Characterization of changes in the electronic structure of platinum sub-nanoclusters supported on graphene induced by oxygen adsorption

Abstract

As the sizes of noble metal catalysts, such as platinum, have been successfully minimized, fundamental insights into the electronic properties of metal sub-nanoclusters are increasingly sought for optimizing their catalytic performance. However, it is difficult to rationalize the catalytic activities of metal sub-nanoclusters owing to their more complex electronic structure compared with those of small molecules and bulky solids. In this study, the adsorption of molecular oxygen on a Pt₁₃ sub-nanocluster supported on a graphene layer was analyzed using density functional theory. Unlike bulk Pt, the Pt₁₃ sub-nanocluster has multiple adsorption sites, and the adsorption energy depends strongly on the type of adsorption site. The O₂ adsorption energy does not correlate with the transferred charge between O₂ and the Pt₁₃ moiety; therefore, to elucidate the differences in the adsorption sites, we propose an original approach for analyzing the electronic structure change in metal sub-nanoclusters caused by molecular adsorption. Our analysis of the integrated local density of state (LDOS) revealed that O₂ adsorption on the Pt₁₃ sub-nanocluster has a distinct feature, different from that on a smaller Pt₂ cluster or rather a larger Pt slab. The change in the electronic structure of the Pt₁₃ moiety was primarily observed near the Fermi level, different from that of the Pt slab whose DOS was distributed over a wide energy range. Furthermore, the change in the integrated LDOS correlated well with the O₂ adsorption energy on the Pt₁₃ sub-nanocluster.

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Introduction

High-cost noble metal catalysts, such as platinum particles, have been successfully downsized to sub-nanocluster levels to economize their usage. With the utilization of metal sub-nanoclusters in various catalytic reactions, their distinct feature has been gradually realized. Earlier, the catalytic activity of Pt catalysts in the oxygen reduction reaction (ORR) was expected to decrease with a decrease in the Pt particle size (diameter) to less than a few nanometers.¹ However, recent experimental studies have demonstrated that Pt clusters with less than 1 nm diameter, that is, Pt sub-nanoclusters, have higher ORR catalytic activities than larger Pt nanoparticles.^2–7 In this context, fundamental insights into metal sub-nanoclusters are sought to develop efficient catalysts.

For controlling the catalytic properties of a metal catalyst, it is necessary to understand the changes in the electronic structure caused by its chemical interaction with reactant molecules. The formation and dissociation of chemical bonds in small molecules are rationalized using so called frontier orbitals near the HOMO–LUMO region (HOMO: highest occupied molecular orbital; LUMO: lowest unoccupied molecular orbital).⁸ When the particle size is large, the energy levels become continuous. Thus, the electronic structure of bulk solids is not expressed using molecular orbitals but using the band structure, considering the lattice translational symmetry. The chemisorption of a molecule on a metal surface has been rationalized using the metal d-band center, the energy of which is lower than the Fermi level energy by a few electron volts.^9,10 However, the d-band center is often unsuitable for characterizing a small metal cluster that is less than 2 nm in diameter.¹⁰ Moreover, metal sub-nanoclusters have a complex electronic structure, in which many orbitals lie near the Fermi level. Thus, a large number of orbitals in metal sub-nanoclusters could contribute to their chemical interaction with the adsorbed molecule; that is, the catalytic behavior of these clusters cannot be explained by analyzing just a few orbitals. It is therefore imperative to understand the electronic structures of metal sub-nanoclusters using another new theoretical/computational approach.

