The role of sulfur vacancies on FeS₂(100) in NO dissociative adsorption: a combined in situ SR-XPS and DFT calculation study

Abstract

Sulfur vacancies (S_vacs) are known to change the reactivity of transition metal sulfides, but their mechanistic role in small-molecule activation remains poorly understood. Here, we carried out synchrotron radiation X-ray photoelectron spectroscopy (SR-XPS) and dispersion-corrected density functional theory (DFT-D3) calculations to elucidate how S_vac sites on FeS₂(100) surfaces promote nitric oxide (NO) dissociation. SR-XPS results reveal progressive Fe oxidation, Fe–N formation, and the growth of adsorbed oxygen species as a function of NO exposure. The N/O atomic ratio evolution suggests recombinative N₂ desorption from the surface. DFT-D3 calculations show that the dissociative adsorption of NO is thermodynamically more stable on the defective FeS₂(100) surface than on the defect-free surface. Based on the Brønsted–Evans–Polanyi relationship, dissociative adsorption of NO may be kinetically favorable on the defective FeS₂(100) surface. Two possible pathways are proposed: (1) O–O bond formation at S_vac sites and (2) oxygen-induced S–S bond cleavage to yield O–S species and new S_mono. The present experimental–computational study demonstrates the atomic-level role of S_vacs in NO activation on FeS₂(100) and provides chemical insight into defect engineering of sulfide-based catalysts for selective nitrogen oxide conversion.

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1. Introduction

Nitric oxide species (NO_x), primarily emitted from fossil fuel combustion in transportation and industrial processes, contribute to severe environmental and health issues, including acid rain, photochemical smog, and respiratory illnesses. Their interaction with volatile organic compounds under sunlight can also produce ground-level ozone, further degrading air quality.^1–4 To mitigate NO_x emissions, a variety of catalytic technologies have been developed. Three-way catalysts (TWCs), employing noble metals such as Pt, Pd, and Rh, are widely used in automobiles for simultaneous reduction of NO_x and oxidation of CO and hydrocarbons.^5–7

Among low-cost transition metal compounds, pyrite (FeS₂) has drawn increasing interest due to its abundance, non-toxic nature, and semiconducting properties. Its magnetic and optoelectronic characteristics have enabled its application in spintronics^8–10 and photovoltaics.¹¹ Furthermore, FeS₂ has demonstrated catalytic activity in reactions such as hydrodesulfurization (HDS),^12,13 hydrodeoxygenation (HDO),¹⁴ and nitrogen reduction reactions (NRRs),¹⁵ offering a sustainable alternative to noble-metal-based catalysts. The demonstrated ability of FeS₂(100) to interact with atomic nitrogen—via ion-beam implantation or exposure to electronically excited N₂—underscores the intrinsic surface reactivity of FeS₂ and provides a mechanistic basis for further investigations into vacancy-assisted activation of nitrogen-containing species.¹⁶ Despite these advantages, the potential of FeS₂ in NO_x reduction remains largely underexplored. This is partly due to the high activation energy (∼2.66 eV)¹⁷ reported for NO dissociation on stoichiometric FeS₂ surfaces, which limits its effectiveness under mild conditions.

Recent studies have shown that defect engineering, particularly the introduction of sulfur vacancies (S_vacs), can dramatically alter the electronic properties of transition metal dichalcogenides (TMDs).^18–21 Previous studies also show that the S_vacs in MoS₂ can act as the active site for the hydrogen evolution reaction (HER),^22,23 while also showing potential for CO₂ capture and conversion.^24,25 The defect engineering of WS₂ is also an indispensable tool for strategically tailoring the excellent electrical and optical properties of TMDs, as well as for optimizing electronic devices and gas sensors.²⁶ Multistate non-volatile memory is achieved in ReS₂ by controlling S_vacs induced via light programming,²⁷ and the S_vacs in ReS₂ also show potential in a highly selective photocatalytic CO₂ reduction.¹⁸

Despite the structural difference from van der Waals TMDs, FeS₂ exhibits analogous S_vac chemistry and catalytic behavior for comparative analysis. For FeS₂ in the catalytic field, S_vacs also tune the surface reactivity.^28,29 S_vacs of FeS₂ reduce the band gap, promote orbital hybridization, and enhance electron transfer capabilities.³⁰ These modifications have been linked to enhanced catalytic performance in diverse reactions, including N₂ reduction³¹ and polysulfide conversion.¹³ Notably, S_vac sites have been proposed as the active centers for the NO reduction reaction³² and NO₂ reduction reaction³³ on FeS₂ surfaces. These findings suggest that creating sulfur-deficient FeS₂ (FeS_2−x) surfaces may decrease the high activation barrier for NO dissociation, providing a new route for efficient NO_x reduction.

