pd/La Al exhibits superior thermal stability relative to the other two catalysts.

Structural characterization revealed that varying the La stoichiometry in La Al does not significantly affect the oxidation state or particle size of supported PdO, but it markedly alters the surface microstructure of PdO. The methane oxidation turnover frequencies (TOF) correlate strongly with the fraction of step sites as a function of La stoichiometry (Supplementary Fig. 18), both peaking for the Pd/La Al catalyst. This trend indicates that a higher density of PdO step sites directly enhances methane combustion activity. Upon PdO reduction by H followed by CO titration, these step sites transform into metallic Pd sites that exhibit strong bridging CO adsorption (Figs. 2g–i).

To verify this relationship, all La Al supports were calcined at 1000 °C prior to Pd loading (denoted Pd/La Al(1000)). Interestingly, in this second catalyst series, Pd/La Al(1000) — rather than Pd/La Al(1000) — displayed the highest methane oxidation activity (Supplementary Fig. 19a). Subsequent CO-DRIFTS measurements after mild H reduction revealed that Pd/La Al(1000) exhibited the strongest bridging CO adsorption (Supplementary Fig. 19b). Consolidating the results from both catalyst series yields a robust linear correlation between the step-site fraction and TOF (Fig. 3c), confirming that PdO step sites act as decisive structural descriptors governing methane combustion activity.

To evaluate the generality of this support-induced strategy, pre-synthesized Pd nanoparticles (approximately 5 nm) prepared via wet-chemical route were loaded onto La Al (denoted as Pd NPs /La Al). As shown in Supplementary Fig. 20, neither catalytic activity nor surface structure of these Pd nanoparticles was affected by La deficiency in the supports. This observation indicates that the defect-induced modulation of PdO surface structures primarily occurs during the nucleation and growth of Pd species on the La Al surface. Furthermore, Pd/La Al catalysts exhibited consistent activity trends in the oxidation of other alkanes, including ethane, propane, n-butane, and n-hexane, with Pd/La Al consistently delivering the highest catalytic performance (Supplementary Fig. 21). This trend was further corroborated in propane oxidation over Pt/La Al catalysts prepared using the same strategy (Supplementary Fig. 22). These findings demonstrate that the proposed defect-engineering approach is broadly applicable across different noble metals and alkane substrates.

For the most active Pd/La Al catalyst, in situ CO-DRIFTS was again performed following methane oxidation under both dry and wet conditions, and after subsequent mild H /N reduction (Supplementary Fig. 23). The fraction of bridging CO remained nearly unchanged after 20 h of reaction at 500 °C in either atmosphere, demonstrating that PdO step sites remain structurally stable under the catalytic operating conditions. To further substantiate the durability of PdO step sites, CO-DRIFTS measurements were performed on fresh samples after thermal treatment at 600 °C and 700 °C for 2 h. The CO-DRIFTS spectra of Pd/La Al after thermal treatment (Supplementary Fig. 24) show a clear decrease in μ -CO bridging adsorption, accompanied by reduced linear CO adsorption and increased μ -CO adsorption, features indicative of particle agglomeration. Consistently, TEM images of Pd/La Al after calcination at 700 °C reveal PdO particle growth beyond 30 nm (Supplementary Fig. 25). Overall, these results demonstrate that the step sites remain structurally stable below 600 °C but undergo sintering and reconstruction at higher temperatures.

Reaction mechanism and the decisive role of PdO step sites in C–H activation. The activation of the first C–H bond is widely recognized as the rate-determining step in lean methane combustion over PdO, which proceeds via a Mars–van Krevelen (MvK) mechanism involving lattice oxygen participation.51,52 To gain direct insight into this process, CH temperature-programmed surface reaction (CH -TPSR) experiments (Fig. 3d) were performed. The profiles reveal methane consumption peaks at 262, 244, and 254 °C for Pd/La Al, Pd/La Al, and Pd/La Al, respectively, accompanied by concurrent CO formation. This trend closely mirrors the activity order observed in the light-off curves (Fig. 3a).

The corresponding H O and CO evolution signals (Supplementary Fig. 26) show that the H O peak appears approximately 5 °C higher than CO , indicating stronger H O adsorption and higher desorption temperatures. This observation partly explains the inhibitory effect of water vapor during catalysis. Trace amounts of CO were detected for Pd/La Al and Pd/La Al, but were absent for Pd/La Al, reflecting the better oxygen reactivity of the latter and its enhanced ability to sustain complete methane oxidation.

To further elucidate the mechanistic pathways of methane oxidation over Pd/La Al catalysts, density functional theory calculations were performed to investigate CH adsorption and activation on three-layer PdO thin films supported on La Al surfaces (x = 1.0, 0.9, and 0.8) (Supplementary Figs. 27a, 27d, and 27g). Although the experimentally observed PdO particles are much thicker, we have demonstrated above that the support morphology effect applies consistently to both model and real systems. Additionally, the C−H bond distances of CH before and after C−H bond dissociation were also compared to validate the rationality of the calculated transition states (Supplementary Table 7).

The calculated CH adsorption energies were –0.30 eV, –0.36 eV, and –0.28 eV for Pd/La Al, Pd/La Al, and Pd/La Al, respectively, indicating the strongest CH binding on the Pd/La Al surface. This enhanced adsorption is primarily attributed to the exposure of low-coordination Pd and O sites. Subsequently, the activation of the first C–H bond in methane was examined (Fig. 4a and Supplementary Fig. 27). On Pd/La Al, C–H cleavage requires overcoming an activation barrier of 0.79 eV (76.23 kJ·mol–1), with an exothermic ity of 0.47 eV. On Pd/La Al, the barrier increases to 1.12 eV (108.07 kJ·mol–1), with a reaction energy of –0.88 eV. The higher barrier on Pd/La Al arises from its crater-like surface morphology, where elongated Pd–O distances are less favorable for C–H bond dissociation despite the presence of low-coordination Pd sites. Notably, for Pd/La Al, the activation barrier is only 0.61 eV (58.86 kJ·mol–1), accompanied by an exothermicity of 0.94 eV, fully consistent with its superior experimental catalytic activity. The C–H bond activation energies obtained from DFT calculations are consistent in trend with the experimentally measured apparent activation energies (inset of Fig. 3a): 68.8, 66.9, and 72.8 kJ·mol–1 for Pd/La Al, Pd/La Al, and Pd/La Al, respectively.

To uncover the electronic origins of these activity differences, the density of states (DOS) was calculated for key intermediates in the heterolytic CH dissociation transition state, namely, the Pd–CH and O–H species, on the Pd/La Al surfaces (Fig. 4b–c). The results reveal that the O–H species formed during CH activation exhibit strong covalent character, with energy levels at –8.19 eV, primarily associated with O sites on the Pd/La Al surface. Furthermore, the Pd–C (CH ) bonds on Pd/La Al and Pd/La Al are predominantly ionic, whereas those on Pd/La Al display significantly greater covalent character and occur at lower energy levels. This feature correlates with the presence of low-coordination Pd sites, which facilitate more effective orbital overlap with adsorbed CH fragments.

From the above discussion, we can clear conclude that CH activation on Pd/La Al surfaces is highly sensitive to the local coordination and electronic structure of PdO clusters, features that are dictated by La-deficiency-induced surface templating of the La Al substrate. In particular, the La Al support can etch or template an optimal PdO structural motif. This motif is characterized by a high density of Pd /O site pairs and more suitable local Pd–O geometric parameters, which simultaneously enhance CH adsorption and markedly lower the first C–H bond cleavage barrier, leading to efficient methane conversion. This provides clear mechanistic validation of our strategy: by engineering La-deficient La Al surfaces with tailored morphologies, one can precisely construct high-activity PdO sites, thereby markedly enhancing hydrocarbon oxidation performance.

In summary, by combining the USPEX global optimization method with density functional theory (DFT), we precisely constructed well-defined surface defects (planar, stepped, and crater-like morphologies) on LaAlO supports through systematic tuning of La stoichiometry. These distinct defect structures act as structural templates, directing the anchoring and restructuring of supported PdO nanoparticles. Guided by theoretical predictions, perovskite materials with controlled defect types were successfully synthesized. The resulting defect sites generate strong metal–support interactions that stabilize step-rich PdO configurations, enabling precise structural control over PdO nanoparticles. Building on these insights, we propose a perovskite surface-defect engineering strategy for atomic-level regulation of noble-metal active sites. A quantitative linear correlation between step-site density and methane oxidation activity establishes the step site as a decisive structural descriptor. Moreover, DFT analysis reveals that the step-rich PdO/La Al configuration promotes C–H bond activation through the formation of stronger covalent O–H and Pd–C bonds at low-coordination Pd and O sites, directly linking atomic-scale geometry to catalytic performance. Overall, this work provides a general framework for the rational design of supported noble-metal catalysts with enhanced activity and stability.

Methods
Catalyst preparation

Synthesis of La Al : The perovskite La Al with different La stoichiometry (x = 1.0, 0.9 and 0.8) were synthesized by the citrate sol-gel method. 10, 9 and 8 mmol of La(NO ) ·6H O (A.R., Adamas-beta), 0.01 mol of Al(NO ) ·9H O (A.R., Sinopharm Chemical Reagent Co., Ltd.) and adequate amounts of citric acid (A.R., Sinopharm Chemical Reagent Co., Ltd.) were dissolved in 30 mL of deionized water, the molar ratio of citric acid to total metal cations was 1.1. Next, the solution was thoroughly stirred and evaporated at 80 °C to get a viscous hydrogel, which was subsequently dried at 110 °C overnight. The obtained spongiform solid was milled and then calcined at 800 °C in air for 3 h with a heating rate of 4 °C·min–1. The resulted samples were denoted as La Al. The actual La and Al contents of the La Al samples are presented in Supplementary Table 1.