First-principles quantum mechanical methods have been used to study various systems, including Pt_n (n = 2–147) clusters and Pt surfaces.^3,9–21 In previous studies, the difference between the ORR energy diagrams of a Pt₁₃/graphene heterostructure and a Pt slab was calculated, revealing that the O–O bond is readily dissociated on the former because of the strong chemical interaction between O₂ and the Pt₁₃ moiety.^16,17 In addition to performing energy calculations, it is essential to analyze the electronic structure of a catalyst for understanding its catalytic activity, as has been widely accomplished using quantum mechanical computational methods. Previously, density of states (DOS) obtained through density functional theory calculations was utilized to evaluate the d-band center.^9,10,22 Furthermore, the electronic structure of a Pt₅₅ nanocluster was analyzed to rationalize the variation in the adsorption energy of molecular species (e.g., O and CO) depending on the adsorption sites on the cluster surface.¹⁴ This analysis was performed considering the d-band center, because the relatively larger Pt₅₅ nanocluster retains the original fcc structure. In another study, the mechanism of charge transfer between O₂ and small Pt_n (n = 2–6) clusters was analyzed in detail, considering the presence of a few discrete orbitals near the HOMO–LUMO region.¹¹ Our research group has previously investigated the ORR catalysis of a Pt₁₇/graphene heterostructure and found that the amount of atomic charge on the Pt₁₇ moiety correlates well with its catalytic activity.⁷ However, the relationship between the electronic structure of the Pt₁₇ cluster and adsorption energy has not been fully clarified. Only a few theoretical approaches have focused on the inherent features of sub-nanoclusters, which are different from those of smaller clusters and bulk metals. So far, there has been a large gap in terms of theoretical insights into the difference between small isolated systems and bulk materials. Indeed, the d-band center is not suitable for discussing small systems of which the d-band is not clearly defined.¹⁰ It is therefore essential to establish a suitable theoretical approach for characterizing the electronic structures of metal sub-nanoclusters.

Herein, we present an original approach for analyzing the electronic structures of metal sub-nanoclusters, considering their inherent chemical properties, which differ from those of small clusters and bulk particles. The present approach is applied to analyze O₂ adsorption on a Pt₁₃/graphite heterostructure, and the results obtained for the heterostructure are compared with those of a Pt₂ cluster and Pt slab. By analyzing the mechanism of O₂ adsorption depending on the Pt size and adsorption sites, we pave the way for investigating the inherent characteristics of metal sub-nanoclusters, which differ from those of small clusters and bulky materials.

Model systems and computational details

This study investigated the adsorption of molecular oxygen on a heterostructure consisting of a Pt₁₃ sub-nanocluster and graphene monolayer, as depicted in Fig. 1. Pt₁₃/graphene heterostructures have been widely studied using theoretical methods, because Pt₁₃ is known to be a stable magic number sub-nanocluster.² Oxygen adsorption onto a Pt catalyst is the initial step in the ORR, and it often determines the ORR activity depending on the adsorption sites of Pt sub-nanoclusters.⁷ This is because platinum is on the left-hand side of the volcano plot peak for the ORR,¹³ and Pt sub-nanoclusters can readily cause O₂ dissociation. Therefore, the strong binding of the reactants is a major problem. Indeed, the energy barrier for the dissociation of the O–O bond of O₂ adsorbed to a Pt sub-nanocluster is rather small because of the strong chemical interaction between the two.¹⁷ In this study, a graphene monolayer was employed to mimic conventional experimental systems in which Pt sub-nanoclusters are supported on graphite (to be precise, carbon black). Indeed, despite the weak Pt₁₃–graphene interaction, the structure of the Pt₁₃ moiety changes significantly when supported on graphene, and various adsorption sites are generated as a result. To analyze the change in the electronic structure owing to O₂ adsorption, an O₂ molecule was located more than 6 Å apart from the Pt moiety, as shown in Fig. 1, to evaluate the alignment of the orbitals of the Pt and O₂ moieties prior to adsorption. We then changed the initial position of O₂ closely placed around the Pt₁₃ surface and optimized the O₂ adsorption structure. For comparison, calculations were also performed on the smallest possible cluster, Pt₂, and also on a Pt slab consisting of four Pt atomic layers.

Fig. 1 Unit cell of the system consisting of a Pt₁₃ sub-nanocluster supported on a graphene monolayer before O₂ adsorption. Pt, C, and O atoms are shown as dark blue, grey, and red spheres, respectively.

All calculations were carried out using the Quantum Espresso program.²³ Spin-polarized density functional theory calculations were performed using the dispersion-corrected PBE functional (PBE-D3)^24–27 and the projector augmented wave (PAW) pseudopotential.²⁸ The cutoff energy for the wave function was 50 Ry. The cell size of the Pt₁₃/graphene heterostructure was 14.8 and 32.6 Å along the horizontal and vertical directions, respectively, with respect to the graphene layer, and that of the Pt slab was 5.4 and 9.4 Å along the Pt surface and 19.8 Å in the perpendicular direction to the surface. For the Pt₂ cluster, a cubic box with a side length of 16 Å was used as the unit cell. Gamma-point (single k-point) sampling was used for the Pt₁₃/graphene heterostructure and Pt₂ cluster, while 4 × 2 × 1 k-points were used for the Pt slab because we utilized a rectangular unit cell with a length along the y-direction (9.4 Å) longer than that along the x-direction (5.4 Å).

