Atomic structure of the La/Pt(111) and Ce/Pt(111) surfaces revealed by DFT+U calculations

Abstract

Platinum–lanthanide surface alloys have attracted great interest as promising catalysts in oxygen reduction reactions, however, our atomistic understanding of the surface structure of these systems is far from satisfactory. In this work, we investigated LnPt₅/Pt(111) systems (Ln = La and Ce) employing ab initio molecular dynamics based on density functional theory with Hubbard model corrections. In the lowest energy structure, the surface layers are stacked as Pt₄/LnPt₂/Pt₃/Pt(111) in the 2 × 2 surface unit cell, which implies a strong preference of the La and Ce atoms as subsurface layers, and hence, a full Pt monolayer is exposed to the vacuum region. Thus, the work function and d-band center of the occupied states of the topmost layer are only slightly affected by the presence of the La and Ce atoms in the subsurface layer compared with the clean Pt(111) results. In contrast, in the highest energy surface structures, LnPt₂/Pt₄/Pt₃/Pt(111), the La and Ce atoms are exposed to the vacuum region, and hence, the work function is about 1.0 eV lower than in the clean Pt(111) surface, and the d-band center is shifted towards the Fermi level by about 0.40 eV. Although one of the Ce 4f-states is occupied and shows a localized nature, the surface structures, geometric parameters, and electronic properties are very similar for both LaPt₅/Pt(111) and CePt₅/Pt(111) systems.

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1 Introduction

Catalysts based on platinum–metal (PtM) alloys have been considered as promising candidates to improve the slow rate of the oxygen reduction reaction (ORR) for low temperature polymer electrolyte membrane fuel cells.¹ Thus, several experimental and theoretical studies have been reported with the aim of identifying a PtM combination that increases the ORR activity compared with traditional Pt catalyts,^2–7 however, most of those studies have focused on the combination of Pt with traditional transition-metal systems (e.g., PtSc, PtTi, PtFe, PtCo, PtNi, PtY, etc.). Recent experimental studies have shown that an alternative class of Pt-based alloys, namely, Pt–lanthanide (e.g., PtLa, PtCe, PtGd, etc.), can increase the activity of the ORR by a factor larger than 2 compared with traditional PtM catalysts at potentials from 0.87 to 0.90 V,^8,9 which was discussed in terms of strain and electronic effects. Although several experimental studies have been reported for La and Ce films supported on Pt(111) in the past twenty years,^10–15 our atomistic understanding is still far from satisfactory (see below).

Films of La and Ce supported on Pt(111) have been studied using several experimental techniques, namely, X-ray photoemission spectroscopy (XPS),^10,15 low energy electron diffraction (LEED),^10–12,15 scanning tunneling microscopy (STM),^11,14 angle resolved X-ray photoelectron spectroscopy (AR-XPS),¹³ etc.¹⁵ All those studies have indicated that the La and Ce coverages and annealing temperature play a crucial role in the surface structure formations on the Pt(111) substrate, which is expected as the mobility and migration of the La and Ce adatoms on and in the surface strongly depend on temperature effects to overcome the energy barriers. For example, XPS and LEED studies have identified that ordered surface structures cannot be formed after deposition at room temperature, while a heat treatment at 770 K induces the formation of ordered structures, namely, a surface (1.94 × 1.94) unit cell (i.e., nearly (2 × 2)) with CePt₃ surface composition was observed for an initial coverage of 0.9–1.8 monolayers (ML), while an increase in the coverage (e.g., 2.1–3.5 ML) induces the formation of a surface (1.96 × 1.96) unit cell with a rotation of about 30°. For both structures, the substrate symmetry plays a key role.¹⁰

An angle-resolved photoemission study has indicated the formation of a (2 × 2) surface unit cell with sixfold symmetry for Ce deposited on Pt(111) at room temperature and annealed to 900 K.¹³ The formation of the (2 × 2) surface unit cell was observed by LEED for La adatoms deposited on Pt(111) at 3 ML coverage and also annealed to 900 K.¹² Thus, similar behavior occurs for both systems, which might be expected as both LaPt and CePt systems form similar bulk structures,^16,17 and their atomic numbers differ only by one unit. Furthermore, STM experiments indicated that the (2 × 2) surface unit cell is composed of a two-dimensional structure with CePt₅ composition,¹⁴ which has also been observed for the respective bulk systems.^16,17