In addition, a series of supports calcined at 1000 °C were also prepared for comparison, recorded as La Al(1000).

Synthesis of Pd/La Al and Pt/La Al: 1 wt.% Pd was loaded onto the La Al supports by the incipient wetness method. Specifically, 0.067 g of Pd(NO ) aqueous solution (0.15 g ·g–1, Heraeus) was first diluted into 2 mL deionized water to form a uniform solution. Then, the as-prepared solution was added into 1 g La Al support dropwise with stirring and ultrasonic treatment for 30 min to get a slurry. After standing at room temperature for 8 h, the slurry was transfer to an 80 °C oven to evaporate for 12 h, followed by calcinating in a muffle furnace at 500 °C for 3 h, with a ramp of 4 °C·min–1. The obtained samples were denoted as Pd/La Al. Likewise, Pd/La Al(1000) catalysts were synthesized using La Al(1000) as the support. The Pt/La Al catalysts were prepared using the same method, except that Pt(NO ) (0.149 g ·g–1) aqueous solution was employed as the precursor.

Synthesis of Pd nanoparticles (Pd NPs ): Pd nanoparticles with a size of approximately 5 nm were prepared using a colloidal chemical method reported in the literature.53 Typically, 75 mg of Pd(acac) was mixed with 15 mL of oleylamine (OAm) in a three-necked flask under a nitrogen atmosphere, and the resulting solution was heated to 60 °C within 10 min. Subsequently, 300 mg of borane tributylamine (BTB) dissolved in 4 mL of OAm was rapidly injected into the above Pd–OAm solution. The temperature was then raised to 90 °C at a ramp rate of 3 °C·min–1 and maintained for 1 h. After the solution was cooled to room temperature, 30 mL of anhydrous ethanol was added, and the resulting suspension was separated by centrifugation (8000 rpm, 8 min). Finally, the obtained Pd NPs were redispersed in n-hexane and stored in a low-temperature environment.

Synthesis of Pd /La Al: Typically, 1 g of La Al support powder was dispersed in 20 mL of n-hexane under magnetic stirring. An appropriate amount of the Pd NP dispersion in n-hexane was then added dropwise to the above mixture, and stirring was continued for 8 h. The resulting solid was collected by centrifugation and dried overnight in a vacuum oven at 60 °C. The dried sample was subsequently heat-treated at 700 °C for 30 s to remove the organic ligands from the nanoparticle surface, followed by calcination at 500 °C for 2 h to obtain the final Pd /La Al catalyst.

Catalysts characterization

The powder X-ray diffraction (XRD) patterns were collected on a Bruker D8 Focus diffractometer with Cu Kα radiation (λ=1.54056 Å) operated at 40 kV and 40 mA. The as-prepared supports were scanned within a region of 2θ from 10 to 80° (6 °/min) to analyse the phase structure. The catalysts were step scanned with the step size of 0.02°, for 1 s per step.

The actual La and Al contents of the La Al samples and Pd contents of the Pd/La Al catalysts were determined by inductively coupled plasma optical emission spectroscopy (ICP-OES) (Agilent 725).

The specific surface areas of the catalysts were determined by nitrogen adsorption at 77.4 K using a NOVA 4200e instrument. Prior to each measurement, the samples were vacuumed at 80 °C for 10 h.

Transmission electron microscopy (TEM) images were obtained on a JEOL 2100F electron microscope operated at 200 kV. The sample powder was dispersed in ethanol and then dropped to carbon films coated on copper mesh grids and dried in calm air.

The X-ray photoelectron spectroscopy (XPS) were obtained on a Thermo Scientific ESCALAB 250Xi spectrometer under an ultrahigh vacuum (6.7 × 10−8 Pa), employing Al Kα radiation (1486.6 eV) as excitation X-ray source. All binding energies (BE) were calibrated by the C 1s peak level at 284.6 eV.

The dispersion of Pd was tested by CO pulse on the same instrument as the O -TPD. 50 mg of catalyst was placed in a U-shaped quartz reactor and pretreated with 5 vol.% H /Ar at 300 °C for 30 min. After cooling to 25 °C in He flow (50 mL·min–1), 1 vol.% CO/He (50 mL·min–1) was injected into the sample cell every two minutes until CO signal was kept constant.

CH -TPSR experiment was carry out on the same instrument as the O -TPD. The catalysts (50 mg) were pretreated in 3 vol.% O /He (50 mL·min–1) at 400 °C for 40 min, and then cooled to room temperature and kept in the gas flow for 40 min. Finally, the catalyst was heated from 30 to 800 °C at a rate of 10 °C·min–1 in a flow of 1 vol.% CH /He (50 mL·min–1). The outlet gas was monitored by a mass spectrometer (HPR-20 QIC) and MS signals of CH (m/z = 15), CO (m/z = 44), H O (m/z = 16), CO (m/z = 18) and H (m/z = 2) were detected.

Temperature-programmed desorption of CO (CO -TPD) for the supports were also carried out on Micromeritics AutoChem II 2920. 100 mg of support was pretreated in He (40 mL·min–1) for 30 min at 400 °C, after the sample was cooled down to 30 °C, it was exposed in 10 vol.% CO /He (40 mL·min–1) at room temperature until reach a saturation state and subsequently purged for 30 min with He. Finally, the sample was heated to 800 °C in He (40 mL·min–1) with a rate of 10 °C·min–1, the MS signal of CO (m/z = 44) was recorded.

Temperature-programmed desorption of NH (NH -TPD) for the supports were carried out on a PX200 apparatus equipped with a (TCD). Firstly, 100 mg of the support was preheated at 450 °C in Ar flow (40 mL·min–1) for 1 h and cooled to 100 °C. Then, the samples were saturated with 5 vol.% NH /Ar (40 mL·min–1) for 40 min and then purged with Ar (40 mL·min–1) for 30 min. Finally, the samples were heated from 100 to 600 °C at a rate of 10 °C·min–1 in Ar (40 mL·min–1). The amount of desorbed NH was determined by a TCD.

In situ diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy of CO adsorbed on the catalysts were recorded on a Nicolet Nexus 670 FT-IR spectrometer equipped with a liquid-nitrogen-cooled HgCdTe (MCT) detector. The samples were pressed into the IR cell with a BaF window. Before the CO adsorption, the sample was reduced in 5% H /He at 150 °C for 30 min and then cooled to 30 °C in Ar. After the background spectra were recorded at 30 °C, Ar was replaced by the gas of 0.5% CO/Ar (50 mL·min–1), and the DRIFTS spectra of the adsorbed CO on the catalyst surface were collected by averaging 64 scans at a resolution of 8 cm−1.

X-ray absorption spectroscopy (XAS) measurements, including X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS), were performed at the Pd K-edge on beamline 14W1 of the Shanghai Synchrotron Radiation Facility, China. The storage ring was operated at an energy of 8.0 GeV with an average electron current below 99 mA. The acquired EXAFS data were extracted and processed following standard procedures using the ATHENA module implemented in the FEFIT software package.54

Computational methods

We used the genetic algorithm optimization method embedded in the Universal Structure Predictor Evolutionary Xtallography (USPEX) code to search for stable catalysts structures, which has been successfully applied for predicting stable structures of bulk crystals, nanoclusters, surface reconstruction, and polymers.29-31 As a global optimization method, the USPEX code uses four ways, namely, random, hereditary, mutation, and transmutation, to produce new structures, and the whole prediction usually requires hundreds or thousands of individual structure relaxations. In our calculations, mixed-metal oxide structures were modelled based on a slab surface model, with the entire surface layer taken into account in generating new structures.

In this work, all spin-polarized DFT calculations were carried out using the Vienna Ab initio Simulation Package (VASP 5.4.1).55 The projector augmented wave (PAW)56 method and the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA)57,58 were applied for geometry optimization, electronic structure, and energy calculations. The kinetic energy cut-off was set to 400 eV, and the k-point mesh of 1 × 1 × 1 suggested by previous studies was used for Brillouin-zone integrations. The force threshold for structural optimizations was 0.05 eV/Å, and a large vacuum region of 15 Å was used to eliminate interactions between neighboring layers.

The transition states (TSs) of surface reactions were located using a constrained optimization scheme59,60 and were verified when (i) all forces on the relaxed atoms vanished and (ii) the total energy was a maximum along the reaction coordinate and a minimum with respect to all other degrees of freedom61. The adsorption energy (E ) was defined as
E = –(E – E – E ) (1)
ads (adsorbate/slab) slab gas
where E is the calculated total energy of the slab model with adsorbate, while E and E are calculated energies of the clean surface and the gas phase adsorbate, respectively. Obviously, a positive E value indicates an exothermic adsorption process. The larger the E value, the stronger the binding between the adsorbate and the surface.

Activity test

The CH combustion was evaluated on a fixed-bed quartz reactor (i.d. = 6 mm). 0.1 g of catalyst (40-60 mesh) was mixed with 0.2 g of quartz sand to eliminate thermal effects. The gas mixture composed of 1 vol.% CH , 20 vol.% O , and 79 vol.% N (and 5 vol.% H O if used) flowed through catalyst bed. The total gas flow rate was 50 mL·min–1, corresponding to a weight hourly space velocity (WHSV) of 30,000 mL·g –1·h–1. The activity was test in the temperature range of 150-600 °C at a heating rate of 4 °C·min–1. Finally, the CH in the reaction gases was monitored on-line by a gas chromatograph (Agilent 7890A, USA) equipped with a flame ionization detector (FID).