The GGA (generalized gradient approximation) functional often underestimates the band gap. However, in a previous B3LYP calculation for the O₂ adsorption on Pt₂, an adsorption energy of 0.94 eV was reported,²⁹ which is slightly lower than but close to the present PBE result of 1.19 eV. Therefore, the error stemming from the choice of the DFT functional is considered to have a minor influence on the discussion within this study. Our focus remains on the qualitative aspect of the Pt₁₃ model, in which the O₂ adsorption energy is ∼1 eV greater than that on Pt₂ and Pt slab models, as elaborated below.

Results and discussion

Geometrical optimizations were performed by changing the initial position of the O₂ molecule around the Pt₁₃ surface, and 23 stable structures were obtained after O₂ adsorption on the Pt₁₃/graphene heterostructure, that is, these 23 structures were optimized after the O₂ adsorption on the Pt₁₃ cluster. All structures are illustrated in Fig. S1 in the ESI.† In this study, we employed only one structure of the Pt₁₃/graphene heterostructure before O₂ adsorption. The employed structure was the most stable among four structures obtained for Pt₁₃/graphene. Therefore, the formation of numerous structures after O₂ adsorption is attributed to the differences in the adsorption sites of the Pt₁₃ moiety.

Table 1 summarizes the adsorption energies of O₂ on different Pt models, viz., the Pt₂ cluster, Pt₁₃/graphene heterostructure (denoted as Pt₁₃), and Pt slab. The adsorption energy, E_ad, is defined as the change in the total energy owing to adsorption, E_ad = E_af − E_bef, where subscripts “bef” and “af” denote the states before and after O₂ adsorption, respectively. E_ad of the Pt₁₃/graphene heterostructure depends strongly on the adsorption site and ranges from −2.78 to −1.11 eV. All the E_ad values of the Pt₁₃/graphene heterostructure chosen for this study are larger than those of the Pt slab. On the other hand, some of them are larger than and others comparable to that of the Pt₂ cluster (−1.19 eV). The energy of each system is shown in Fig. S1 (ESI†).

Table 1 Adsorption energy and electronic charge of different Pt models

	Pt2	Pt13	Pt slab
E ad/eV	−1.19	−2.78 to −1.11	−0.63
Variation in charge on O2/e	−0.46	−0.72 to −0.56	−0.41

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Table 1 also lists the variation in the Bader charge on O₂ owing to O₂ adsorption. Here, we show the sum of the charges on the two O atoms. The O₂ moiety becomes negatively charged after adsorption on Pt, regardless of the adsorption site or the Pt model employed. Notably, the amount of negative charges on O₂ adsorbed on the Pt₁₃ model is the largest among the Pt models. We further analyzed the atomic charge on each Pt atom and observed that charge variation mainly occurred in the Pt–O bond region (Fig. S2 in the ESI†). Therefore, the charging of O₂ indicates the charge transfer from Pt to O₂ moiety.

Fig. 2(a) shows the dependence of the electronic charge transferred to O₂ on the O–O bond distance. A linear relationship is observed, independent of the Pt model (Pt₂, Pt₁₃, or the Pt slab). This result also indicates the Pt-to-O₂ charge transfer. Nevertheless, the adsorption energy of O₂ on the Pt₁₃ model did not exhibit a clear correlation with the transferred charge as shown in Fig. 2(b), presumably due to complex changes in the electronic and geometrical structures of the Pt₁₃ model, as discussed below.

Fig. 2 (a) Dependence of the charge transferred to O₂ on the O–O distance and (b) the relationship between the adsorption energy and charge transferred to O₂.