Furthermore, AR-XPS indicated the formation of Pt overlayers (3 ML) on the surfaces with LaPt₅ and CePt₅ composition,⁹ (i.e., a strong preference of the La and Ce atoms for subsurface sites), however, recent studies have found indications for La atoms on the LaPt₃/Pt(111) substrate,⁸ which might be explained by the deposition and annealing temperatures. Based on experimental observations and bulk structures, it was suggested that the CePt₅ surface structure is composed of alternating CePt₂ layers and Pt Kagomé net (ABAB layered arrangements of the surface),¹¹ however, this suggestion has not been confirmed by theoretical studies. To our knowledge, there is only one density functional theory (DFT) investigation of the La/Pt(111) system,⁸ which found that the most stable configurations are formed by an LaPt surface alloy, and hence, the La atoms are exposed to the vacuum region, which is not consistent with experimental observations.^10–15

Although several studies have been reported, our atomistic understanding of the surface structure models formed on the Ln/Pt(111) systems is still incomplete for Ln = La, Ce. Therefore, in this work, we report a first-principles investigation of the La/Pt(111) and Ce/Pt(111) systems; in particular, we will focus on the formation of surface structures with LnPt₅ compositions on Pt(111) employing a (2 × 2) surface unit cell. Our calculations combine first-principles molecular dynamics (MD) with zero temperature geometric optimization, which can provide a clear picture for the atomistic surface models.

2 Theoretical approach and computational details

2.1 Total energy calculations

We carried out spin-polarized DFT^18,19 calculations within the generalized gradient approximation²⁰ formulated by Perdew–Burke–Ernzerhof²¹ (PBE) to the exchange–correlation (XC) energy functional. To improve the description of the Ce 4f-states, which can show itinerant or localized behavior according to the chemical environment,²² we employed the rotationally invariant approach proposed by Dudarev et al.²³ We used an effective Hubbard parameter (U_eff = U − J) of 4.50 eV, which has been successfully employed in previous DFT+U calculations for cerium-based compounds.^22,24–28 In contrast with the Ce 4f-states, the La 4f-states show only an itinerant behavior to our knowledge, however, their relative position with respect to the Fermi level is not properly described by semilocal XC functionals such as PBE. Thus, we added also a U_eff of 4.50 eV for the Ln 4f-states. To solve the DFT+U equations, we employed the all-electron projected-augmented wave (PAW) method^29,30 and the PAW projectors³¹ as implemented in the Vienna Ab initio Simulation Package.^32,33

For the total energy Ln/Pt(111) calculations, we employed a cutoff energy of 342 eV, however, for the equilibrium volume calculations using stress tensor and atomic forces minimization, we employed a cutoff energy of 609 eV for bulk LnPt₅ in the hexagonal structure, while for bulk Pt in the face-centered cubic structure, we employed 497 eV. For the Brillouin zone (BZ) integration, we employed a 6 × 6 × 1 k-point mesh for the Ln/Pt(111) calculations, while for the bulk systems, we employed 12 × 12 × 13 and 22 × 22 × 22 k-point meshes for LnPt₅ and Pt, respectively. To obtain high quality density of states (DOS), fine k-meshes were employed, namely, 12 × 12 × 1 and 8 × 8 × 1 for LaPt₅/Pt(111) and CePt₅/Pt(111), respectively. For the total energy convergence, we employed a criteria of 10⁻⁵ eV, and all the geometries reached equilibrium once the atomic force on every atom was smaller than 0.05 eV Å⁻¹.

2.2 Atomic structure generation

As mentioned in the introduction, experimental studies¹⁴ found evidence for the formation of a 2 × 2 surface structure with LnPt₅ composition on Pt(111), which will also be considered in this work. In the Pt(111)-2 × 2 surface unit cell, there are four Pt atoms per layer, and hence, a LnPt₅ composition requires at least two layers to be achieved. For example, using two layers with the same number of atoms (e.g., LnPt₂ and Pt₃) or layers with different numbers of atoms (e.g., LnPt and Pt₄). The hexagonal bulk LnPt₅ structure is characterized by alternating stacking of LnPt₂ and Pt₃ (Kagomé net) layers along the [0001] direction.^16,17 Thus, to obtain a correct description of the surface atomic structure for LnPt₅/Pt(111), we employed the repeated slab geometry with 7 layers of Pt(111)-2 × 2 slabs separated by a vacuum region of 12 Å, and the addition of the two layers of LnPt₅ yields a slab with 9 layers. Thus, our challenge is the identification of the atomic positions of the LnPt₅ atoms on Pt(111). Therefore, we considered several initial model structures, which are schematically indicated in Fig. 1. We considered the exchange of the topmost three layers in the LnPt₅/Pt(111) slab, and hence, six different initial surface structure models were designed (numbered from M1 to M6).