On the other hand, mineral surfaces such as pyrite (FeS₂) and pyrrhotite (Fe_1−xS) are central to the “iron–sulfur world” hypothesis proposed by Wächtershäuser in the 1990s, which links Fe–S minerals to the autotrophic origin of life.³⁴ Beyond its catalytic applications, FeS₂ has also been implicated in origin-of-life scenarios,^35,36 with sulfur-deficient surfaces shown to adsorb L-cystine³⁷ and support primitive reaction networks under hydrothermal conditions.³⁸ Exploring NO interactions on such surfaces may not only aid environmental catalysis but also offer implications for prebiotic chemistry. Previous studies have demonstrated that the adsorption and surface transformation of nitrogen-containing molecules on FeS₂(100) are highly sensitive to surface structure and sulfur defect states. Notably, the adsorption geometry of cystine has been shown to depend on the degree of surface ordering, whereas glycine undergoes defect-mediated chemical evolution on sulfur-deficient surfaces.^39,40 These findings highlight that sulfur vacancy sites serve as key reactive centres not only for simple adsorbates but also for more complex, nitrogen-containing molecules. Recent near-ambient-pressure X-ray photoelectron spectroscopy (NAP-XPS) studies revealed that FeS₂ can adsorb L-cystine even under O₂ and CO₂ atmospheres, bridging surface processes relevant to both modern environmental catalysis and early Earth prebiotic chemistry.⁴¹ Moreover, UV-irradiated FeS₂ has been shown to photocatalytically fix atmospheric nitrogen into ammonium salts under both Earth- and Mars-like conditions, highlighting its dual role as a catalytic and prebiotic surface.⁴² These findings indicate that FeS₂ is active not only toward nitrogen oxides but also toward ammonium-related reactions, underscoring the broader relevance of nitrogen-containing species on FeS₂ surfaces and motivating further surface science investigation.

In this study, we investigated the role of S_vacs in facilitating NO dissociation on an FeS₂(100) surface. Using in situ synchrotron radiation X-ray photoelectron spectroscopy (SR-XPS), we examined the surface processes of NO on both low-/high-S_vac surfaces. Density functional theory (DFT) calculations, including D3 van der Waals corrections (DFT-D3), were employed to simulate the adsorption energetics, dissociation pathways, and binding energies of residual oxygen species. The present findings deliver atomic-scale insights into NO activation mechanisms on FeS₂(100) and underscore the effectiveness of defect engineering in transition metal sulfides as a strategy for enhancing NO_x reduction catalysis.

2. Experimental

2.1. Sample preparation

A natural FeS₂ crystal from Spain (1.0 cm³) was used as the sample. FeS₂(100) surfaces were prepared by cutting 1 cm² × 0.1 cm slices along the 〈100〉 direction from a cubic natural crystal, similar to the preparation of the low-S_vac FeS₂(100) surface in the previous study.⁴³ Each slice was then divided into two 0.5 cm² samples and mirror-polished. Prior to installing them in an ultra-high-vacuum (UHV) chamber, both samples were cleaned by sequential ultrasonic treatment in (1) acetone and (2) ethanol, for 30 minutes each. To minimize surface carbon contamination, the low-S_vac sample was lightly etched in a dilute acid solution (3 drops of 14 M HCl in 40 mL H₂O) for 2 minutes, followed by a procedure reported in the previous research.⁴³ The S_vac concentrations on FeS₂(100) surfaces were controlled by Ar⁺ sputtering at 200 eV and 600 eV for the low- and high-S_vac samples at 2.0 µA for 10 minutes, respectively, followed by annealing at 560 K for 5 minutes. We observed a (1 × 1) LEED pattern of a low-S_vac sample, as shown in Fig. S1.

