Understanding supported noble metal catalysts using first-principles calculations

The vast majority of chemical production processes rely on heterogeneous catalysts. Of particular interest is the use of transition metals in the manufacture of medicines, textiles, building materials, and fuels.^1,2 However, the issue of long-term sustainability arises for technologies that depend heavily on these precious metals due to the limited availability of known ore deposits.³ One viable alternative to reduce catalytic loading is the use of nanomaterials such as nanoparticles (NPs) or metal clusters (MCs), which exploit quantum confinement effects for use in catalysis.^4–6 Metal agglomerates of unknown size and shape distribution are referred to as NPs, while MCs have well defined dimensions. For instance, the general consensus is that the reactivity of clusters consisting of 40 atoms or less is dictated by the number of surface atom coordination sites. On the other hand, the reactivity of NPs (>40 atoms) is mainly driven by the surface energy of the different exposed metal facets. The morphology of such metal facets on NPs often conforms to the combination of the lowest energy Miller index available for a given number of atoms.⁷ Nevertheless, both NPs/MCs are often used interchangeably when describing small aggregations or conglomerations of metal atoms in the literature.

A special group of catalysts exists when NPs/MCs in the form of finely divided transition metals are dispersed over reducible or irreducible support substances,⁸ e.g., TiO₂,^9,10 RuO₂,¹¹ CeO₂,¹² γ-Al₂O₃,¹³ and MgO.¹⁴ Within this class of materials, the support provides metal particles with greater surface-to-volume ratios, enabling a larger number of low coordination sites that increase the catalytically active area for reactions to occur.^15–19 The role of the support offers several distinct benefits, the most obvious being protection toward sintering, catalyst activation processes, and deactivation mechanisms.^20–23 Furthermore, charge transfer and quantum hybridization at the interface have been shown to influence the catalytic activity via several compounding effects.^24–26 The understanding of metal–support interaction (MSI) and the surrounding reaction environment is key for the rational optimization of the catalytic activity and longevity of metal nanoparticles in industrial applications.

Several experimental techniques have been developed allowing for the gradual buildup of an atomic-level understanding of such systems. For instance, low energy electron diffraction (LEED) spectroscopy,²⁷ temperature programmed desorption (TPD),^28,29 scanning tunneling microscopy (STM),³⁰ atomic force microscopy techniques (AFM),³¹ and high-pressure X-ray photoelectron spectroscopy (HPXPS)³² have all been extremely successful for understanding reactants and products in the gas and aqueous phase.

Despite these advancements, we can only obtain a clear description of the reactants and products, while the transition state and reaction pathway remain elusive. In addition, reactions that occur at the solid-liquid interface add another layer of complication, as UHV conditions cannot be applied to these systems under working conditions, as shown in Fig. 1. Thus, elucidating features such as the reaction kinetics, free energy barriers, and the atomistic structures of intermediates remain a formidable challenge.^33–36 To solve these issues, the development of several theoretical methods,^37–43 such as density functional theory (DFT), microkinetic modeling, and molecular dynamics (MD), have become powerful tools for understanding the structural nuances and reaction mechanisms on NPs and their supports. DFT not only allows for an accurate description of crystal structures and accurate energetics but also can determine the transition states and various other reaction intermediates with relative ease.^44,45 This, in tandem with microkinetic modeling, allows for a more complete picture of reaction cycles on heterogeneous systems.

To this end, this work primarily focuses on developments regarding the structure and catalytic activity of supported metal catalysts using electronic structure calculations (ESCs). It should be noted that, however, there already exists several excellent reviews on supported and unsupported nanoparticles^46–49 that introduce current research and recent advances of design and stabilization based mostly on experimental endeavors. Here, we begin by discussing several significant developments before introducing the state-of-the-art in nanoparticle and support catalyst research. These perspectives also highlight design strategies as well as the primary challenges in the field. Furthermore, several key advances in heterostructure design are discussed, emphasizing the importance of interactions with the support and reactants on the catalytic activity using ESCs. Additionally, the dominating factors affecting the adsorption and reaction pathways, such as the environment effects and surface defects, have been addressed. To conclude this work, a brief perspective on the challenges and possibilities within this field is presented.