Fig. 1 Side views of the initial structure configurations for the (2 × 2) surface unit cell models employed for the ab initio molecular dynamics simulations (T_initial = 2000 K, T_final ≈ 0 K) for the LnPt₅/Pt(111), Ln = La, Ce, systems. Here, Ln and Pt atoms are presented in light green and gray, respectively.

To identify the lowest energy configuration for every initial model structure, the following steps were performed. Ab initio molecular dynamics (MD) calculations for about 30 ps (time step of 3 fs) were performed for LnPt₅/Pt(111), employing T_initial = 2000 K and T_final ≈ 0 K for each of the initial configurations indicated in Fig. 1. For those MD calculations, only the topmost four layers were relaxed, while the remaining Pt atoms were frozen in their bulk-like positions. Along the MD calculations, seven configurations were selected for each initial model (called A, B, C, D, E, F, G), and those configurations were optimized using the conjugated gradient algorithm as implemented in VASP, and a large value for the atomic displacements was employed in order to help to identify the lowest energy local minimum configuration. For those optimizations, all the topmost 8 layers were relaxed. Thus, a set of 42 local minimum configurations was obtained for each system, which contained representative structural models that provide the possibility to build up a deep understanding of the LaPt₅/Pt(111) and CePt₅/Pt(111) systems. Although the configuration with LnPt and Pt₄ layers supported on Pt(111) was not initially considered, we would like to point out that along the MD simulation all configurations are equally possible to obtain.

3 Results and discussion

3.1 Bulk results

The bulk LnPt₅ systems crystallize in the hexagonal CaCu₅-type structure (space group P6/mm) with one formula unit (f.u.) per unit cell.^16,17 Thus, it has hexagonal symmetry and a six-fold symmetry axis perpendicular to the (0001) plane. The crystal structure can be seen as a layered structure, in which the LnPt₂ (A) and Pt₃ (B) layers are stacked along the [0001] direction (i.e., an ABABABAB sequence). The top and side views of the LnPt₂ and Pt₃ layers are shown in Fig. 2. We found a₀ = 5.46 Å and c₀ = 4.43 Å for LaPt₅, and a₀ = 5.41 Å and c₀ = 4.44 Å for CePt₅, which are larger than the experimental results by up to 1.3% for both a₀ and c₀ parameters (a₀ = 5.39 Å and c₀ = 4.38 Å for LaPt₅,¹⁷ and a₀ = 5.37 Å and c₀ = 4.38 Å for CePt₅ (ref. 16)).

Fig. 2 Top and side views of the bulk LnPt₅ structures (Ln = La, Ce): (a) first and (b) second topmost layers.

For bulk Pt, we obtained a lattice constant of 3.98 Å, which is 1.53% larger than the experimental findings (i.e., 3.92 Å).³⁴ Thus, the lattice constant of the hexagonal 2 × 2 surface unit cell is equal to 5.63 Å, which is 3.1% and 3.5% larger than a₀ obtained for LaPt₅ and CePt₅ in the hexagonal structure, respectively. Therefore, we can conclude that the deposition of two layers (LnPt₂ and Pt₃) on Pt(111) leads to an expansive strain on the LnPt₅ layers. Furthermore, the interlayer spacing along the [111] direction is 2.30 Å, while the interlayer separation is 2.22 Å for both LnPt₅ systems, and hence, we would expect interlayer spacing contractions for the cases in which the La and Ce atoms are located in subsurface positions.

In the LnPt₂ layer, all the Ln atoms are surrounded by six Pt atoms. Furthermore, we can describe the LnPt₂ layer as a hexagonal unit cell with lattice parameter a₀ with two Pt atoms located in the fcc (face-centered cubic) and hcp (hexagonal close-packed) sites. In the Pt₃ layer, the Pt atoms form a Kagomé net, in which the Pt atoms form an array of connected triangular structures. The hole site at the center of the Kagomé net is located directly above the Ln atoms in the layer below and above the Pt₃ layer, which helps to minimize the strain energy of the system as the Ln and Pt atoms have different atomic radii. For example, Ln atoms have a larger atomic radius than Pt atoms (e.g., the ionic radii of La, Ce, and Pt in high coordinated metals are 1.88, 1.82, and 1.39 Å).