To further analyze the differences between the O₂ adsorption energies of Pt₂, Pt₁₃, and the Pt slab, we compared the local DOS (LDOS) of the O₂ and Pt₂ moieties involved in Pt–O bond formation. The LDOS was obtained by summing the LDOS of two Pt or O atoms, where the selected Pt atoms are labeled as 3 and 7 in Fig. 1. LDOSs projected towards the two Pt atoms are useful for excluding the contribution of Pt atoms other than the O₂ adsorption sites. Using the same number of Pt atoms, we investigated the inherent characteristic of the Pt₁₃ sub-nanocluster, other than the trivial difference in the number of Pt atoms, that is, the integrated amount of DOS. For example, the Pt slab consists of 32 atoms per unit cell; thus, its DOS is more than 10 times larger than that of Pt₂ as shown in Fig. S3 in the ESI.†Fig. 3 shows the LDOS before O₂ adsorption. The profiles of the LDOS of each Pt species are significantly different from each other. The Pt₂ cluster has discretized LDOS with sharp peaks in the range of −5 to 1 eV (Fig. 3(a)), whereas the LDOS of the Pt slab is distributed over a wide energy range from the Fermi level energy to approximately −9 eV (Fig. 3(c)). Remarkably, the Pt₁₃ moiety exhibits an intermediate characteristic between those of the Pt₂ cluster and Pt slab. Its LDOS (Fig. 3(b)) is distributed down to a low energy region of approximately −7 eV, and the peak height of the LDOS around the Fermi level is ∼10, almost twice that of the Pt slab (∼5).

Fig. 3 Local density of states (LDOS) of the Pt (blue) and O₂ (red) moieties before O₂ adsorption for the (a) Pt₂, (b) Pt₁₃/graphene heterostructure, and (c) Pt slab. The band energy is given as the energy difference from the Fermi level energy, E_F.

The LDOS peaks of the O₂ moiety near the Pt₁₃/graphene heterostructure (Fig. 3(b)) are located at −2.1 and 0.2 eV, which are lower by ∼1 eV than those of the O₂ moiety near the Pt slab at −1.2 and 1.1 eV (Fig. 3(c)). As the O₂ molecules are located far from the Pt species before adsorption, this difference does not arise from the O₂ moiety itself. Here, the band energy is given as a relative value with respect to the Fermi level. Therefore, the peak positions of the O₂ moiety indicate that the occupied orbitals of the Pt₁₃/graphene heterostructure are distributed up to a higher energy region than those of the Pt slab; this is because the Pt₁₃ sub-nanocluster is not as chemically stable as the Pt slab.

The above analysis indicates that the differences between the O₂ adsorption energies of different Pt models can be attributed to the strength of the interaction between the d-orbital of the Pt moiety and the π* orbital of approaching O₂. Indeed, the energies of the occupied orbitals of the Pt₁₃ sub-nanocluster are higher than those of the Pt slab; consequently, the former can interact more strongly with the π* orbitals of O₂ owing to the closeness of their energy levels. This strong interaction could be one of the key reasons for the significant stabilization of the Pt₁₃ system after O₂ adsorption. The detailed analysis presented below further supports this inference.

The central objective of this study is to examine the inherent features of the electronic structures of Pt sub-nanoclusters that are different from those of larger Pt particles and smaller Pt clusters. In the following, we further discuss the changes in the electronic structure of the Pt₁₃ moiety following O₂ adsorption. Nevertheless, the geometrical structure of Pt₁₃ also changed substantially following O₂ adsorption. The significance of the geometry of the metal surface in its reactivity has been discussed in earlier reports.^30,31 However, they focused on the bulk solid surface, and metal sub-nanoclusters were not discussed. Therefore, we here evaluated the contribution of the change in the electronic structure to the adsorption energy. For this, we divided the adsorption process into two steps, as illustrated in Fig. 4. Then, we calculated the energy of an intermediate state, which has the geometry of the Pt₁₃ moiety observed post O₂ adsorption, although the O₂ molecule is located far away from it. The ellipsoidal and hexagonal shapes of the system in Fig. 4 represent the geometrical structures of the Pt₁₃ moiety before and after O₂ adsorption, respectively, while the solid and hatched colors indicate its electronic structures before and after adsorption, respectively. Based on this scheme, we defined the changes in the geometry (Fig. 4(a)) and electronic structure (Fig. 4(b)) of the system to determine their contributions. The energy of the former is given by E_geom = E_Int – E_bef while that of the latter is given by E_elec = E_af − E_Int, where Int denotes the intermediate state. The sum of E_geom and E_ele is equal to the total adsorption energy, E_ad.

Fig. 4 Scheme of the adsorption process separated into changes in the (a) geometrical and (b) electronic structures. The red and blue regions denote the O₂ and Pt₁₃ moieties, respectively.

The geometrical and electronic changes are, of course, interdependent; thus, their quantitative contributions could depend on the definition. However, the main purpose of this study is to understand the electronic structure of the Pt sub-nanoclusters. Developing a more sophisticated approach to define these two contributions is beyond the scope of this study.