The properties of NPs are highly size dependent, making them versatile materials that can be precisely tuned for a desired purpose. Therefore, understanding how the properties of NPs scale with size is important for their rational design. Traditionally, when modeling catalysts, low index single crystalline surfaces are most often used, as it is important to relate the mechanism and kinetic parameters to the surface structure. However, the confined nature of NPs means that they are prone to defects and step edges at their surfaces as well as multiple facet grain boundaries between planes.⁵¹ This leads to a broad range of catalytic activities on the different crystal phases, making it important to understand the link between particle morphology and catalyst performance. The challenge for theorists is to obtain reliable structures that best represent the number of inequivalent active sites, before reaction barriers and kinetic parameters can be obtained—the issue is further complicated when multiatom types are present and/or if the reaction environment changes.

Early, GGA-DFT (generalized gradient approximation) calculations by Fernández et al.⁵² showed that the structures of various metal clusters are intrinsically related to the atomic charge and the number of surface atoms. These features are captured well in advancements in gold (Au) catalysis. Despite being described as “the most noble of metals” in its bulk form,⁵³ Au possesses a reactivity that varies depending on the particle size.^54–56 DFT has shown great promise in unraveling the fundamental characteristics of these small metal clusters. For instance, Figs. 2(a) and 2(b) highlight the applications of ESCs to find the lowest energy geometry of Au clusters (AuN) by Cleveland et al.⁷ and later by Assadollahzadeh and Schwerdtfeger.⁵⁰ This strategy has helped us to identify shape dependent trends that subsequently alter the fundamental properties, even with the addition or removal of single Au atoms.⁵⁷ Here, it is found that due to quantum hybridization effects, planar Au structures are the most stable for clusters up to ∼10 atoms, resulting in an increased reactivity and progression to nonmetallic properties.⁵⁸ While on transitioning from the 2D-to-3D limit, the surface atoms hybridize with internal cluster atoms, increasing the coordination number and leaving a lower charge density for atoms to react with interacting molecules. Many of these properties are not unique to Au; however, they have paved the way for a vast range of NPs to be examined under more realistic conditions.

For modeling chemical reactions on NPs, CO oxidation (2CO + O₂ → 2CO₂) and the hydrogen evolution reaction (HER: 2H⁺ + 2e⁻→ H₂) are often used as prototypical model systems for obtaining a fundamental understanding of catalytic activity. Heiz et al.⁵⁷ investigated CO oxidation on platinum (Pt) clusters; the geometry of the clusters show significant variation as a function of the number of atoms, i.e., “each atom counts.” Yudanov et al.⁵⁹ found that the adsorption energy of CO varies as a function of palladium (Pd_N) cluster size [Fig. 3(a)]. They identified a critical size below N = 50 atoms, whereby the shift of the metal d-band induces a higher activity for CO adsorption. When the Pd cluster is dominated by closed packed faces, the CO-Pd bond strength becomes weaker with decreasing cluster size.

The Liu group also investigated the photocatalytic activity of anatase TiO₂ nanoparticles toward the oxygen evolution reaction (OER) in aqueous solvent.⁵ The surrounding water environment was simulated using DFT combined with a modified Poisson-Boltzmann continuum solvation model. They identified the optimal size of NPs for OER and provided quantitative information regarding the desired morphology, wherein particles dominated by (101) facets are found to be more reactive by exposing more active Ti_5c terrace sites. These sites have been identified as having an optimal HOMO/LUMO spatial separation, leading to more efficient covalent bonding between OH species and Ti_5c while reducing the effects of electron-hole pair recombination.