From our analysis, the LnPt₂ layer plays a key role in the size of the a₀ lattice parameter. For example, both layers have 3 atoms, namely, LnPt₂ and Pt₃, however, as the atomic radii of the Ln atoms are larger than that of Pt, we would need a large space to accommodate the Ln and Pt atoms that form the LnPt₂ layer, while the same is not true for the Pt₃ layer. The mesh of both LnPt₂ and Pt₃ layers plays a key role in the c₀ lattice parameter. c₀/2 is the interlayer spacing between the layers, and hence, the location of the hole in the Kagomé net plays a crucial function in the c₀ parameter, as it provides further space to fit the Ln atoms. As discussed through the paper, this feature is of critical importance in the atomic structure, as it determines the magnitude of the strain energy in the xy-plane and the interlayer distances between the topmost surface layers.

3.2 LaPt₅ and CePt₅ supported on Pt(111)

3.2.1 Surface model structures. Using the procedure discussed above, we obtained a set of 42 local minimum configurations for each system. The relative total energies with respect to the lowest energy configuration (ΔE = E^{config i}_tot − E^lowest_tot) are shown in Fig. 3. For both systems, all the relative total energies are spread from 0 to 1.6 eV for LaPt₅/Pt(111) and from 0 to 2.4 eV for CePt₅/Pt(111), however, there are clear differences among the systems. Although the same procedure was applied for both systems, we found several plateaus, in particular for LaPt₅/Pt(111), which can be explained as follows. Using a global optimization algorithm such as the Revised Basin Hopping Monte Carlo (RBHMC),³⁵ we would obtain the same result for different initial configurations (i.e., a plateau with 42 identical energies), however, using local optimization algorithms such as the conjugated gradient implemented in VASP, the final optimized structure depends on the initial structure. Thus, our results indicate that LaPt₅/Pt(111) is less sensitive to the initial configuration as several different configurations lead to the same structure, which explains the plateaus, however, the same does not hold for CePt₅/Pt(111), which shows a much more complex potential energy surface due to the occupation of the Ce 4f-states.

Fig. 3 Relative total energy for all calculated CePt₅/Pt(111) and LaPt₅/Pt(111) configurations. Here, the configurations are represented by surface structural models (from M1 to M6) and different isomers (the alphabetic letters from A to G).

For each surface model indicated in Fig. 1, we obtained the lowest energy configuration, and these are shown in Fig. 4, namely, 4A, 6F, 3F, 2C, 1F, 5E for LaPt₅/Pt(111) and 4B, 6F, 3A, 2F, 1E, 5F for CePt₅/Pt(111). Although the initial surface models were different for every case, the final optimized configurations indicated that some models were unstable, and large structure reorganization occurred along the MD calculations and geometric optimizations. For example, the M3 and M6 models, in Fig. 3, differ in the number of Pt atoms exposed to the vacuum region, namely, there are four Pt atoms exposed to the vacuum in model M3, while there are only 3 Pt atoms in model M6, however, once the optimization was performed both models had 4 Pt atoms exposed to the vacuum region. Thus, there is a strong preference for Pt vacancies in subsurface sites, which explains the degenerate configurations for both systems (e.g., 3F and 6F for LaPt₅/Pt(111) and 3A and 6F for CePt₅/Pt(111)).

Fig. 4 Top and side views of the lowest energy configurations for each of the surface structure models of the LaPt₅/Pt(111) and CePt₅/Pt(111) systems (see Fig. 1) along with their relative total energies. The lowest energy configurations are presented by the model (from M1 to M6) and corresponding isomer.

The atomic configurations derived from the surface models M1 and M5 by MD simulations yield the highest energy surface structures, in which the LnPt₂ plane is exposed to the vacuum region. The relative energies are 1.36 eV (5E) for LaPt₅/Pt(111) and 1.77 eV (5F) for CePt₅/Pt(111). Thus, La and Ce atoms have a strong preference for subsurface layers. The location of La and Ce adatoms on Pt(111) depends strongly on the experimental conditions, for example, surface annealing treatments, which play a crucial role in the surface structure.