Similarly, the C H combustion was performed in a U-shaped quartz tube (i.d. = 4 mm). 0.1 g of catalyst (40-60 mesh) was mixed with 0.2 g of quartz sand. The reaction mixture consisted of 0.2 vol.% C H , 2 vol.% O and 97.8 vol.% Ar with total flow rate of 50 mL·min−1, and the corresponding WHSV was 30,000 mL·g –1·h–1. The conversion of C H was measured after the catalytic reaction by an on-line gas chromatograph (GC-2060) that was equipped with a FID. In addition, the catalytic oxidation of other volatile organic compounds (1000 ppm), including ethane, n-butane and n-hexane, was evaluated under the same reaction conditions using air as the balance gas. For the tests involving n-hexane, the liquid reactants were injected into a vaporization chamber via a syringe pump prior to entering the reactor.

The conversion of CH or other reactants (𝑋 ) was calculated using the following equation:
𝑋 = (CHx)in−(CHx)out / (CHx)in × 100% (2)
where (CH ) and (CH ) express the CH or C H concentration in the inlet and outlet gas, respectively.

The CH reaction rate and TOF were calculated by the following equation:
𝑟 = (P∙𝑉CH4 ∙𝑋CH4) / (R𝑇∙𝑚cat∙𝑐Pd) (3)
TOF = (𝑟CH4 ∙𝑀Pd) / 𝐷Pd (4)
Where r is the reaction rate, P is the pressure of the reaction, 𝑉 is the volumetric flow rate of CH , 𝑋 is the conversion of methane, R is the universal gas constant (8.314 Pa·m3·mol−1·K−1), T is the room temperature, m is the mass of the catalyst in the bed, c is the content of Pd in the catalyst measured by ICP, M is the relative atomic mass of Pd (106.4 g·mol−1), D is the dispersion of the catalysts as measured by CO chemisorption.

The cyclic stability of the Pd/La Al samples were conducted by three reaction cycles under the same conditions. For each cycle, the temperature was increased from 200 to 500 °C and then cooled to 100 °C. The long-term stability with and without 5 vol.% H O was evaluated at 450 °C.