Moreover, several machine learning (ML) strategies have been evaluated by Jäger et al.⁶⁵ to model hydrogen adsorption on MoS₂ and Au₄₀Cu₄₀ nanoclusters, providing potential alternative strategies for investigating HER and OER. ML methods are expected to be highly desirable for current/future simulations of the structure and reactivity of NPs,^66–69 providing the chemical accuracy of DFT coupled with MD simulation time scales typically reserved for classical force fields. Furthermore, they allow for the extraction of key properties for reactions beyond HER and with system sizes much larger than those currently feasible.

Metal–support interactions (MSI) have long been regarded as key in rationalizing the interfacial properties of supported NPs.⁷⁰ Integral to this, ESCs have emerged as a fundamentally important tool for understanding NPs on support materials at the atomic level using quantitative descriptors. Both the activity and stability are found to be inversely proportional to the diameter of the supported metal particles. Despite small particles often having higher activities, these effects can be countered by their tendency for degradation,^20,71 resulting in a double-edged effect. Consequently, the activity of supported metal catalysts is highly dependent on the metal particle size in tandem with the metal-support interactions, adding additional levels of complexity for theoretical models.^72–74 Thus, due to the myriad of bonding mechanism and tendency for degradation, a unified theory for understanding NP–support interactions is missing from the current literature.^68–70 

A key feature when investigating interfacial interaction is electron transfer, resulting from the requirement to satisfy the Schottky–Mott rule, which assumes that the vacuum levels for metal NPs and supports are aligned at the interface. The resulting Fermi energy tunability sees a redistribution of electrons until the Fermi energy on both sides of the interface reaches an equilibrium point.⁷⁵ Depending on the band alignment energies, this often creates a charged interface, with electron accumulation on one side (reduction) and electron depletion on the other side (oxidation).^76,77 This, in turn, will influence the catalytic properties and durability due to charge transfer stabilization.^{11,17,78–80}

These features are highlighted well by Vayssilov et al.²⁶ who investigated the interaction between nanostructured CeO₂ (ceria) and Pt NPs, by combining DFT+U calculations and resonant photoelectron spectroscopy (RPES), as shown in Fig. 5. They identified two types of metal–oxide (MO) interaction, namely, electron transfer from Pt to ceria and transfer of activated oxygen from ceria to Pt (reverse spillover). Here, the Pt states essentially fill the whole bandgap and contribute to the valence band and conduction band region. The charge transfer results in oxidation of Pt, while Ce³⁺ ions are formed due to a partial reduction of the support. Furthermore, the transfer of oxygen is found to be a unique feature of nanostructured ceria surfaces interacting with Pt NPs, which results in a previously unreported interaction channel between nanostructured metal-oxide supports and NPs, leaving much more to be learned than initially anticipated.

Furthermore, the lack of size control of NPs on supports makes them unstable at high temperatures and under reaction conditions, due to growth through Ostwald ripening (OR), diffusion, and other recombination mechanisms.⁸⁵ Prieto et al.⁸⁶ exemplified that size control along with the interparticle distance is crucial in affecting the stability of copper catalysts for methanol synthesis under reaction conditions. On an atomistic level, OR is driven by the difference in chemical potential between particles of various sizes redistributing to remove any dipole fluctuations on the surface. Ouyang et al.⁸⁷ developed an atomistic theory for OR and disintegration in the presence of reactants, wherein the energetics and kinetics data can be readily extracted from first-principles calculations and applied to the understanding of macroscale problems. The general consensus is that it would be highly desirable to control the size of all metal NPs on the support to be compositionally homogeneous. It emerges that at this limit of homogeneity, where NPs of equal size are uniformly distributed over a surface, there is no net-difference in the NP chemical potential leading to a complete suppression of Ostwald ripening.⁸⁸ 