The surface structure derived from the M4 model, Pt₄/LnPt₂/Pt₃/Pt(111), and MD simulations yield the lowest energy surface structure for both systems, in which the LnPt₂ plane is located in the second layer, and a full Pt monolayer is exposed to the vacuum region, namely, model 4A for LaPt₅/Pt(111) and model 4B for CePt₅/Pt(111) in Fig. 4. To obtain a better understanding of the atomic structure of the lowest energy surface model, we show the top and side views of the topmost four surface layers in Fig. 5. For both systems, the topmost layer is a full Pt monolayer (Pt₄), the Ln atoms are surrounded by six Pt atoms in the second layer, LnPt₂, (i.e., the Ln atoms are located in the center of the hexagon), the third layer contains only Pt atoms, and a vacancy site is located exactly below the Ln atom located in the second layer (Pt Kagomé net), and the forth layer is composed only of Pt atoms and forms a full Pt monolayer following the stacking of the Pt(111) surface. The location of the Ln atoms is connected to the vacancy sites due to the large size of the atomic radius of the Ln atoms compared with the Pt atoms. For example, the ionic radii of La, Ce, and Pt in high coordinated metals are 1.88, 1.82, and 1.39 Å, respectively. Our findings are consistent with electrochemical experimental results^9,14,15 and previous DFT calculations for the surface atomic structure of Pt–transition-metal alloys, which indicates the importance of a Pt skin on the stability of those systems.⁵

Fig. 5 The lowest energy surface structure models for the LaPt₅/Pt(111) and CePt₅/Pt(111) systems: top and side views of the first, second, third, and fourth layers.

3.2.2 Structural parameters. To obtain a better understanding of the structure models, we calculated the interlayer relaxations of the topmost interlayer spacings, , where d_ij is the interlayer distance between the layers i and j, while , where a₀ is the lattice constant of bulk Pt. The results are summarized in Table 1. Our results for the clean Pt(111) surface are in good agreement with previous DFT calculations,^36,37 as well as with experimental results (Δd₁₂ = +0.5 to +2.5%).³⁸

Table 1 Surface properties of the LaPt₅/Pt(111) and CePt₅/Pt(111) systems: relative total energies for the surface configurations, ΔE, interlayer relaxations, Δd_ij, of the topmost surface layers, work function, Φ, center of gravity of the occupied d-states for the topmost four layers, ε¹_d, ε²_d, ε³_d, and ε⁴_d for the surface configurations shown in Fig. 4

Stack layers		ΔE (eV)	Δd12 (%)	Δd23 (%)	Δd34 (%)	Δd45 (%)	Φ (eV)	ε^1d (eV)	ε^2d (eV)	ε^3d (eV)	ε^4d (eV)
LaPt2/Pt3/Pt4/Pt(111)	5E	1.36	−13.83	−2.36	+0.11	−0.34	4.73	−2.14	−2.87	−3.03	−3.08
LaPt2/Pt3/Pt4/Pt(111)	1F	1.36	−13.78	−2.34	+0.11	−0.18	4.90	−2.14	−2.95	−3.03	−3.08
Pt3/LaPt2/Pt4/Pt(111)	2C	0.72	−15.42	+4.51	+1.38	−0.10	5.38	−2.48	−2.78	−3.04	−3.04
Pt4/Pt3/LaPt2/Pt(111)	3F	0.65	−2.38	−15.06	+5.15	+1.49	5.71	−2.44	−3.06	−2.86	−3.01
Pt4/Pt3/LaPt2/Pt(111)	6F	0.65	−2.55	−15.46	+5.01	+1.54	5.71	−2.43	−3.08	−2.88	−3.02
Pt4/LaPt2/Pt3/Pt(111)	4A	0.00	+3.48	−13.27	−2.36	+0.24	5.52	−2.54	−2.84	−3.13	−3.03
CePt2/Pt3/Pt4/Pt(111)	5F	1.77	−14.39	−2.56	+1.35	+0.88	4.79	−2.18	−2.95	−3.00	−3.03
CePt2/Pt3/Pt4/Pt(111)	1E	1.37	−14.78	−2.33	+0.16	−0.15	4.80	−2.19	−2.96	−3.03	−3.08
Pt3/CePt2/Pt4/Pt(111)	2F	0.92	−16.11	+3.48	+2.44	+0.73	5.37	−2.51	−2.85	−3.03	−2.99
Pt4/Pt3/CePt2/Pt(111)	3A	0.67	−2.64	−16.51	+4.17	+1.00	5.70	−2.44	−3.19	−3.02	−3.06
Pt4/Pt3/CePt2/Pt(111)	6F	0.66	−2.76	−16.03	+4.43	+1.17	5.70	−2.45	−3.18	−3.00	−3.06
Pt4/CePt2/Pt3/Pt(111)	4B	0.00	+2.83	−14.15	−2.65	+0.11	5.46	−2.58	−2.94	−3.19	−3.03
Pt(111)			+0.64	−0.90	−0.55	−0.55	5.70	−2.51	−3.06	−3.16	−3.13