The kinetic data were measured under a WHSV of 100,000 mL·h–1·g –1 (30 mg of catalyst mixed with 0.2 g of quartz sand and 50 mL·min–1 of gas flow rate) at different temperature with the CH conversion below 10%, and the data were collected at steady state as determined by a stable CO production signal. The turnover frequency (TOF) was calculated on the basis of kinetic rates at 300 °C and the Pd dispersion calculated from CO chemisorption measurements.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a combined experimental and computational study on La-deficient LaAlO3 perovskite supports for the\ncontrolled growth of PdO nanoparticles and their application in methane oxidation. By tuning the La stoichiometry, they claim\nto modify the surface morphology and thereby the density of PdO step sites that promote C–H activation. The work combines\nDFT modeling with a set of characterization techniques and proposes a linear correlation between step-site density and\ncatalytic activity. Overall, the manuscript is technically sound, carefully executed, and clearly written. In particular, the\nperovskite-based surface defect engineering strategy is crucial for the development of heterogeneous catalysts with highly\ndispersed active sites for oxidation and combustion reactions. Therefore, I recommend the manuscript for publication in\nNature Communications after revision. Detailed comments are attached below.\nMajor Comments\n1. The concept of tuning PdO structure and reactivity via support defect engineering or surface reconstruction has already\nbeen explored in many previous studies. The current work is nicely executed but doesn’t introduce a fundamentally new\nidea or mechanistic insight. The authors should clearly explain what is new and different here compared to prior work on\nPdO/perovskite systems and “step-site” catalysis.\n2. A large part of the paper focuses on the correlation between PdO step sites and methane oxidation activity, but this\nrelationship has already been demonstrated (Angew. Chem. Int. Ed., 2017, 56, 15993). The authors need to better justify\nwhy revisiting this correlation adds new understanding, or what unique aspects the La-deficient support contributes.\n3. The DFT calculations use simplified three-layer PdO slabs and don’t directly link to the experimental TOF values. Effects\nsuch as particle size, strain, and the dynamic PdO–Pd transition (which are known to influence methane oxidation) are not\nconsidered. The DFT discussion would be more convincing if the authors could connect the computed barriers to\nexperimental kinetics or include some microkinetic interpretation.\n4. The central idea of “defect-engineered perovskite” needs more direct evidence. Right now, there’s no quantitative\nmeasurement of La deficiency or oxygen vacancy concentration. Some supporting analysis would make this part more\ncredible.\n5. The claim of “superior hydrocarbon oxidation” is overstated. The activity should be compared with recent literature under\nsimilar conditions. Because methane combustion is exothermic, the authors must ensure that the data are free from heat-\ntransfer effects. Also, stability and water-tolerance tests should not be done at very high conversions, since that makes it\nhard to compare true intrinsic activity.\n6. The long-term test (10 h at 450 °C) and three light-off cycles up to 500 °C are too short to support strong claims of stability\nor durability. I suggest extending the time-on-stream test to at least 100 h and including high-temperature aging tests (e.g.,\n800 °C). Post-reaction characterization would also strengthen the claims.\n7. The authors emphasize that the method is “generalizable,” but the study focuses solely on PdO/LaAlO3. To support this\nstatement, it would help to show at least a brief example or discussion involving another metal (Pt, Rh) or another reaction\n(such as CO or C3H8 oxidation).\nMinor Comments\n1. The synthesis method should be described more clearly, and the actual La and Al contents in the samples need to be\nclarified.\n2. The experimental section mentions propane (C3H8) oxidation, but there are no results in the main text—either include\nthem or remove the description.\n3. The abstract and conclusion somewhat overstate the generality and significance; these should be toned down.\n4. Update the references to include recent benchmark PdO works for a fairer performance comparison.", "reviewer_2": "The precise regulation of noble-metal active sites remains a long-standing challenge in heterogeneous catalysis. In this\nwork, Yu et al. propose a perovskite-based surface-defect engineering strategy that enables atomic-level regulation of PdO\nactive sites. By systematically tuning La stoichiometry in LaAlO3, three distinct surface morphologies are created and shown\nto act as structural templates for anchoring and replicating supported PdO nanoparticles. Among them, the step-rich PdO\nconfiguration stabilized on La0.9AlO3-δ exhibits the highest activity for methane oxidation, and a clear linear correlation\nbetween Pd step-site density and catalytic performance is established across the Pd/LaxAlO3-δ series. The enhanced\nactivity is convincingly attributed to low-coordination Pd atoms at step sites, which form stabilized Pd-C(CH3) species and\nfacilitate C-H bond activation. Overall, this study is innovative and provides valuable insights into noble-metal catalyst\ndesign. I therefore recommend publication after minor revision. The specific comments are listed below.\n1. The title refers to “hydrocarbon oxidation” whereas the catalytic evaluation presented in the manuscript is largely limited to\nmethane oxidation. It would be helpful if the authors could clarify this scope, or alternatively provide catalytic data for at least\none additional hydrocarbon to better support the generality implied by the title.\n2. The manuscript presents an interesting concept in which surface defects of the LaAlO₃ support regulate the exposure and\nstructure of PdO active sites. It would be informative to discuss whether a similar structural effect could be achieved by\ndepositing pre-synthesized Pd nanoparticles onto LaxAlO3-δ supports, and how this approach might differ from the in-situ\nreplication strategy proposed here.\n3. On page 7, the CO-DRIFTS spectra in Fig. 2g–i would benefit from clearer labeling. In particular, the peaks assigned to\nlinear CO adsorption on Pd corner sites should be explicitly marked on the corresponding spectra to improve readability.\n4. For completeness, the k3-weighted k-space EXAFS spectra and corresponding fitting curves for the reference samples\n(Pd foil and PdO) should also be included in Supplementary Fig. 13. In addition, key XAS measurement conditions should\nbe briefly summarized in the Catalyst Characterization section.\n5. The thermal stability of the proposed PdO “step sites” deserves further clarification. The current stability evaluation\nfocuses on long-term operation at 500 oC. It would be useful to comment on whether these step sites are expected to remain\nstructurally stable at higher temperatures, or under more severe thermal aging conditions relevant to practical applications.\n6. Based on the adsorption energy definition provided in the manuscript, a larger positive Eads corresponds to stronger\nadsorption. However, this sign convention may cause confusion, as exothermic adsorption is typically associated with\nnegative adsorption enthalpies (∆H < 0) according to IUPAC definitions. The authors are encouraged to revise the sign\nconvention or clarify the definition to avoid ambiguity.\n7. The constrained optimization scheme used to locate transition states for C-H bond activation may have limitations when\nmultiple bonds are simultaneously broken and formed. Additional discussion or validation would be helpful to support the\nreliability of the reported transition-state structures and energy barriers.\n8. As La content decreases, the manuscript shows a progressive reduction in electron transfer from the La2O3 component to\nPdO, while the highest methane oxidation activity is observed for the La0.9 system. Although the authors attribute this\nbehavior mainly to the stability of transition-state intermediates, further clarification would be valuable. In particular, beyond\nelectronic effects, the potential contribution of PdO morphological differences to methane activation should be more explicitly\ndiscussed."}, "author_response": "Responses to the comments:\nWe appreciate the comments from the reviewers and have made corrections based on these\nsuggestions. Point-by-point responses to the reviewer comments are listed below. In addition,\ncorrections to the manuscript are highlighted in Red so you can easily determine the changes\nthat were made.\nReviewer #1:\nThe authors present a combined experimental and computational study on La-deficient LaAlO3\nperovskite supports for the controlled growth of PdO nanoparticles and their application in\nmethane oxidation. By tuning the La stoichiometry, they claim to modify the surface\nmorphology and thereby the density of PdO step sites that promote C–H activation. The work\ncombines DFT modeling with a set of characterization techniques and proposes a linear\ncorrelation between step-site density and catalytic activity. Overall, the manuscript is\ntechnically sound, carefully executed, and clearly written. In particular, the perovskite-based\nsurface defect engineering strategy is crucial for the development of heterogeneous catalysts\nwith highly dispersed active sites for oxidation and combustion reactions. Therefore, I\nrecommend the manuscript for publication in Nature Communications after revision. Detailed\ncomments are attached below.\n1. The concept of tuning PdO structure and reactivity via support defect engineering or surface\nreconstruction has already been explored in many previous studies. The current work is nicely\nexecuted but doesn’t introduce a fundamentally new idea or mechanistic insight. The authors\nshould clearly explain what is new and different here compared to prior work on\nPdO/perovskite systems and “step-site” catalysis.\nResponse: We appreciate the reviewer’s thoughtful comment regarding the conceptual\nnovelty of this work. It is true that many previous studies have proposed the concept of\ntuning PdO structure and reactivity via support defect engineering or surface\nreconstruction. However, such regulation of noble metals often involves simultaneous\nchanges in multiple parameters, including particle size, valence state, and surface\nmicrostructure. For example, Murata et al. (Angew. Chem. Int. Ed., 2017, 56, 15993)\nsystematically tuned Pd loading and calcination temperature on Al O with different\n2 3\ncrystalline phases, producing PdO particles with distinct surface structures and revealing\na strong correlation between PdO step-site density and CH oxidation activity, which was\n4\nattributed to phase-dependent surface defects of Al O . While these studies provide\n2 3\nvaluable insights into structure–activity relationships, the concurrent evolution of multiple\nstructural descriptors makes it difficult to achieve precise single-variable regulation.