Fig. 5(a) shows the relationship between E_geom and E_ad, revealing that E_geom makes a non-negligible contribution to the total adsorption energy. However, we could not obtain any physically meaningful insights into the variation in E_geom and E_ad depending on the geometrical characteristic of the adsorption sites. In fact, E_ad was not related to the coordination number (CN) (Fig. S4, ESI†), which was defined using the nearest neighbor Pt–Pt bond length as the upper limit of the bond length.³²E_ad was also not correlated with the distance from the graphene layer. For example, the 2–6 model was similar to the 8–13 model regarding the distance, but the values of E_ad were significantly different (Fig. S1 in the ESI†).

Fig. 5 Contributions of the changes in the (a) geometrical and (b) electronic structures of different Pt₁₃/graphene models. (c) Models used in electronic structure analysis at the atomic scale. Enclosed in blue, dark green, light blue, and orange boxes are 3–12, 7–11, 10–12, and 8–13 models, respectively.

The value of E_geom is positive if the Pt₁₃/graphene model has a global minimum structure. Therefore, the large adsorption energy for the Pt₁₃ model (Table 1) is mainly attributed to E_ele. Indeed, E_ele is lower than E_geom (Fig. S5 in the ESI†). In practice, E_geom becomes a negative value in some Pt₁₃ models because the O₂ adsorption often causes a substantial structure change in the Pt₁₃ moiety and thereby its stabilization.

We further confirmed that no correlation exists between E_geom and E_elec, which indicated that the dependence of E_elec on E_geom is negligible (Fig. S5 in ESI†). Therefore, we can reasonably focus on E_elec without considering E_geom. Further detailed investigation of the geometric contribution is beyond the scope of this study, as the focus of this study is to determine the characteristic of the electronic structure of Pt sub-nanoclusters.

Fig. 5(b) shows the relationship between E_elec and E_ad, revealing a linear correlation. Although the correlation is weak owing to the contribution of E_geom, E_elec of three models (i.e., Pt₁₃, Pt₂, and Pt slab) exhibits the same order as E_ad, showing that the difference in E_ad among the three models is determined by E_ele.

To elucidate the variation in E_elec depending on the Pt₁₃ adsorption sites, we focus on four models (denoted as 3–12, 7–11, 10–12, and 8–13 based on different adsorption sites) shown in Fig. 5(c). For example, two O atoms in the 8–13 model are adsorbed on 8th and 13th Pt atom (see Fig. 1 for the number of Pt atoms). The plot points in Fig. 5(a) and (b) and the four models in Fig. 5(c) are linked using different colors. Fig. 5(a) shows that the geometrical contributions of the four models are almost the same; thus, the difference in E_ad among the four models is solely determined by the electronic contributions. Therefore, we employed the four models to investigate the relationship between E_ad and the electronic structure change by O₂ adsorption. It should be noted that the values of E_ad of the four models are almost independent of the degree of charge transfer, which is almost common to the four systems: −0.61 e (3–12), −0.62 e (7–11 and 10–12), and −0.64 e (8–13).

We first analyzed the LDOSs of the four O₂ adsorption sites in the Pt₁₃ moiety. However, no clear feature was found in the LDOS because of the complex spectral profiles with multiple peaks (see Fig. S6, ESI†). Therefore, we herein present an original approach of electronic structure analysis, focusing on the feature of metal sub-nanoclusters, that is, a large number of electronic states around the Fermi level. The data in Table 1 and Fig. 2 and 3 suggest that the adsorption of O₂ on the Pt₁₃/graphene heterostructure is mainly governed by chemical interactions between the unoccupied orbitals in O₂ and the occupied orbitals in the Pt moiety. Thus, we introduce the integrated LDOS defined as

where E is the band energy, E_F is the Fermi level energy, and d_α(E) is the LDOS of the αth adsorption site, i.e., the two Pt atoms on which O₂ is adsorbed.

Fig. 6 shows the difference in the D_α(E) owing to O₂ adsorption, defined as

ΔD_α(E) ≡ D_α,af(E) − D_α,bef(E) (2)

for the four systems. For example, the result of “8–13” was obtained using the sum of the LDOSs of 8th and 13th Pt atoms, of which the number is shown in Fig. 1. The integration of LDOS using eqn (1) yields a smooth profile, whose characteristics can be clearly determined, because multiple peaks and troughs in the LDOS profile (see Fig. S6(c), ESI†) are smoothed. The respective contributions, D_α,af and D_α,bef(E), are given in the ESI,† Fig. S7.