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In the lowest energy surface structures, we obtained an expansion of the topmost interlayer spacing by +3.48% for LaPt₅/Pt(111) and +2.83% for CePt₅/Pt(111), while the second interlayer spacing contracts by −13.27% and −14.15%, respectively. Several effects contribute to explain those results: (i) the interlayer spacing in the bulk LnPt₅ systems is 2.22 Å for both systems, which is smaller by 3.5% than d₀, and hence, we would expect a contraction in the second interlayer spacing (LnPt₂–Pt₃). The interlayer LnPt₂–Pt₃ contraction has similar magnitude for different locations of the double layer. (ii) One of the Pt atoms in the topmost layer is located exactly on top of the Ln atoms in the second layer, and hence, a strong repulsive force is built-in, which moves the topmost layer up and pushes down the second layer. (iii) Furthermore, there is an expansive strain in the double layer formed by LnPt₂Pt₃ due to the differences in the lattice constants, which will also affect the interlayer spacings.

3.2.3 Work function and density of states. To characterize the electronic properties of the LnPt₅/Pt(111) systems, we calculated the work function, Φ, and d-band center of the occupied states (four topmost layers) for all the surface model structures shown in Fig. 4, which are summarized in Table 1. The local DOS (LDOS) are shown in Fig. 6 for the lowest energy configurations. For the clean Pt(111) surface, we obtained a work function of 5.70 eV, while previous DFT calculations gave 5.69 eV (ref. 36), and the experimental results are spread from 5.70 to 6.40 eV.^39,40

Fig. 6 Local density of states for the lowest energy LaPt₅/Pt(111) and CePt₅/Pt(111) structures. The dashed vertical lines indicate the Fermi levels, while the continuous lines indicate the d-band center of the respective layers. The two numbers within every figure are the d-band center of the corresponding layer, ε¹_d, for LnPt₅/Pt(111) and the clean Pt(111) surface.

For LaPt₅/Pt(111) and CePt₅/Pt(111) in the lowest energy structures, we obtained Φ = 5.52 and 5.46 eV, which yield a substrate work function reduction by 0.18 and 0.24 eV, respectively. The slight change in the work function is due to the Pt surface termination in both systems. For example, both Pt(111) and LnPt_n/Pt(111) are terminated by a full Pt monolayer exposed to the vacuum region. This argument is also supported by the work function of 5.71 eV obtained for 3F and 6F (LaPt₅/Pt(111)) and of 5.70 eV for 3A and 6F (CePt₅/Pt(111)). In contrast with those results, we found large changes in the Pt(111) work function (from 0.80–1.0 eV) for the surface model structures with La and Ce atoms exposed to the vacuum region, which is the case of the 1F and 5E models for LaPt₅/Pt(111) and 1E and 5F for CePt₅/Pt(111). Thus, the substrate work function depends strongly on the location of the La and Ce atoms, and hence, on the experimental annealing temperature.

We found that the d-band center follows a similar pattern to the work function, i.e., the d-band center of the topmost layer, ε¹_d, is very similar for both Pt(111), −2.51 eV, and the lowest energy surface models for LaPt₅/Pt(111), −2.54 eV, and CePt₅/Pt(111), −2.58 eV, which can be seen in Fig. 6. Thus, the effects induced by the second layer, LnPt₂, are almost negligible, however, the same is not the case for the highest energy configuration with the La and Ce atoms exposed to the vacuum region (ε = −2.14 eV for LaPt₅/Pt(111) and −2.18 eV for CePt₅/Pt(111)). Thus, based on the d-band model proposed by Nørskov et al.,^41,42 we would expect similar adsorption energies for molecular adsorbates on the Pt(111) and Pt₄/LnPt₂/Pt₃/Pt(111) substrates, however, we would observe a strong adsorption energy for molecular systems on LnPt₂/Pt₄/Pt₃/Pt(111) as the d-band center is closer to the Fermi energy than for the Pt(111) surface.