\nIn this study, we propose a defect-induced surface templating strategy, which\nintroduces surface defects by adjusting the La content in LaAlO and then directionally\n3\nconstructs highly active step sites on PdO. Importantly, this approach selectively tailors\nthe surface structure of PdO while keeping its particle size and valence state unchanged.\nThis enables the precise design and optimization of noble metal surface structures\nindependently of other structural parameters.\nWe have supplemented the background and novelty for this study in the introduction\nsection of the revised manuscript.\nRevision: see Page 2 to Page 3\n……Surface defect engineering of supports is a commonly employed strategy for\nmodulating MSI, introducing controlled defects can strengthen metal–support interactions\nand create opportunities for tailoring the geometric and electronic structure of supported\nnoble metals.2,17-19 However, increasing surface defect density often comes at the cost of\nstructural stability of the support.\nPerovskite oxides (ABO ), which consist of a rigid three-dimensional network of\n3\ncorner-sharing BO octahedra, exhibit exceptional structural tolerance over a wide range\n6\nof compositions and distortions owing to the Goldschmidt tolerance factor.20,21 This\ninherent structural robustness makes them an ideal platform for precisely regulating the\nsurface active sites of supported noble metals while maintaining support integrity. Previous\nstudies have demonstrated that perovskite oxides can modulate the particle size, the\nelectronic structure and redox behavior of the supported metals through tuning A- or B-\nsite cation compositions or introducing lattice defects.22-27 Whereas, these approaches\noften involve the simultaneous variation of multiple parameters, making precise single-\nvariable control difficult and thereby preventing the decoupling of the individual\ncontributions of each factor to the overall catalytic performance. More importantly,\ncompared with macroscopic descriptors such as particle size and oxidation state, probing\nand deliberately tailoring the atomic-scale microstructure of supported noble metal\nparticles remain far more challenging. These bottlenecks hinder the rational design of\ncatalysts with predictable performance and obscure the establishment of unambiguous\nstructure–activity relationships.\n2. A large part of the paper focuses on the correlation between PdO step sites and methane\noxidation activity, but this relationship has already been demonstrated (Angew. Chem. Int. Ed.,\n2017, 56, 15993). The authors need to better justify why revisiting this correlation adds new\nunderstanding, or what unique aspects the La-deficient support contributes.\nResponse: The primary novelty of this work lies not in revalidating the correlation\nbetween PdO step sites and methane oxidation activity, but rather in proposing a defect-\ninduced surface templating strategy that directionally constructs highly active step sites on\nPdO while keeping its particle size and valence state unchanged. On the other hand,\nbecause the only varying parameter among the different catalysts is the surface structure\nof PdO, this approach enables a more accurate establishment of a linear dependence\nbetween the methane oxidation turnover frequency (TOF) and the proportion of PdO step\nsites—an observation consistent with literature reports. Furthermore, we performed DFT\ncalculations to elucidate the mechanistic role of step sites in C–H bond activation.\nSpecifically, the Pd and O atoms at the step sites form strong covalent bonds with the C\nand H atoms of CH , respectively, thereby conferring enhanced C–H bond activation\n4\ncapability. To the best of our knowledge, this direct bonding mechanism at PdO step sites\nhas not been previously reported.\nWe have also supplemented the introduction section of the revised manuscript with\nadditional explanations to further clarify the background and novelty.\nRevision: see Page 2 to Page 3\n……Surface defect engineering of supports is a commonly employed strategy for\nmodulating MSI, introducing controlled defects can strengthen metal–support interactions\nand create opportunities for tailoring the geometric and electronic structure of supported\nnoble metals.2,17-19 However, increasing surface defect density often comes at the cost of\nstructural stability of the support.\nPerovskite oxides (ABO ), which consist of a rigid three-dimensional network of\n3\ncorner-sharing BO octahedra, exhibit exceptional structural tolerance over a wide range\n6\nof compositions and distortions owing to the Goldschmidt tolerance factor.20,21 This\ninherent structural robustness makes them an ideal platform for precisely regulating the\nsurface active sites of supported noble metals while maintaining support integrity. Previous\nstudies have demonstrated that perovskite oxides can modulate the particle size, the\nelectronic structure and redox behavior of the supported metals through tuning A- or B-\nsite cation compositions or introducing lattice defects.22-27 Whereas, these approaches\noften involve the simultaneous variation of multiple parameters, making precise single-\nvariable control difficult and thereby preventing the decoupling of the individual\ncontributions of each factor to the overall catalytic performance. More importantly,\ncompared with macroscopic descriptors such as particle size and oxidation state, probing\nand deliberately tailoring the atomic-scale microstructure of supported noble metal\nparticles remain far more challenging. These bottlenecks hinder the rational design of\ncatalysts with predictable performance and obscure the establishment of unambiguous\nstructure–activity relationships.\n3. The DFT calculations use simplified three-layer PdO slabs and don’t directly link to the\nexperimental TOF values. Effects such as particle size, strain, and the dynamic PdO–Pd\ntransition (which are known to influence methane oxidation) are not considered. The DFT\ndiscussion would be more convincing if the authors could connect the computed barriers to\nexperimental kinetics or include some microkinetic interpretation.\nResponse: We sincerely appreciate the reviewer’s valuable comments. Regarding the\nmodel construction, in our original work we primarily employed USPEX algorithm to\nperform a global structural search. From more than 800 candidate configurations, we\nidentified the thermodynamically most stable LaAlO surface structures under different\nthe most probable stable structures from a thermodynamic perspective.\nTo more clearly illustrate the theoretical modulation effect of LaAlO with varying\ntypically confined to the top few atomic layers (deeper structures have limited influence\non surface reaction energy barriers), we adopted a three-layer PdO slab as a compromise\nand commonly used surface model to represent the primary surface structure and reaction\ncharacteristics of PdO.\nFurthermore, we agree with the reviewer’s point that the dynamic PdO–Pd transition\nmay influence CH oxidation behavior. According to our theoretical calculations and\n4\nrelated experimental characterizations, PdO is the key active phase in the catalytic\noxidation of CH . Although PdO may be locally reduced to metallic Pd during CH\n4 4\noxidation, the reaction atmosphere still contains a high partial pressure of O , which can\n2\nrapidly re-oxidize the reduced Pd back to PdO, thereby maintaining/restoring the active\nphase and allowing it to participate in subsequent reaction cycles.\nTo more directly link the computational results with experimental kinetics, we further\ncompared the energy barriers of key steps with the experimental apparent activation\nenergies. Theoretical calculations show that the activation energy barriers for CH\n4\ndissociation on Pd/La Al surfaces are 108.07, 58.86, and 76.23 kJ·mol–1, respectively; this\nx\ntrend is consistent with the experimentally measured apparent activation energies (72.8,\n66.9, and 68.8 kJ·mol–1, respectively), thereby supporting our conclusion that “different\nLa defects influence methane activation by modulating the surface reaction energy barriers\nof PdO.” However, it should be noted that TOF depends not only on the intrinsic energy\nbarrier of a single step, but also on factors such as surface active site density, coverage of\nkey intermediates/reactants, and the size, strain, and phase transition kinetics of real\nparticles. Given that this study employs a relatively simplified slab model and lacks a\nrigorous description of site statistics and coverage, it is currently challenging to\nquantitatively correlate the computed “intrinsic reaction energy barriers/trends” with\nexperimental TOF values on a one-to-one basis.\nRevision: see Page 16\nOn Pd/La Al, C–H cleavage requires overcoming an activation barrier of 0.79 eV\n1.0\n(76.23 kJ·mol–1), with an exothermicity of 0.47 eV. On Pd/La Al, the barrier increases to\n0.8\n1.12 eV (108.07 kJ·mol–1), with a reaction energy of –0.88 eV. The higher barrier on\nPd/La Al arises from its crater-like surface morphology, where elongated Pd–O distances\n0.8\nare less favorable for C–H bond dissociation despite the presence of low-coordination Pd\nsites. Notably, for Pd/La Al, the activation barrier is only 0.61 eV (58.86 kJ·mol–1),\n0.9\naccompanied by an exothermicity of 0.94 eV, fully consistent with its superior\nexperimental catalytic activity. The C–H bond activation energies obtained from DFT\ncalculations are consistent in trend with the experimentally measured apparent activation\nenergies (inset of Figure 3a): 68.8, 66.9, and 72.8 kJ·mol–1 for Pd/La Al, Pd/La Al, and\n1.0 0.9\nPd/La Al, respectively.\n0.8\n4. The central idea of “defect-engineered perovskite” needs more direct evidence. Right now,\nthere’s no quantitative measurement of La deficiency or oxygen vacancy concentration. Some\nsupporting analysis would make this part more credible.\nResponse: We have performed supplementary quantitative analysis of La deficiency,\nincluding ICP and XPS measurements of La Al. The results are summarized in Table R1.\nx\nThe ICP results show that the overall La/Al ratios of La Al are close to the theoretical\nx\nvalues, whereas the La/Al ratios on the catalyst surface obtained from XPS are lower than\nthe theoretical values, indicating that La defects are mainly enriched at the surface of La Al.\nx\nIn addition, we attempted to characterize both the atomic-scale structure and La\ndeficiency of the support surface using high-resolution electron microscopy. However,\nbecause the support was prepared via a sol–gel method, its surface flatness is relatively\npoor, which made it difficult to obtain reliable and clear atomic-resolution images.\nTherefore, these results are not presented here.\nTable R1. La/Al ratios in the bulk and on the surface of La Al determined by ICP and XPS\nx\nICP (atomic, %) XPS (atomic, %)\nSamples\nLa Al La/Al La Al La/Al\nLa Al 18.3 18.4 99.6 17.9 20.4 88.2\n1.0\nLa Al 17.1 19.7 86.9 15.3 21.6 70.7\n0.9\nLa Al 15.7 20.0 78.7 13.3 22.9 58.2\n0.8\nRevision: see Page 7\n……To determine the distribution of La defects, ICP and XPS were used to analyze\nthe bulk and surface La and Al contents of the La Al support (Supplementary Table 2).\nx\nThe ICP results reveal that the overall La/Al ratios are consistent with the theoretical values,\nwhile the surface La/Al ratios measured by XPS are lower, suggesting that La defects are\nmainly concentrated on the surface of La Al.