Fig. 6 ΔD_α(E) of the Pt₁₃ moiety and Pt slab. The adsorption energies, E_ad, of the different systems are given in the figure. The decrease (A) and increase (B) from the Fermi level are indicated by black arrows.

Fig. 7 shows a schematic of the relationship between ΔD_α(E) (solid line) and the associated LDOSs (dash line). The reduction in ΔD_α(E) from the Fermi level (arrow A in Fig. 6 and 7) is caused by the decrease in the LDOS in the Pt moiety following O₂ adsorption. For example, ΔD_α(E′) in Fig. 7 is given by the area D_α,bef in which the orbitals are expended to form bonding orbitals with the orbitals of O₂. The increase in ΔD_α (arrow B in Fig. 6 and 7) is mainly attributed to the generation of bonding orbitals after O₂ adsorption. Fig. 7 illustrates the increase in ΔD_α around E′′ caused by the generated LDOS in the area of ΔD_α,af. Therefore, the profile of ΔD_α indicates the mechanism of the orbital mixing of O₂ and the Pt₁₃ moiety of which most of the Pt orbitals before O₂ adsorption below the Fermi level are assigned to d-orbitals that can interact with the orbitals of O₂ (Fig. S8 in the ESI†). Indeed, the LDOSs of Pt and O are distributed in a wide energy region after O₂ adsorption (Fig. S9 in ESI†).

Fig. 7 Scheme of relationship among the integrated LDOS of Pt expended for Pt–O bonding D_α,bef (red dash), generated via O₂ adsorption D_α,af (blue dash), and their difference ΔD_α (black solid).

The sharp trough in the LDOS at −2 eV in Fig. 6, which is common to the different Pt₁₃ models, except for the 8–13 model (orange plot), indicates that the occupied orbitals in the Pt moiety with energies exceeding −2 eV are used to generate bonding orbitals with energies less than −2 eV. Indeed, compared to the result of the four models (i.e., 3–12, 7–11, 10–12, and 8–13), the adsorption energy increases as the trough becomes deep near the Fermi level (above −2 eV). The order of the trough depth confirms that the adsorption energy is determined by the electronic interactions between the occupied orbitals of the Pt moiety near the Fermi level and the orbitals of the O₂ molecule. The correlation between D_α,af(E) or D_α,bef (E) and the adsorption energy is weak (Fig. S7 in ESI†). However, at least, D_8−13,bef(E) is small near the Fermi level compared with those of the other three models, indicating that the large LDOS in the Pt₁₃ moiety plays a crucial role in its large adsorption energy.

Previous studies on Pt sub-nanoclusters suggested that the atomic charge on each Pt atom is closely correlated with the Pt–O interaction.^6,7 This result is partially reasonable, because the atomic charge tends to become more negative as the LDOS near the Fermi level increases. However, the tendency is not always observed, because the LDOS profiles of respective atoms in a metal sub-nanocluster often differ significantly. Indeed, in this study, the O₂ adsorption energy on the Pt₁₃ model was found to be almost independent of the atomic charge of Pt (Fig. S10, ESI†).

For comparison, the results of the Pt slab are also shown in Fig. 6. The LDOS profiles of the Pt slab and Pt₁₃/graphene heterostructure are remarkably different. The ΔD_α(E) of the Pt slab does not have a sharp trough; instead, it has a broad distribution in the range of −4 to −1 eV. This broad distribution of ΔD_α(E) is attributed to the negation of the decrease in the occupied orbitals in the Pt moiety with the increase in the Pt–O bonding orbitals; that is, the electronic interaction between the Pt slab and O₂ occurs over a wide energy range because of the delocalized DOS compared with that of the Pt₁₃ model (see Fig. 3(b) and (c)). The mechanism of the electronic structure change for the Pt slab is reminiscent of the d-band center model.¹⁰ In this model, the adsorption energy is rationalized based on a low energy region located away from the Fermi level by a few eV, and the details near the Fermi level have a minor contribution. The analysis presented in Fig. 6 reveals a strong contribution of the orbitals near the Fermi level as an inherent characteristic of sub-nanoclusters, which is significantly different from the results of the Pt slab used for modeling a large Pt particle. The integrated LDOS shows that the amount of LDOS change governs the O₂ adsorption energy on the Pt sub-nanocluster.