2.2. Synchrotron radiation X-ray photoelectron spectroscopy

SR-XPS measurements were performed in a chamber equipped with a hemispherical electron energy analyzer (Scienta SES200) at BL-13B of Photon Factory, KEK, Japan.⁴⁴ The base pressure in the UHV chamber was below 2 × 10⁻¹⁰ mbar. The incident and emission angles were 65° and 0°, respectively. Samples were exposed to NO_(g) in a preparation vacuum chamber. All XPS spectra were acquired at room temperature using a photon energy of 800 eV. Binding energies were calibrated against the Fermi level of deposited gold on the sample holder. The total energy resolution of the XPS system was approximately 0.26 eV. The binding energies and line widths of the Fe 2p, S 2p, N 1s, and O1s core levels were determined by fitting the spectra with a Voigt function and a Shirley-type background.

2.3. DFT calculations

DFT calculations were performed using the OpenMX code.^45,46 For the exchange–correlation functional, a generalized gradient approximation by the Perdew, Burke, and Ernzerhof functional (GGA-PBE) was used.⁴⁷ For each Fe atom, three, two, and one optimized radial functions were allocated for the s, p, and d orbitals, respectively. A cutoff radius of 5.5 Bohr was chosen for the basis functions as denoted by Fe5.5H-s3p2d1. For the S atom, S7.0-s2p2d1f1 basis functions were adopted. For the N atom, N6.0-s2p2d1 basis functions were adopted. For the O atom, O6.0-s2p2d1 basis functions were adopted. The basis functions and pseudopotential used were validated by the delta gauge method.⁴⁸ A (1 × 3 × 3) mesh of k points and a regular mesh size of 350 Ry in real space were used for the numerical integrations and for the solution of the Poisson equation.

The geometry was optimized using a threshold of 0.0003 Hartree per Bohr for the forces. The FeS₂ surface was modeled by a (3 × 2 × 2) slab with six Fe layers along the a-axis, where the unit cell of FeS₂ contains two Fe layers in this direction. A vacuum region of 20 Å was introduced along the a-axis. The slab contained 48 Fe and 96 S atoms, enabling the description of surface, subsurface, and bulk-like layers, with slab models shown in Fig. S5. No atoms were fixed during the calculations. The vdW interaction was taken into account in the dispersion-corrected density functional theory approach.^49,50 In the geometry optimization calculations, conventional pseudopotentials and optimized basis functions provided on the OpenMX website were used.^48,51–54 Spin-polarized calculations were performed in this study. For the adsorption systems, unequal initial spin populations were assigned to the adsorbed N, O, and the Fe atoms neighboring the S_vac site as the initial state. After self-consistent-field (SCF) convergence, the results showed almost no residual spin polarization.

The core-level binding energies of the O 1s states were calculated by the delta self-consistent field (ΔSCF) method,⁵⁵ in which the final states with a core hole were self-consistently determined by the penalty function method⁵⁵ and the exact Coulomb cutoff method⁵⁶ with fully relativistic norm-conserving pseudopotentials.^52,53 This approach has been applied to several substrates (Pd/Cu, MoS₂, Si on ZrB₂, Ge on ZrB₂, borophene on Ag, and polycarbonate on Ti/Al/TiAl).^57–62 The structures used for the ΔSCF calculations were taken from the fully optimized geometries obtained in the geometry optimization step, and no further structural relaxation was performed during the core-level calculations. For the geometry optimization, the O pseudopotential treated six valence electrons (2s²2p⁴), whereas for the O 1s ΔSCF calculations, a different norm-conserving pseudopotential was employed in which the 1s state was also treated explicitly, resulting in eight explicitly treated electrons (1s²2s²2p⁴). Fully relativistic pseudopotentials and pseudoatomic orbitals for O 1s excitation were used for core-level excitation calculations.^54,55 The systems were treated as insulators, and the exact Coulomb cutoff method was used to eliminate spurious Coulombic interactions between core-hole images under periodic boundary conditions. A (2 × 3 × 3) slab model was adopted for the core-level calculations. Compared with the slab used for geometry optimization, the model was expanded in the b- and c-axis directions and reduced along the a-axis as a compromise between computational cost and accuracy. Noncollinear spin polarization and spin–orbit coupling were included in absolute binding energy calculations. The molecular and surface structure models presented in this work were rendered using VESTA software.^63,64