\nx\n5. The claim of “superior hydrocarbon oxidation” is overstated. The activity should be\ncompared with recent literature under similar conditions. Because methane combustion is\nexothermic, the authors must ensure that the data are free from heat-transfer effects. Also,\nstability and water-tolerance tests should not be done at very high conversions, since that\nmakes it hard to compare true intrinsic activity.\nResponse: We agree that the original phrasing was overstated. Accordingly, we have\nrevised the relevant statements throughout the manuscript to avoid exaggeration and to\nmore accurately reflect the performance of our catalyst. A comparative summary of the\ncatalytic activity of Pd/La AlO with representative Pd-based catalysts reported in recent\n0.9 3\nliterature is now provided in Table R2. Although direct comparison is complicated by\ndifferences in testing conditions, our catalyst exhibits competitive catalytic activity under\nthe evaluated conditions.\nTo address potential heat-transfer effects, we would like to clarify that this aspect was\nalready considered during the catalytic testing. Specifically, 0.1 g of catalyst (40–60 mesh)\nwas mixed with 0.2 g of quartz sand to effectively eliminate thermal effects in both activity\nand kinetic measurements. This information has now been explicitly stated in the revised\nmanuscript to ensure clarity.\nWe have re-evaluated the stability and water resistance at a lower temperature (380 °C)\nto achieve a conversion level of ~90%, thereby better reflecting the intrinsic catalyst\nperformance. As shown in Figure R1, CH conversion remained nearly constant for\n0.9 0.8 1.0\n54%, 72% to 67%, respectively. Upon the addition of 5 vol.% H O, CH conversion for all\n2 4\ncatalysts decreased by approximately 25%, which is attributed to H O inhibition, and\n2\npossible PdO deactivation, e.g., hydroxylation of the PdO surface.43,45 After returning to\ndry conditions, Pd/La Al rapidly recovered its initial conversion indicating H O\n0.9 2\ninhibition alone; in contrast, the conversion of Pd/La Al and Pd/La Al displayed much\n1.0 0.8\nslower activity recovery and can only restored to 45% and 60%, respectively, suggesting\ncombined H O inhibition and H O-induced PdO deactivation. Over the total reaction time\n2 2\nof 100 h, Pd/La Al showed only a 5% loss in activity, confirming its high catalytic\n0.9\nstability and enhanced resistance to H O.\nFig. 14. Corresponding discussion has also been added to the revised manuscript.\nTable R2. Comparison of the activity of the Pd/La Al catalysts for CH oxidation with Pd based catalysts\n0.9 4\nreported in the literatures\nSpace T 50 TOF Test\nCatalysts The feed gas Reference\nvelocity (°C) (10-3, s-1) Temp. (°C)\n30,000\n1% CH , 20%\nPd/La Al 4 ml·g - 307 30.4 300 This work\n0.9 cat\nO\n2 1·h-1\n1% CH , 4%\nO\n2\n200,000\n0.5% CH ,\n2\n/H-Al\n3\nml·g\ncat\n- ~225 47 250 [2]\n2% O\n2\n1·h-1\n120,000\n0.2% CH ,\n4\n2.1 nm Pd/γ-Al O ml·g - 350 7.4 320 [3]\n2 3 cat\n0.4% O\n2\n1·h-1\nPd/CeO (HHA) 1% CH , 15000 ~300 37.3 300 [4]\n2 4\n20%O ml·g -\n2 cat\n1·h-1\n40 000\n0.5% CH ,\n2 3 Pd\n2.0% O\n2\n1\n36,000\n1% CH , 21%\ncat\nO\n2\n1·h-1\n60000\n0.5% CH ,\n4\n1Pd/ceria-800* ml·g - 420 1.7 300 [7]\ncat\n2.5% O\n2\n1·h-1\n60000\n2% CH , 8%\nPd/Al2O3-x\n4\nml·g\ncat\n- 320 [8]\nO in N\n2 2\n1·h-1\n18000\n1% CH ,\n2 cat\n21 % O\n2\n1·h-1\n680 ppm 300\n1Pd/2Pt@CeO CH , 14% O , L·g - 330 3.27 [10]\n2 4 2 cat\n5% CO 1·h-1\n4 4\n20 vol.% O , 5 vol.% H O (when applied), balanced with N ; WHSV = 30,000 mL·g −1·h−1.\n2 2 2 cat\nRevision:\n(1) see Page 11\n……To contextualize its performance, the activity of Pd/La Al was compared with\n0.9\nrecently reported Pd-based catalysts using T and TOF as key metrics (Supplementary\nand experimental setups, Pd/La Al exhibits one of the most competitive catalytic activity\n0.9\namong the evaluated catalysts.\n(2) see Page 23\n……The CH combustion was evaluated on a fixed-bed quartz reactor (i.d. = 6 mm).\n4\n0.1 g of catalyst (40-60 mesh) was mixed with 0.2 g of quartz sand to eliminate thermal\neffects.\n(3) see Page 13\n……Stability tests at 380 °C (Fig. 3b) revealed that CH conversion remained nearly\n4\nconstant for Pd/La Al over the first 30 h, whereas Pd/La Al and Pd/La Al declined\n0.9 0.8 1.0\nfrom 61% to 54%, 72% to 67%, respectively. Upon the addition of 5 vol.% H O, CH\n2 4\nconversion for all catalysts decreased by approximately 25%, which is attributed to H O\n2\ninhibition, and possible PdO deactivation, e.g., hydroxylation of the PdO surface.43,45 After\nreturning to dry conditions, Pd/La Al rapidly recovered its initial conversion indicating\n0.9\nH O inhibition alone; in contrast, the CH conversion for Pd/La Al and Pd/La Al only\n2 4 1.0 0.8\nrestored to 45% and 60%, respectively, suggesting combined H O inhibition and H O-\n2 2\ninduced PdO deactivation. Over the total reaction time of 100 h, Pd/La Al showed only\n0.9\na 5% loss in activity, confirming its high catalytic stability and enhanced resistance to H O.\n2\n6. The long-term test (10 h at 450 °C) and three light-off cycles up to 500 °C are too short to\nsupport strong claims of stability or durability. I suggest extending the time-on-stream test to\nat least 100 h and including high-temperature aging tests (e.g., 800 °C). Post-reaction\ncharacterization would also strengthen the claims.\nResponse: We thank the reviewer for the constructive suggestions. In response, we have\nsignificantly extended the stability evaluation and included additional thermal aging tests\nto better substantiate the durability claims.\nStability and water resistance tests were conducted on the Pd/La Al catalysts at\nx\n380 °C, and the time-on-stream was extended to 100 h (Figure R1). Over this entire period,\nPd/La Al exhibited only a 5% loss in activity. For comparison, Pd/La Al and Pd/La Al\n0.9 0.8 1.0\nwere re-evaluated under identical conditions; however, their activities declined by about\n8% and 5%, respectively, within the first 30 h. Owing to their inferior stability, full 100 h\ntests were not pursued for these samples. These results have been updated in Figure 3b of\nthe main text.\nIn addition, ten consecutive light-off cycles were performed on Pd/La Al up to\n0.9\n500 °C (Figure R2). The activity remained essentially unchanged throughout the cycles,\ndemonstrating good cyclic stability. These data have been included as Supplementary Fig.\nS15.\nTo further assess thermal durability of the catalysts, the fresh Pd/La Al catalysts were\nx\nthermally aged at 600 °C and 700 °C for 2 h (Figure R3). After aging at 600 °C, the T\n90\nvalues of Pd/La Al and Pd/La Al increased by only 8 °C and 6 °C, respectively,\n0.8 0.9\nindicating largely preserved catalytic performance. In contrast, Pd/La Al showed a\n1.0\npronounced activity loss, with T increasing by 23 °C. When the aging temperature was\n90\nraised to 700 °C, the T increases for Pd/La Al, Pd/La Al, and Pd/La Al were 25, 18,\n90 0.8 0.9 1.0\nand 45 °C, respectively, reflecting more severe deactivation. Notably, Pd/La Al still\n0.9\nexhibited the smallest T increase among the three catalysts at both aging temperatures.\n0.9\nother two catalysts.\nFigure R2. (a) The three-cycle activity tests of Pd/La Al, and (b) ten-cycle activity tests for Pd/La Al.\nx 0.9\nReaction conditions: 1 vol.% CH + 20 vol.% O + N , WHSV = 30,000 mL·g-1·h-1.\n4 2 2\nFigure R3. (a-c) Light-off curves of the catalysts after calcination at 600 and 700 °C, and (d) the\ncorresponding increase in T relative to the fresh catalysts.\ncharacterization to further substantiate the durability claims. In fact, we have already\nperformed in situ CO-DRIFTS measurements on the most active Pd/La Al catalyst after\n0.9\nmethane oxidation under both dry and wet atmospheres, as well as after subsequent mild\nH /N reduction, and these results are presented in Supplementary Fig. 23. The fraction\n2 2\nof bridging CO (a signature of step sites) remained nearly unchanged after 20 h of reaction\nat 500 °C in either condition, demonstrating that the PdO step sites are structurally stable\nunder catalytic operating conditions.\nTo further substantiate the durability claims, we further performed CO-DRIFTS\nmeasurements of the fresh samples after thermal treatment at 600 °C and 700 °C for 2 h.\nAs shown in Figure R4, as the aging temperature increased, the intensity of linearly\nadsorbed CO bands gradually decreased, while the relative contribution of CO adsorption\non hollow sites increased, due to sintering of Pd species. STEM images of Pd/La Al after\n0.9\ncalcination at 700 °C further showed that PdO particles had grown to sizes exceeding 30\nnm (Figure R5). These results indicate that Pd/La Al exhibits thermal stability below\n0.9\n600 °C; however, under more extreme conditions, aggregation and growth of Pd species\nremain unavoidable. The corresponding discussion has been added to the revised\nmanuscript.\nAll corresponding revisions have been incorporated into the main text and\nSupplementary Information.\nFigure R4. CO-DRIFT spectra of the fresh Pd/La Al samples after thermal treatment at 600 and 700 °C\nx\nfor 2h.\nFigure R5. HAADF-STEM image and corresponding EDS mapping of Pd for the fresh Pd/La Al catalyst\n0.9\nafter thermal treatment at 700 °C for 2h.\nRevision:\n(1) see Page 13\n……Stability tests at 380 °C (Fig. 3b) revealed that CH conversion remained nearly\n4\nconstant for Pd/La Al over the first 30 h, whereas Pd/La Al and Pd/La Al declined\n0.9 0.8 1.0\nfrom 61% to 54%, 72% to 67%, respectively. Upon the addition of 5 vol.% H O, CH\n2 4\nconversion for all catalysts decreased by approximately 25%, which is attributed to H O\n2\ninhibition, and possible PdO deactivation, e.g., hydroxylation of the PdO surface.43,45 After\nreturning to dry conditions, Pd/La Al rapidly recovered its initial conversion indicating\n0.9\nH O inhibition alone; in contrast, the CH conversion for Pd/La Al and Pd/La Al only\n2 4 1.0 0.8\nrestored to 45% and 60%, respectively, suggesting combined H O inhibition and H O-\n2 2\ninduced PdO deactivation. Over the total reaction time of 100 h, Pd/La Al showed only\n0.9\na 5% loss in activity, confirming its high catalytic stability and enhanced resistance to H O.\n2\n(2) see Page 12\n……In contrast, Pd/La Al showed only a modest 6 °C increase in T during the second\n0.9 50\ncycle, and no significant decrease in activity was observed over the subsequent 10-cycle\ntest (Supplementary Fig. 15b), indicating substantially enhanced durability.\n(3) see Page 13\n……To further evaluate the thermal durability of the catalysts, the fresh Pd/La Al catalysts\nx\nwere thermally aged at 600 °C and 700 °C for 2 h (Supplementary Fig.17). After aging\nat 600 °C, the T values of Pd/La Al and Pd/La Al increased by only 8 °C and 6 °C,\n90 0.8 0.9\nrespectively, indicating largely preserved catalytic performance. In contrast, Pd/La Al\n1.0\nshowed a pronounced activity loss, with T increasing by 23 °C. When the aging\n90\ntemperature was raised to 700 °C, the T increases for Pd/La Al, Pd/La Al, and\n90 0.8 0.9\nPd/La Al were 25, 18, and 45 °C, respectively, reflecting more severe deactivation.\n1.0\nNotably, Pd/La Al still exhibited the smallest T increase among the three catalysts at\n0.9 90\nboth aging temperatures. These findings confirm that Pd/La Al exhibits superior thermal\n0.9\nstability relative to the other two catalysts.