Based on the above analysis, we summarize the scheme of O₂ adsorption in Fig. 8, where the schematic electronic states of O₂ (left-hand side) and Pt (right-hand side) are shown, with the thickness of the orange bar representing the number of DOS. Fig. 8(a) shows the energy diagram for Pt₂–O₂ interaction, in which the electronic states of the Pt₂–O₂ complexes are shown in the middle. The orbitals of the Pt₂ cluster are discretized because the number of atoms is significantly small. As the particle size increases, the orbital distribution becomes broad. Consequently, as shown in Fig. 8(b), the orbitals in the Pt₁₃ moiety illustrated with the thick bar are largely distributed near the Fermi level and thus strongly interact with the π* orbitals of O₂ (black dotted box in Fig. 8(b)), resulting in large stabilization following O₂ adsorption. The electronic states in the Pt slab (Fig. 8(c)) are delocalized over a wider energy range compared with those in the Pt₂ and Pt₁₃ models. The LDOS near the Fermi level is small owing to the delocalized distribution of the states. Therefore, the interaction between the occupied orbitals of the Pt slab and the π* orbitals of O₂ has a relatively smaller contribution than in the case of the Pt₁₃ sub-nanocluster. The present analysis of the electronic structure reveals the inherent characteristic of Pt sub-nanoclusters, which differs from that of a Pt slab, in terms of the mechanism of O₂ adsorption.

Fig. 8 Schematic showing the change in the electronic structure following O₂ adsorption onto (a) Pt₂, (b) Pt₁₃, and (c) a Pt slab.

Conclusion

We elucidated the inherent characteristics of the electronic structure change in a Pt sub-nanocluster caused by oxygen adsorption, which differs from the change in a Pt slab. The adsorption energy depends strongly on the atomic sites in the Pt sub-nanocluster owing to its complex electronic structure. The d-band center is not useful to investigate metal sub-nanoclusters; thus, we present an original scheme for analyzing the electronic structure of metal sub-nanoclusters. The integrated LDOS was introduced to analyze the electronic states near the Fermi level. The analysis revealed a clear relationship between the variation in the LDOS near the Fermi level and the adsorption energy for the Pt sub-nanocluster. Furthermore, the variation in the LDOS of the Pt sub-nanocluster was found to be markedly different from that of the Pt slab. The proposed analysis suggests that the mechanism of O₂ adsorption onto a Pt sub-nanocluster is significantly different from that observed with a large Pt particle.

The present scheme of analysis is expected to contribute to the investigation of various metal sub-nanoclusters, because it focuses on the general features of metal sub-nanoclusters whose orbitals tend to be distributed near the Fermi level compared with those of large particles. Another topic that needs to be investigated is geometrical changes in metal sub-nanoclusters during a chemical process. Understanding the electronic structure is a preliminary but essential step in the investigation of the changes in the geometry of a system. In this regard, the present study paves the way for investigating chemical processes governed by the inherent features of metal sub-nanoclusters.

Author contributions

K. I. and J. H. planned the study. H. H., K. I., and J. H. drafted the manuscript. H. H. performed the calculations. All authors have approved the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This study was financially supported by JSPS KAKENHI (Grant No. 23K17898 and 24K08346) and the Collaborative Research Program of the Institute for Chemical Research, Kyoto University (Grant No. 2022-61 and 2023-70). This work was also supported by the MEXT project, “Integrated Research Consortium on Chemical Sciences” and the Photo-excitonix Project of Hokkaido University. Most of the theoretical computations were performed using the computational resources of the Grand Chariot supercomputer provided by Hokkaido University through the HPCI System Research Project (Project ID: hp230155 and hp240155). Some of the computations were performed at the RCCS (Okazaki, Japan; Project: 23-IMS-C002), Super Computer System, Institute for Chemical Research (Kyoto University), and ACCMS (Kyoto University).

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Footnote

† Electronic supplementary information (ESI) available: Relative energies and atomic charges after O₂ adsorption; dependence of the coordination number on O₂ adsorption energy; relationship between the contributions of changes in geometric and electronic structures to O₂ adsorption energy; local density of states before and after O₂ adsorption; integrated local density of states. See DOI: https://doi.org/10.1039/d4cp00555d

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