3. Results and discussion

3.1. SR-XPS investigation of NO adsorption on FeS₂(100)

3.1.1. Comparative NO adsorption on low- and high-S_vac surfaces. To investigate the role of S_vacs on an FeS₂(100) surface in modulating reactivity toward NO, we compared low- and high-S_vac surfaces under the same NO exposure conditions. This experiment aimed to establish a direct correlation between the vacancy density and NO adsorption behavior.

Fig. 1 presents the models of ideal and defective FeS₂(100) surfaces. Key surface atomic sites are labeled, including bulk Fe (Fe_bulk, 6-coordinated), surface Fe (Fe_surf, 5-coordinated), unsaturated Fe (Fe_unsat, 4-coordinated), surface S (S_surf), sulfur monomer (S_mono), and bulk S (S_bulk).

Fig. 1 Structure of defect-free and defective FeS₂(100) surface models. Top and side views are shown for both models. The light-yellow spheres represent sulfur atoms, and the brown spheres represent iron atoms. In the defective model, key atomic sites are labeled, including surface Fe (Fe_surf), unsaturated Fe (Fe_unsat), surface S (S_surf), sulfur monomer (S_mono), sulfur vacancies (S_vacs), and bulk Fe and S atoms (Fe_bulk and S_bulk).

The S_vac concentration was tuned via controlled Ar⁺ sputtering and quantified from the S_mono component in the S 2p spectra on the clean surface (Fig. 2(b) and Table 1). On the low-S_vac surface, S_mono accounted for 10.6% of the total S signal, increasing to 23.9% for the high-S_vac surface, confirming a substantial enhancement in vacancy density. This controlled variation provides a platform for probing defect–reactivity relationships.

Fig. 2 SR-XPS spectra of FeS₂(100) surfaces with low- and high-S_vacs before and after exposure to 2.67 Pa NO for 15 min at room temperature. (upper panel) Low-S_vac surface; (lower panel) high-S_vac surface. (a) Fe 2p, (b) S 2p, (c) N 1s, and (d) O 1s regions are shown from left to right, respectively. Deconvoluted components are overlaid in the S 2p, N 1s, and O 1s spectra. Peak fitting was conducted using Voigt peaks with a Shirley background. Sulfur components are deconvoluted into S_vacs, S_surf, S_bulk, S_n, and SO_x species. Oxygen species are labeled as O P1 and O P2, and nitrogen species are assigned as Fe–N bonding.

Table 1 Peak analysis of SR-XPS spectra for low-S_vac and high-S_vac FeS₂(100) surfaces before and after NO exposure (267 Pa, 15 min). Binding energies (BEs), full width at half maximum (FWHM) values, and relative component ratios are shown for the S 2p, O 1s, and N 1s regions. Sulfur components are deconvoluted into S_mono, S_surf, S_bulk, S_n, and SO_x species. Oxygen species are labeled as O P1 and O P2, and nitrogen species are assigned as Fe–N bonding

FeS2(100)	Exp. condition		S 2p					O 1s		N 1s
Sample			Smono	Ssurf	Sbulk	Sn	SOx	O P1	O P2	Fe–N
Low-Svacs	Clean	B.E. (eV)	161.2	161.8	162.6	164.7
		FWHM (eV)	0.6	0.6	0.7	1.0
		Ratio (%)	10.6	21.7	62.2	5.5
	NO 267 Pa 15 min	B.E. (eV)	161.2	161.8	162.6	164.7	166.8	529.8	531.2	399.5
		FWHM (eV)	0.4	0.6	0.7	1.0	1.1	1.1	1.8	2.0
		Ratio (%)	0.9	9.5	76.6	6.6	6.4	45.3	54.7
High-Svacs	Clean	B.E. (eV)	161.1	161.7	162.4	164.3
		FWHM (eV)	0.7	0.6	0.9	1.6
		Ratio (%)	23.9	34.8	36.6	4.6
	NO 267 Pa 15 min	B.E. (eV)	161.0	161.6	162.5	164.7	166.8	529.7	531.1	399.4
		FWHM (eV)	0.8	0.6	0.9	0.9	1.0	1.1	1.6	2.0
		Ratio (%)	30.2	11.0	48.3	2.6	7.9	57.2	42.8