\n(4) see Page 15\n……To further substantiate the durability of PdO step sites, CO-DRIFTS measurements\nwere performed on fresh samples after thermal treatment at 600 °C and 700 °C for 2 h.\nThe CO-DRIFTS spectra of Pd/La Al after thermal treatment (Supplementary Fig. 24)\n0.9\nshow a clear decrease in μ -CO bridging adsorption, accompanied by reduced linear CO\n2\nadsorption and increased μ -CO adsorption, features indicative of particle agglomeration.\n0.9\ngrowth beyond 30 nm (Supplementary Fig. 25). Overall, these results demonstrate that\nthe step sites remain structurally stable below 600 °C but undergo sintering and\nreconstruction at higher temperatures.\n7. The authors emphasize that the method is “generalizable,” but the study focuses solely on\nPdO/LaAlO . To support this statement, it would help to show at least a brief example or\n3\ndiscussion involving another metal (Pt, Rh) or another reaction (such as CO or C H oxidation).\n3 8\nResponse: To demonstrate the generalizability of our proposed strategy, we have\nextended the investigation in two directions.\nFirst, we evaluated the catalytic performance of Pd/La Al catalysts toward the oxidation\nx\nof other alkanes, including ethane, propane, n-butane, and n-hexane. As shown in Figure R6,\nthe activity trend across these alkanes remains consistent with that observed for methane\noxidation, with Pd/La Al consistently exhibiting the highest catalytic activity.\n0.9\nSecond, to assess the extensibility of the support design to other noble metals, we loaded\nPt onto La Al and La Al(1000) using the same preparation method and evaluated their\nx x\nperformance in propane oxidation. As shown in Figure R7, the resulting activity trend closely\nresembles that observed for Pd/La Al and Pd/La Al(1000) in methane oxidation.\nx x\nCollectively, these results indicate that the defect-induced surface templating strategy\noffers a certain degree of generality and can be extended to other alkane substrates and noble\nmetal catalysts.\nRelevant discussions have been added to the revised manuscript.\nFigure R6. The light-off curves of the Pd/La Al catalysts for the oxidation of (a) ethane, (b) propane, (c)\nx\nn-butane and (d) n-hexane.\nFigure R7. The light-off curves of the Pt/La Al catalysts for C H oxidation.\nx 3 8\nRevision: see Page 14\nTo evaluate the generality of this support-induced strategy,……Furthermore, Pd/La Al\nx\ncatalysts exhibited consistent activity trends in the oxidation of other alkanes, including\nethane, propane, n-butane, and n-hexane, with Pd/La Al consistently delivering the\n0.9\nhighest catalytic performance (Supplementary Fig. 21). This trend was further\ncorroborated in propane oxidation over Pt/La Al catalysts prepared using the same strategy\nx\n(Supplementary Fig. 22). These findings demonstrate that the proposed defect-\nengineering approach is broadly applicable across different noble metals and alkane\nsubstrates.\nMinor Comments\n1. The synthesis method should be described more clearly, and the actual La and Al contents\nin the samples need to be clarified.\nResponse: The experimental section has been supplemented to provide more detailed\ninformation. The actual La and Al contents in the supports were determined by ICP, and\nthe results are presented in Table R1.\n2. The experimental section mentions propane (C H ) oxidation, but there are no results in the\n3 8\nmain text—either include them or remove the description.\nResponse: We have now included the results of propane oxidation over Pd/La Al and\nx\nPt/La Al catalysts in the main text (as shown in Figure R6) to support the generality of\nx\nour strategy. Corresponding descriptions have also been added in the revised manuscript\n(Supplementary Fig. 15).\n3. The abstract and conclusion somewhat overstate the generality and significance; these\nshould be toned down.\nResponse: We conducted a series of supplementary experiments to substantiate the\ngeneralizability of the proposed strategy. These included the catalytic oxidation of ethane,\npropane, n-butane, and n-hexane over Pd/La Al catalysts, as well as propane oxidation\nx\nover Pt/La Al catalysts. In all cases, catalysts supported on La Al consistently exhibited\nx 0.9\nthe highest activity, demonstrating a certain degree of extensibility across different alkane\nsubstrates and noble metals. In addition, we have revised the manuscript to tone down the\nclaims regarding catalytic activity, stability, and generality, ensuring they more accurately\nreflect the scope of this work.\nRevision:\n(1) The title of “Defect-Engineered Nonstoichiometric Perovskite Hosting High-\nActivity PdO Sites for Superior Hydrocarbon Oxidation” was revised to “Defect-\nEngineered Nonstoichiometric Perovskite Hosting High-Activity PdO Sites for Enhanced\nHydrocarbon Oxidation”.\n(2) We delete the description of “Extending perovskite defect engineering to other\nsystems may open new avenues for selective oxidation, hydrogenation, and energy-\nconversion catalysis, where precise control of active-site structure is crucial” in the\nconclusion.\n4. Update the references to include recent benchmark PdO works for a fairer performance\ncomparison.\nResponse: We have supplemented a performance comparison between the Pd/La Al\n0.9\ncatalyst and recently reported Pd-based catalysts from the literature. The results are\nsummarized in Table R2.\nReviewer #2:\nThe precise regulation of noble-metal active sites remains a long-standing challenge in\nheterogeneous catalysis. In this work, Yu et al. propose a perovskite-based surface-defect\nengineering strategy that enables atomic-level regulation of PdO active sites. By systematically\ntuning La stoichiometry in LaAlO , three distinct surface morphologies are created and shown\n3\nto act as structural templates for anchoring and replicating supported PdO nanoparticles.\nAmong them, the step-rich PdO configuration stabilized on La AlO exhibits the highest\n0.9 3-δ\nactivity for methane oxidation, and a clear linear correlation between Pd step-site density and\ncatalytic performance is established across the Pd/La AlO series. The enhanced activity is\nx 3-δ\nconvincingly attributed to low-coordination Pd atoms at step sites, which form stabilized Pd-\nC(CH ) species and facilitate C-H bond activation. Overall, this study is innovative and\n3\nprovides valuable insights into noble-metal catalyst design. I therefore recommend publication\nafter minor revision. The specific comments are listed below.\n1. The title refers to “hydrocarbon oxidation” whereas the catalytic evaluation presented in\nthe manuscript is largely limited to methane oxidation. It would be helpful if the authors could\nclarify this scope, or alternatively provide catalytic data for at least one additional\nhydrocarbon to better support the generality implied by the title.\nResponse: To demonstrate the generalizability of our proposed strategy, we evaluated the\ncatalytic performance of Pd/La Al catalysts toward the oxidation of other alkanes,\nx\nincluding ethane, propane, n-butane, and n-hexane. As shown in Figure R6, the activity\ntrend across these alkanes remains consistent with that observed for methane oxidation,\nwith Pd/La Al consistently exhibiting the highest catalytic activity.\n0.9\nRelevant discussions have been added to the revised manuscript.\nFigure R6. The light-off curves of the Pd/La Al catalysts for the oxidation of (a) ethane, (b) propane, (c)\nx\nn-butane and (d) n-hexane.\nRevision: see Page 14\n……Furthermore, Pd/La Al catalysts exhibited consistent activity trends in the\nx\noxidation of other alkanes, including ethane, propane, n-butane, and n-hexane, with\nPd/La Al consistently delivering the highest catalytic performance (Supplementary Fig.\n0.9\n21).\n2. The manuscript presents an interesting concept in which surface defects of the LaAlO3\nsupport regulate the exposure and structure of PdO active sites. It would be informative to\ndiscuss whether a similar structural effect could be achieved by depositing pre-synthesized Pd\nnanoparticles onto LaxAlO3-δ supports, and how this approach might differ from the in-situ\nreplication strategy proposed here.\nResponse: We prepared a series of reference catalysts, Pd /La Al, by depositing pre-\nNPs x\nsynthesized Pd nanoparticles onto La Al supports. Subsequently, CH catalytic activity\nx 4\ntests and CO-DRIFTS characterization were conducted (Figure R8). The results revealed\nthat the Pd /La Al catalysts exhibited consistent activity, and CO-DRIFTS spectra\nNPs x\nexclusively displayed CO bridge adsorption peaks and hollow-site adsorption, indicating\nthat the surface defects of La Al did not influence the surface structure of the pre-\nx\nsynthesized Pd nanoparticles. This further demonstrates that such defect-induced\ndifferences in PdO surface structure occur exclusively during the nucleation and growth\nprocesses of Pd species.\nRelevant discussions have been added to the revised manuscript.\nFigure R8. (a) The light-off curves of the Pd /La Al catalysts for CH oxidation and (b) their CO-DRIFT\nNPs x 4\nspectra.\nRevision: see Page 14\n……\nTo evaluate the generality of this support-induced strategy, pre-synthesized Pd\nnanoparticles (~5 nm) prepared via wet-chemical route were loaded onto La Al (denoted\nx\nas Pd /La Al). As shown in Supplementary Fig. 20, neither catalytic activity nor surface\nNPs x\nstructure of these Pd nanoparticles was affected by La deficiency in the supports. This\nobservation indicates that the defect-induced modulation of PdO surface structures\nprimarily occurs during the nucleation and growth of Pd species on the La Al surface.\nx\n3. On page 7, the CO-DRIFTS spectra in Fig. 2g–i would benefit from clearer labeling. In\nparticular, the peaks assigned to linear CO adsorption on Pd corner sites should be explicitly\nmarked on the corresponding spectra to improve readability.\nResponse: We have revised the CO-DRIFTS spectra in Fig. 2g–i (herein Figure R9) to\nexplicitly label the bands corresponding to linear CO adsorption on Pd corner sites, as well\nas other relevant adsorption configurations.\nRevision: see Page 8\nFigure R9. CO-DRIFTS spectra of Pd/La Al catalysts with (g) x = 1.0, (h) x = 0.9 and (i) x = 0.8.\nx\n4. For completeness, the k3-weighted k-space EXAFS spectra and corresponding fitting curves\nfor the reference samples (Pd foil and PdO) should also be included in Supplementary Fig. 13.\nIn addition, key XAS measurement conditions should be briefly summarized in the Catalyst\nCharacterization section.\nResponse: We have supplemented the k3-weighted k-space EXAFS spectra and\ncorresponding fitting curves of Pd foil and PdO in Supplementary Fig. 13 (herein Figure\nR10).\nRevision: see Page 13 of Supplementary information\nFigure R10. The k3 weighted k space EXAFS functions for the catalysts.\n5. The thermal stability of the proposed PdO “step sites” deserves further clarification. The\ncurrent stability evaluation focuses on long-term operation at 500 oC. It would be useful to\ncomment on whether these step sites are expected to remain structurally stable at higher\ntemperatures, or under more severe thermal aging conditions relevant to practical applications.