Furthermore, it can be seen in Fig. 6 that an occupied Ce 4f-state is located near to the Fermi level, indicating the localized character of the Ce 4f-state, however, similar behavior is not observed for LaPt₅ as the La 4f-states are unoccupied. Although the behavior of the 4f-states is completely different, we found that the work function and d-band center of the occupied states in both systems follow the same pattern. Therefore, the occupation of the 4f-states does not play a crucial role in the surface properties, as least in the lowest energy configurations terminated by a Pt ML.

4 Conclusion

In this work, we carried out DFT+U calculations of the atomic structures of the LaPt₅/Pt(111) and CePt₅/Pt(111) systems. Using ab initio MD simulations, we built a hierarchical set of 42 surface model structures for each system. The most important conclusions are the following.

Although both La and Ce atoms have different electronic structures due to the localization of the occupied Ce 4f-states, we found similar surface model structures for both LaPt₅/Pt(111) and CePt₅/Pt(111) systems. In the lowest energy structure, the surface layers are stacked as Pt₄/LnPt₂/Pt₃/Pt(111) in the 2 × 2 surface unit cell, which implies a strong preference of the La and Ce atoms by subsurface layers. Thus, a full Pt monolayer is exposed to the vacuum region, which is consistent with experimental results. Furthermore, we confirmed the formation of alternating layers of LnPt₂ and Pt Kagomé net.¹¹ We found that the surface properties, such as the work function and d-band center of the occupied states (topmost layer), are only slightly affected by the presence of the La and Ce atoms in the second layer compared with the clean Pt(111) results.

In contrast, in the higher energy surface structures, LnPt₂/Pt₄/Pt₃/Pt(111), the La and Ce atoms are exposed to the vacuum region, and hence, the work function is about 1.0 eV lower than in the clean Pt(111) surface, which indicates a strong effect in the surface potential. Thus, the d-band center of the occupied states is also affected, for example, the d-band center shifts closer to the Fermi level in the high energy configurations, and hence, based on the d-band model, we would expect a stronger adsorption energy for molecular systems on LnPt₂/Pt₄/Pt₃/Pt(111) than on Pt(111).

Furthermore, we found large interlayer relaxations between the LnPt₂–Pt₃ layers, which is due to the smaller interlayer separation of those layers in the bulk LnPt₅ systems, the location of a Pt atom directly above the Ln atom, and the expansive strain due to the smaller lateral lattice constant. In short, we have provided a picture of the atomistic surface models for Ln/Pt(111) systems (Ln = La, Ce), which could become promising candidates to improve the chemical and physical properties of the common catalysts.

Acknowledgements

The authors thank the São Paulo Research Foundation (FAPESP), Rio Grande do Sul Research Foundation (FAPERGS), National Council for Scientific and Technological Development (CNPq), and Coordination for Improvement of Higher Level Education (CAPES) for financial support. The authors also thank the Department of Information Technology – Campus São Carlos for the infrastructure provided to our computer cluster.