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During NO exposure, the low- and high-S_vac surfaces were simultaneously dosed in the same preparation vacuum chamber at room temperature. Post-exposure SR-XPS spectra (Fe 2p, S 2p, N 1s, and O 1s; Fig. 2 and Table 1) exhibit pronounced oxidation features in the Fe 2p and O 1s regions. The N 1s signal is weak, with an N/O atomic ratio of ∼0.01 (corrected for the photo-ionization cross-section at hν = 800 eV and the inelastic mean free path of electron kinetic energy), indicating that most of the nitrogen recombines and desorbs as N₂ from the surface, which will be discussed later. A residual N 1s feature is found at 399.4–399.5 eV, which is characteristic of Fe–N coordination.⁶⁵

The O 1s region resolves into two distinct peaks, P1 at 529.7–529.8 eV and P2 at 531.1–531.2 eV, revealing the coexistence of different oxygen species after NO dissociation. O 1s peaks at binding energies of around 529.7–530.5 eV are reported as atomic O on the FeS₂ surface,^41,66,67 while O 1s peaks at binding energies of around 531.0–531.3 eV are assigned as adsorbed O₂ or FeOOH/FeSO₄ according to the previous studies.^41,67 Higher binding energy species around 532.0 eV are assigned as OH or O₂ species from the dissociative adsorbed H₂O.⁶⁶ Note that, in the case of NO_(g), an O 1s peak was observed at 538.8 eV and multiplet splitting peaks of N 1s were observed at 405.8 eV and 407.1 eV;⁶⁸ in the case of NO_(ads), an O 1s peak was observed at 531.8 eV and multiplet splitting peaks of N 1s were observed at 396.8 eV.⁶⁹ Combined with Fe oxidation and N 1s detection, these results clearly indicate dissociative adsorption of NO on FeS₂(100) with S_vacs. The process can be summarized as follows:

NO_(g) → N_(ads) + O_(ads) ΔH_ideal FeS2 = −0.17 eV (1.1)

ΔH_{defective FeS2} = −2.60 eV (1.2)

NO_(g) + N_(ads) + O_(ads) → N_2(g) + 2O_(ads) ΔH_{defective FeS2} = −1.61 eV (2)

Overall conversion:

2NO_(g) → N_2(g) + 2O_(ads) ΔH_{defective FeS2} = −4.21 eV (3)

(ΔH values are evaluated from DFT-D3 calculations, which will be discussed in Section 3.2.2.)

Fe 2p spectra (Fig. 2(a)) show that the low-S_vac surface retains a clear Fe²⁺ component (∼707.4 eV), indicating limited oxidation, while the high-S_vac surface exhibits a marked shift to Fe³⁺ (∼710.9 eV), consistent with extensive oxidation.⁷⁰ This difference supports the view that S_vac sites act as active sites for NO dissociation, selectively promoting Fe oxidation.

The assignments of S 2p spectra follow established literature values: S_mono (160.95–161.25 eV), S_surf (161.70–162.00 eV), S_bulk (162.35–162.70 eV), polysulfide S_n⁰/S_n²⁻ or core–hole effects (163.40–164.50 eV), and SO_x species (166.20–168.50 eV).^43,71–76 After NO exposure, the S_mono and S_surf intensities decrease (Fig. 2(b)) on both surfaces. The decreased intensity of S_mono suggests O incorporation at S_vac sites, while the concurrent reduction of S_surf indicates that adjacent surface sulfur dimers also participate in the NO dissociation process (see (Fig. 2)).

3.1.2. Evolution of surface chemistry during progressive NO adsorption on high-S_vac surfaces. To probe the stepwise reaction of NO dissociation at defective sites, a progressive NO exposure experiment was performed on a high-S_vac FeS₂(100) surface at 2 Pa as a function of time (from 0 to 150 min), and finally exposure up to 243 000 Pa s.