\nResponse: To assess thermal durability of the catalysts, the fresh Pd/La Al catalysts were\nx\nthermally aged at 600 °C and 700 °C for 2 h (Figure R3). After aging at 600 °C, the T₉₀\nvalues of Pd/La Al and Pd/La Al increased by only 8 °C and 6 °C, respectively,\n0.8 0.9\nindicating largely preserved catalytic performance. In contrast, Pd/La Al showed a\n1.0\npronounced activity loss, with T increasing by 23 °C. When the aging temperature was\n90\nraised to 700 °C, the T increases for Pd/La Al, Pd/La Al, and Pd/La Al were 25, 18,\n90 0.8 0.9 1.0\nand 45 °C, respectively, reflecting more severe deactivation. Notably, Pd/La Al still\n0.9\nexhibited the smallest T increase among the three catalysts at both aging temperatures.\n0.9\nother two catalysts.\nFigure R3. (a-c) Light-off curves of the catalysts after calcination at 600 and 700 °C, and (d) the\ncorresponding increase in T relative to the fresh catalysts.\nafter thermal treatment at 600 °C and 700 °C for 2 h. As shown in Figure R4, as the aging\ntemperature increased, the intensity of linearly adsorbed CO bands gradually decreased,\nwhile the relative contribution of CO adsorption on hollow sites increased, due to sintering\nof Pd species. STEM images of Pd/La Al after calcination at 700 °C further showed that\n0.9\nPdO particles had grown to sizes exceeding 30 nm (Figure R5). These results indicate that\nPd/La Al exhibits thermal stability below 600 °C; however, under more extreme\n0.9\nconditions, aggregation and growth of Pd species remain unavoidable. The corresponding\ndiscussion has been added to the revised manuscript.\nAll corresponding revisions have been incorporated into the main text and\nSupplementary Information.\nFigure R4. CO-DRIFT spectra of the fresh Pd/La Al samples after thermal treatment at 600 and 700 °C\nx\nfor 2h.\nFigure R5. HAADF-STEM image and corresponding EDS mapping of Pd for the fresh Pd/La Al catalyst\n0.9\nafter thermal treatment at 700 °C for 2h.\nRevision:\n(1) see Page 13\n……To further evaluate the thermal durability of the catalysts, the fresh Pd/La Al catalysts\nx\nwere thermally aged at 600 °C and 700 °C for 2 h (Supplementary Fig. 17). After aging at\n600 °C, the T values of Pd/La Al and Pd/La Al increased by only 8 °C and 6 °C,\n90 0.8 0.9\nrespectively, indicating largely preserved catalytic performance. In contrast, Pd/La Al\n1.0\nshowed a pronounced activity loss, with T increasing by 23 °C. When the aging\n90\ntemperature was raised to 700 °C, the T increases for Pd/La Al, Pd/La Al, and\n90 0.8 0.9\nPd/La Al were 25, 18, and 45 °C, respectively, reflecting more severe deactivation.\n1.0\nNotably, Pd/La Al still exhibited the smallest T increase among the three catalysts at\n0.9 90\nboth aging temperatures. These findings confirm that Pd/La Al exhibits superior thermal\n0.9\nstability relative to the other two catalysts.\n(2) see Page 15\n……To further substantiate the durability of PdO step sites, CO-DRIFTS measurements\nwere performed on fresh samples after thermal treatment at 600 °C and 700 °C for 2 h.\nThe CO-DRIFTS spectra of Pd/La Al after thermal treatment (Supplementary Fig. 24)\n0.9\nshow a clear decrease in μ -CO bridging adsorption, accompanied by reduced linear CO\n2\nadsorption and increased μ -CO adsorption, features indicative of particle agglomeration.\n0.9\ngrowth beyond 30 nm (Supplementary Fig. 25). Overall, these results demonstrate that the\nstep sites remain structurally stable below 600 °C but undergo sintering and reconstruction\nat higher temperatures.\n6. Based on the adsorption energy definition provided in the manuscript, a larger positive Eads\ncorresponds to stronger adsorption. However, this sign convention may cause confusion, as\nexothermic adsorption is typically associated with negative adsorption enthalpies (∆H < 0)\naccording to IUPAC definitions. The authors are encouraged to revise the sign convention or\nclarify the definition to avoid ambiguity.\nResponse: We thank the reviewer for this valuable suggestion. The surface adsorption\nprocess is inconsistent with the chemical reaction process. In our original manuscript, we\ntake the definition of the adsorption energy from the textbook of “Introduction to Surface\nChemistry and Catalysis” by G. A. Somorjai et al. (Verlag: Wiley-VCH, 2010.), as quoted\nfrom the Chapter One of the book, “The process that involves trapping of atoms or\nmolecules that are incident on the surface is called adsorption. It is always an exothermic\nprocess. For historic reasons, the heat of adsorption ∆H is always denoted as having a\nads\npositive sign-unlike the enthalpy ∆H, which for an exothermic process would be negative\naccording to the usual thermodynamic convention.” Accordingly, in our manuscript we\ndefined that a positive E indicates an exergonic adsorption process, and the more positive\nads\n(larger) the E is, the more strongly the adsorbate molecule binds on the surface. This\nads\nkind of definition can be found in our previous studies and many other literatures (Phys.\nRev. Lett., 1998, 80, 3650-3653; J. Am. Chem. Soc., 1999, 121, 7931-7932; Adv. Chem.\nEng., 2014, 44, 1-60; J. Am. Chem. Soc., 2003, 125, 1958-1967).\n7. The constrained optimization scheme used to locate transition states for C-H bond activation\nmay have limitations when multiple bonds are simultaneously broken and formed. Additional\ndiscussion or validation would be helpful to support the reliability of the reported transition-\nstate structures and energy barriers.\nResponse: We thank the reviewer for this valuable suggestion. The commonly used\nmethods for transition state (TS) calculations include CI-NEB, Dimer, and Constrained\napproaches. In our present work, we primarily adopted the Constrained method, as\ndescribed in our original manuscript: “The transition states (TSs) of surface reactions were\nlocated using a constrained optimization scheme53,54 and were verified when (i) all forces\non the relaxed atoms vanished and (ii) the total energy was a maximum along the reaction\ncoordinate and a minimum with respect to all other degrees of freedom55.” Furthermore,\nto validate the rationality of the calculated transition states, we first compared the C−H\nbond distances of CH before and after C−H bond dissociation (Table R3). The results\n4\nshow that the C−H bond length in the transition state is longer than that in the CH , but\n4\nshorter than that in the dissociated CH species (Table R3). In addition, we further\n4\ncalculated the vibrational frequencies of the CH dissociation transition states on the\n0.8 0.9 1.0\none imaginary frequency (the corresponding frequencies are -2254.26, -3773.30 and -\n2673.75 cm−1, respectively). These findings clearly demonstrate that the transition states\nobtained in this work are reasonable.\nTable R3. Calculated C−H bond distances (Å) of the key structures involved in CH dissociation on the\nx\nC−H Bond distance (Å) Frequency\nSamples\n*CH TS*(H C−H) *CH , *H (cm−1)\n4 3 3\nPd/La Al 1.097 1.381 3.058 -2254.26\n0.8\nPd/La Al 1.096 1.339 3.215 -3773.30\n0.9\nPd/La Al 1.133 1.413 2.795 -2673.75\n1.0\nRevision: see Page 16\n……that the support morphology effect applies consistently to both model and real\nsystems. Additionally, the C−H bond distances of CH before and after C−H bond\n4\ndissociation were also compared to validate the rationality of the calculated transition\nstates (Supplementary Table 7).\n8. As La content decreases, the manuscript shows a progressive reduction in electron transfer\nfrom the La2O3 component to PdO, while the highest methane oxidation activity is observed\nfor the La0.9 system. Although the authors attribute this behavior mainly to the stability of\ntransition-state intermediates, further clarification would be valuable. In particular, beyond\nelectronic effects, the potential contribution of PdO morphological differences to methane\nactivation should be more explicitly discussed.\nResponse: We thank the reviewer for this valuable suggestion. As the reviewer pointed\nout, our calculations show that on Pd/La Al surfaces the number of electrons gained by\nx\nPdO decreases with decreasing La content, with the corresponding Bader charges of\n−1.413, −1.241, and −0.901 |e|. However, CH exhibits the highest dissociation activity on\n0.61 eV, whereas the barriers on Pd/La Al and Pd/La Al are 1.12 eV and 0.79 eV,\n0.8 1.0\nrespectively. This clearly indicates that the observed activity trend cannot be explained\nsolely by a single descriptor such as the “average charge transfer”. In our original\nmanuscript, we rationalized this behavior from the following aspects. First, regarding CH\n4\nadsorption, the calculated adsorption energies are −0.30 eV (La ), −0.36 eV (La ), and\n1.0 0.9\n−0.28 eV (La ), demonstrating the strongest CH binding on Pd/La Al. This is mainly\n0.8 4 0.9\nattributed to the higher exposure of low-coordination Pd and O sites on Pd/La Al,\n2c 2c 0.9\nwhich provides more favorable adsorption configurations and strengthens the interaction\nwith methane. Second, although Pd/La Al also exposes Pd and O sites, its “crater-like”\n0.8 2c 2c\nsurface morphology leads to locally elongated Pd−O distances. Such geometric distortion\nis unfavorable for forming the transition-state configuration required for heterolytic C−H\ncleavage, thereby significantly increasing the activation barrier (to 1.12 eV). Finally, we\nemphasize that the key “electronic effect” governing methane dissociation is the local\nbonding and orbital interactions in the transition state, rather than the average net charge\ntransfer from La O to PdO. Our density of state (DOS) analyses shows that the OH species\n2 3\nformed during CH activation exhibits strong covalent character. Moreover, the Pd−C (CH )\n4 3\nbond is predominantly ionic on Pd/La Al and Pd/La Al, while it becomes significantly\n1.0 0.8\nmore covalent and shifts to lower energy levels on Pd/La Al.\n0.9\nThese features suggest that\nthe local electronic structure on Pd/La Al is more effective in stabilizing key transition-\n0.9\nstate intermediates, thus lowering the C−H cleavage barrier. In general, these results\ndemonstrate that CH dissociation activity cannot be determined by the magnitude of\n4\ncharge transfer alone; the morphology of PdO (in particular, the local coordination\nenvironment and geometric parameters of Pd and O) is also crucial. In other words, the\nreactivity is jointly dictated by the charge state of PdO and the exposed surface geometric\nstructure.\nRevision: see Page 17\n……, features that are dictated by La-deficiency-induced surface templating of the La Al\nx\nsubstrate. In particular, the La Al support can “etch/template” an optimal PdO structural\n0.9\nmotif. This motif is characterized by a high density of Pd /O site pairs and more suitable\n2c 2c\nlocal Pd–O geometric parameters, which simultaneously enhance CH adsorption and\n4\nmarkedly lower the first C–H bond cleavage barrier, leading to efficient methane\nconversion. This provides clear mechanistic validation of our strategy …...”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The author has appropriately revised the paper and addressed my concerns; it is now ready for publication.", "reviewer_2": "The authors well addressed the questions and concerns in this revised version of manuscript. Therefore, I can recommend\nthe publication of this manuscript in Nat Commun now."}, "author_response": ""}]

Decision letter