References

1. H. A. Gasteiger, S. S. Kocha, B. Sompalli and F. T. Wagner, Appl. Catal., B, 2005, 56, 9–35.
2. V. R. Stamenkovic, B. S. Mun, K. J. J. Mayrhofer, P. N. Ross and N. M. Markovic, J. Am. Chem. Soc., 2006, 128, 8813–8819.
3. V. R. Stamenkovic, B. S. Mun, M. Arenz, K. J. J. Mayrhofer, C. A. Lucas, G. Wang, P. N. Ross and N. M. Markovic, Nat. Mater., 2007, 6, 241–247.
4. V. R. Stamenkovic, B. Fowler, B. S. Mun, G. Wang, P. N. Ross, C. A. Lucas and N. M. M. rkovic, Science, 2007, 315, 493–497.
5. J. Greeley, I. E. L. Stephens, A. S. Bondarenko, T. P. Johansson, H. A. Hansen, T. F. Jaramillo, J. Rossmeisl, I. Chorkendorff and J. K. Nørskov, Nat. Chem., 2009, 1, 552–556.
6. I. E. L. Stephens, A. S. Bondarenko, U. Grønbjerg, J. Rossmeisl and I. Chorkendorff, Energy Environ. Sci., 2012, 5, 6744–6762.
7. R. L. H. Freire, A. Kiejna and J. L. F. Da Silva, J. Phys. Chem. C, 2014, 118, 19051–19061.
8. S. J. Yoo, S. J. Hwang, J.-G. Lee, S.-C. Lee, T.-H. Lim, Y.-E. Sung, A. Wieckowski and S.-K. Kim, Energy Environ. Sci., 2012, 5, 7521–7525.
9. P. Malacrida, M. Escudero-Escribano, A. Verdaguer-Casadevall, I. E. Stephens and I. Chorkendorff, J. Mater. Chem. A, 2014, 2, 4234–4243.
10. J. Tang and J. M. Lawrence, Phys. Rev. B: Condens. Matter, 1993, 48, 15342–15352.
11. C. J. Baddeley, A. W. Stephenson, C. Hardacre, M. Tikhov and R. M. Lambert, Phys. Rev. B: Condens. Matter, 1997, 56, 12589–12598.
12. A. Ramstad and S. Raaen, Phys. Rev. B: Condens. Matter, 1999, 59, 15935–15941.
13. T. Pillo, J. Hayoz, P. Aebi and L. Schlapbach, Phys. B, 1999, 259–261, 1118–1119.
14. U. Berner and K.-D. Schierbaum, Phys. Rev. B: Condens. Matter, 2002, 65, 235404.
15. B. Vermang, M. Juel and S. Raaen, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 033407.
16. D. T. Adroja, S. K. Malik, B. D. Padalia and R. Vijayaraghavan, Solid State Commun., 1989, 71, 649–651.
17. Z. Blazina, J. Alloys Compd., 1995, 216, 251–254.
18. P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864–B871.
19. W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133–A1138.
20. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter, 1992, 46, 6671–6687.
21. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
22. J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 75, 045121.
23. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57, 1505–1509.
24. G. Kresse, P. Blaha, J. L. F. Da Silva and M. V. Ganduglia-Pirovano, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 237101.
25. J. L. F. Da Silva, M. V. Ganduglia-Pirovano and J. Sauer, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 125117.
26. J. L. F. Da Silva, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 193108.
27. M. V. Ganduglia-Pirovano, A. Hofmann and J. Sauer, Surf. Sci. Rep., 2007, 62, 219–270.
28. M. V. Ganduglia-Pirovano, J. L. F. Da Silva and J. Sauer, Phys. Rev. Lett., 2009, 102, 026101.
29. P. E. Blöchl, Phys. Rev. B: Condens. Matter, 1994, 50, 17953–17979.
30. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
31. Lanthanum (PAW_PBE La 06Sep2000 5s²5p⁶5d¹6s²), Cerium (PAW_PBE Ce_GW 26Mar2009 4f²5s²5p⁶6s²), Platinum (PAW_PBE Pt_GW 10Mar2009 6s¹5d⁹).
32. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter, 1993, 48, 13115–13126.
33. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter, 1996, 54, 11169–11186.
34. C. Kittel, Introduction to Solid State Physics, John Wiley & Sons, New York, 7th edn, 1996.
35. G. G. Rondina and J. L. F. Da Silva, J. Chem. Inf. Model., 2013, 53, 2282–2298.
36. J. L. F. Da Silva, C. Stampfl and M. Scheffler, Surf. Sci., 2006, 600, 703–715.
37. N. E. Singh-Miller and N. Marzari, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 235407.
38. J. Van Der Veen, R. Smeenk, R. Tromp and F. Saris, Surf. Sci., 1979, 79, 219–230.
39. H. B. Michaelson, J. Appl. Phys., 1977, 48, 4729–4733.
40. P. Zeppenfeld, Physics of Covered Solid Surfaces, Landolt-Börnstein, New Series, Group III, Vol. 42: Numerical Data and Functional Relationships in Science and Technology, Subvol. A: Adsorbed Layers on Surfaces, Springer-Verlag, Berlin, 2001, p. 67.
41. J. K. Nørskov, M. Scheffler and H. Toulhoat, MRS Bull., 2006, 31, 669–674.
42. T. Bligaard and J. K. Nørskov, Electrochim. Acta, 2007, 52, 5512–5516.

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