The SR-XPS spectra (Fig. 3) capture the sequential evolution of surface chemistry during NO exposure, with the N/O atomic ratio profile (Fig. 4) providing further insight into the reaction sequence. Very initially, NO adsorption at S_vac sites yields a relatively high N/O atomic ratio (∼0.66). As exposure progresses, the ratio steadily decreases to ∼0.08, indicating that adsorbed nitrogen reacts with NO to form N_2(g), which then desorbs, leaving oxygen on the surface (discussed later in the DFT-D3 calculation section).

Fig. 3 Progressive SR-XPS spectra of high-S_vac FeS₂(100) during NO exposure. Spectra were acquired after sequential exposure to 2 Pa NO for increasing durations (10–150 min), followed by a final 15 min exposure at 267 Pa. Fe 2p, S 2p, N 1s, and O 1s regions. Deconvoluted peaks in S 2p correspond to S_mono, S_surf, S_bulk, S_n, and SO_x components; O 1s peaks are assigned to O P1 and O P2.

Fig. 4 SR-XPS evolution of the N 1s and O 1s core-level signals during progressive NO exposure on high-S_vac FeS₂(100). Spectra were acquired at 2 Pa NO for increasing exposure times (10–150 min), followed by a final 15 min exposure at 267 Pa. The N/O atomic ratio (left axis) and integrated peak areas of N 1s and O 1s (right axis) are plotted as a function of NO exposure dose (Pa s).

The N 1s spectra at a binding energy of about 399.4 eV show the emergence of Fe–N bonding,⁶⁵ while the O 1s spectra reveal the growth of two different oxygen components, confirming the formation of different oxygen-containing species. The reproducibility of these spectral changes across a series of spectra indicates a stepwise dissociative adsorption process at S_vac sites. Changes in the oxygen environment are further detailed in Fig. 5. Upon early exposure, the O 1s spectra display both P1 (low-binding-energy) and P2 (high-binding-energy) species, with P2 intensifying markedly at higher O coverage. This trend suggests that P2 formation is favored at elevated oxygen surface densities, likely via the interaction between adsorbed O atoms to form an O–O bond (discussed later in the DFT-D3 calculation section).

Fig. 5 SR-XPS evolution of O 1s spectral components and surface oxygen coverage during progressive NO exposure on high-S_vac FeS₂(100). (left axis) O P1 and P2 peak intensities and their relative P2 component ratio [P2/(P1 + P2)] as a function of NO exposure dose (Pa s). (right axis) Estimated oxygen surface coverage (θ, in monolayer, ML). Spectra were acquired at 2 Pa NO for increasing exposure times (10–150 min), followed by a final 15 min exposure at 267 Pa.

The sulfur component trends are summarized in Fig. 6. The S_surf component decreases continuously with increasing exposure, while S_mono exhibits an initial increase followed by a decline. This behavior suggests that, in the early stages of reaction, the interaction between an adsorbed oxygen atom and surface sulfur dimer disrupts the S–S bond, and one of the surface sulfur atoms becomes S_mono (discussed later in the DFT-D3 calculation section). At later stages, as O coverage increases, S_vac sites become occupied by oxygen atoms, leading to a net decrease in S_mono.

Fig. 6 SR-XPS evolution of S 2p spectral components during progressive NO exposure on high-S_vac FeS₂(100). Area intensities of deconvoluted sulfur species (S_mono, S_surf, S_bulk, S_n, and SO_x) are plotted as a function of NO exposure dose (Pa s). Spectra were acquired at 2 Pa NO for increasing exposure times (10–150 min), followed by a final 15 min exposure at 267 Pa.