The catalytic activity of metal-support systems has an additional complexity that can be tuned on changing the support and the size of the adsorbed NPs. In a number of cases, this is related to the presence of a triple phase boundary (TPB) and the formation of high-coordination interfacial sites that play a significant role in catalysis.^9,13,89–91 Here, the interface can modify the energy profiles of catalytic processes by providing a larger number of adsorption sites where key reaction intermediates can be stabilized, compared with the bare NP. Additionally, opening alternative reaction paths with lower activation energy sees a marked speed-up of the reaction rates, making them applicable for a wide variety of reactions [e.g., water-gas shift (WGS), CO oxidation, and HER]. From Fig. 6, the TOF of CO oxidation at the NP_N/CeO₂ (NP_N = Ni, Pd, and Pt) interface is shown to vary significantly depending on the NP size and the mode of contact with the support, providing a direct relationship between the structure and function.⁹² However, it is often the case that the influence of the support on the catalytic activity cannot be explained by disentangling the contribution of each component. Theoretical analysis of the TPBs under operating conditions are, therefore, inherently difficult, with great care being required when analyzing results.

In particular, due to favorable band alignments, NP-support systems have been widely utilized in photocatalytic reactions, such as the photoreduction of CO₂ and the photocatalytic HER.^93–95 Here, the NP provides additional trapping sites for enhanced electron-hole separation, while the support can modify the electronic structure to promote the adsorption of reactants. For instance, the mechanism for the photocatalytic HER on metal NPs is particularly challenging using DFT. As unlike with typical thermally activated reactions, photocatalytic reactions involve photogenerated electron transfer from the support to the metal NP as well as the catalytic formation of H₂ on the NP surface. Experiments have suggested that HER preferentially occurs on small Pt NPs of ∼1 nm diameter supported on TiO₂,^96,97 while large Pt NPs have the tendency to accept photoinduced charge carriers, resulting in electron-hole recombination pathways that lead to decreased photoactivity.⁹⁸ This strongly suggests that the size of the NPs/MCs is crucial for describing the rate-determining step of HER.

To tackle these issues, Wang et al.⁷⁹ used hybrid DFT (HSE06⁹⁹) calculations and AIMD simulations to reveal the precise size-dependent activity of photocatalytic HER over Pt/TiO₂ at the atomic level [Fig. 7(a)]. They exemplify how the electronic properties of supported metals vary with the particle size while the electron-transfer efficiency follows different size-dependent trends. From the density of states (DOS) spectra, shown in Fig. 7(b), the deposition of Pt clusters on TiO₂ varies the electronic properties by splitting the metallic Pt states and opening a gap between 0.5 eV and 1.3 eV. This indicates that the rate-determining step of photocatalytic HER on supported metal catalysts actually changes with the particle size, as shown in Fig. 7(c). They were able to match the exact size and morphology of Pt nanoparticles for HER, whereby particle sizes between 0.70 and 1.52 nm are the most active from free energy calculations.

Furthermore, photochemical strategies have been used in the fabrication of stable atomically dispersed Pd/TiO₂ catalysts with organic ligands. Recently, Liu et al.¹⁰⁰ exemplified how such systems exhibit high catalytic activity in hydrogenation reactions by studying H₂ reacting with C=C bonds. In the presence of multiple Pd-O interfaces, Pd₁/TiO₂ activates H₂ via a heterolytic pathway, rather than the traditional homolytic pathway on conventional Pd catalysts. DFT+U calculations revealed that the hydrogenation of styrene using Pd₁/TiO₂ followed a stepwise process. They considered two possible pathways, wherein the energetically favorable process was found to be H-transfer from Pd to C=C, proceeding with a barrier of only 0.47 eV. These calculations highlight the promotional effects of support catalysts for hydrogenation, compared with the traditional slab systems.

Thus far, the discussion has mainly addressed static DFT and AIMD calculations, which provide useful information about the reaction energetics, crystal structure, and activation barriers. However, for industrial applications, the choice of catalyst is based on improving the rate and selectivity of forming a desired product. On combining with transition state theory and microkinetic modeling, DFT calculations can be used to rationalize the rate of elementary chemical reactions under various reaction conditions. Several excellent kinetics studies have emerged regarding the WGS (CO + H₂O → CO₂ + H₂) reaction, which is the key step in many industrial processes. DFT calculations predict that the dissociation of H₂O is the rate determining step for WGS. It is found that a cooperative effect between the support and adsorbed NP is key in describing the selectivity and reactivity.

Ammal and Heygen¹⁰¹ investigated the temperature dependent WGS reaction at the Pt₈/TiO₂ interface using DFT coupled with a rigorous microkinetic model. They suggest that at low temperatures (473–623 K), CO adsorbed on the Pt NP reacts with O from the TiO₂ surface, whereby the reduced surface is then reoxidized by H₂O, forming H₂. At temperatures above 673 K, CO reacts with TiO₂ OH groups forming a carboxyl or formate intermediate, which subsequently dissociates, giving CO₂ and H₂ and leaving an O vacancy at the interface that is filled via water dissociation. The overall reaction scheme is shown in Fig. 8(a), along with the calculated rates. Noteworthy is that the NP/support system gives TOFs ∼2 orders of magnitude greater than those predicted for pristine Pt(111), highlighting the importance of multiple reaction facets on support-metal systems.

Later, Foppa et al.¹⁰² used a combined DFT/microkinetic modeling approach coupled with experiments to investigate the reactivity and selectivity of the Ni/γ-Al₂O₃ interface toward water–gas shift (WGS, 573 K) and the dry reforming of methane reactions (DRM: CH₄ + CO₂ → CO + 2H₂, >873 K). They found that, similarly to CeO₂, the γ-Al₂O₃(110) surface provides sites for O_ads and OH_ads via H₂O or CO₂ dissociation, which are key for controlling the selectivity. From Table I, static-DFT calculations predict that the interface significantly enhances the rate for both WGS and DRM reactions since the free energy barriers for H₂O and CO₂ activation are both ∼0.6 eV smaller at interface sites compared with the bare NP. However, the catalytic activity of the interface is also related to the population of intermediates taking part in the RDSs, with CO coverage of the NP being a key factor in favoring the WGS reaction at low temperatures. The overall reaction scheme is shown in Fig. 8(b), highlighting the importance of Ni/Al₂O₃ interface for WGS, but not in DRM.

In the above discussion, we have presented a number of theoretical investigations that highlight the critical factors in explaining the catalytic activity of supported transition metal catalysts. While not exhaustively complete, we emphasize the importance of ESCs for investigating how properties scale as a function of size, NP stability, and support-metal interactions. Additionally, the dominating factors affecting product selectivity and reaction pathways such as environment effects, surface defects, and catalytic activity toward industrially significant reactions have been addressed. We highlight that using first-principles calculations can aid the understanding of dynamic processes, which, in turn, provide strategies for the rational design of new materials via a precise understanding of atomic scale properties.

We have presented computational contributions for simulating thermal and photochemical reactions on supported and unsupported nanoparticles using a variety of first-principles calculation techniques. Despite numerous theoretical and experimental achievements over the past decades, our understanding toward supported and unsupported metal catalysts is far from complete. Considerable challenges exist, such as understanding how these properties scale with the size on different support materials. More open challenges include simulating reactions in the presence of surface ligands under electro- or photocatalytic conditions in aqueous solutions and the description of charge transport properties using theories that go beyond time-independent DFT [e.g., time-dependent DFT (TDDFT), many-body perturbation theory^103,104 (within the GW approximation), random phase approximation¹⁰⁵ (RPA), and Bethe-Salpeter Equation¹⁰⁶ (BSE)]. In the future, a deeper understanding of the structure-function relationships of supported and unsupported nanoparticles will accelerate the screening and design of better catalysts for use in the chemical and energy conversion industries.

We acknowledge the use of computational resources at the UK National High-performance Computing Service, ARCHER, and the U.K. Materials and Molecular Modelling Hub for access to THOMAS, for which access was obtained via the UKCP consortium and EPSRC Grant ref EP/P022561/1. P.S.R. thanks his Ph.D. studentship funding by the Northern Ireland Department for the Economy (NI-DfE) at the Queen’s University of Belfast.