3.2. DFT calculations on NO dissociation mechanisms

The bulk FeS₂ structural parameters obtained from DFT-D3 calculations are as follows: S–S bond length (d_S–S) = 2.22 Å, Fe–S bond length (d_Fe–S) = 2.26 Å, and lattice constant (a₀) = 5.417 Å. These values are consistent with the reported experimental data (d_S–S = 2.15 Å, d_Fe–S = 2.26 Å, and a₀ = 5.417 Å).¹⁹ Based on the geometry optimizations shown in Fig. S2, S3 and Tables S1, S2, the most stable NO adsorption site on the defect-free FeS₂(100) surface involves N-end coordination to a surface Fe atop site, in agreement with previous studies.¹⁷ For the defective FeS₂(100) surface, the most stable configuration likewise features N-end coordination to the S_vac site, consistent with the previous report.³²

3.2.1. O 1s core-level binding energy calculations for identifying residual oxygen species. The presence of two distinct oxygen species in the SR-XPS O 1s spectra after NO_(g) exposure at room temperature motivated an investigation into their geometries and chemical environments on an FeS₂(100) surface. To this end, oxygen-adsorbed models were first constructed for the defect-free FeS₂(100) surface to assess whether the residual O species could interact with surface atoms adjacent to S_vac sites.

The optimized geometries and calculated O 1s binding energies for the defect-free surface are shown in Fig. 7 and Table 2. Among the adsorption configurations examined, only oxygen bound to the atop site of S_surf yields a binding energy (529.46 eV) close to the experimental P1 feature (529.7–529.8 eV).

Fig. 7 Top- and side-view structural models used for absolute O 1s binding energy calculations on the defect-free FeS₂(100) surface. (a) Fe_surf–O: single oxygen atom bonded atop the iron site. (b) S_surf–O: single oxygen atom bonded atop the sulfur site. (c) S_surf–O–S_surf: oxygen atom simultaneously bonded between a surface sulfur and a subsurface sulfur, forming a bridge. The yellow, brown, and red spheres represent sulfur, iron, and oxygen atoms, respectively.

Table 2 Comparison of computed and experimental O 1s binding energies for defect-free FeS₂(100) adsorption models

Defect-free FeS2(100) surface model
Model	O Species	State	Experiment B.E. (eV)	Computed B.E. (eV)
(a)	Fesurf–O	O 1s	529.7–529.8 (P1)	527.31
(b)	Ssurf–O	O 1s	531.1–531.2 (P2)	529.46
(c)	Ssurf–O–Ssurf	O 1s		530.57

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Defective surface models used for O 1s absolute binding energy calculations are presented in Fig. 8 and Table 3. Oxygen adsorbed directly at the S_vac site (Fig. 8(b), (c) and Table 3(b), (c) (O_Svac)) gives the computed binding energies of 529.26–529.75 eV, in good agreement with the P1 species. Another plausible configuration involves oxygen adsorbed on a surface sulfur atop site with a binding energy of 529.69 eV (Fig. 8(c) and Table 3(c) (O_S-atop)), also matching the P1 range. In addition, the O on the bridge side between Fe_unsat and S_surf geometries (Fig. 8(d) and Table 3(d) (O_bridge-1 and O_bridge-2)), where dissociated O interacts with one side of a sulfur dimer to disrupt the S–S bond and the other side interacts to form a new S_mono species, yielding a binding energy of 529.22–529.67 eV. These results further support an additional contribution to P1 and the observed S_mono increases at the initial stage of NO exposure.

Fig. 8 Top- and side-view structural models used for absolute O 1s binding energy calculations on defective FeS₂(100) surfaces. (a) Fe_unsat–O–O–Fe_unsat: oxygen atoms bridging two adjacent surface unsaturated Fe atoms neighboring S_vacs. (b) O–Fe_unsat–O–S_mono: one oxygen atom bound at the S_vac site, and the atop site of unsaturated Fe coordinated with an additional surface O. (c) Fe_unsat–O–S_surf–O: one oxygen atom bound at the S_vac site, and the atop site of S_surf coordinated with an additional surface O. (d) Fe_unsat–S_surf–O: oxygen atoms bridging the unsaturated Fe atoms neighboring S_surf. The yellow, brown, and red spheres represent sulfur, iron, and oxygen atoms, respectively.

Table 3 Comparison of computed and experimental O 1s binding energies for adsorption models on defective FeS₂(100) surfaces

Defective FeS2(100) surface model
Model	O Species	State	Experiment B.E. (eV)	Computed B.E. (eV)
(a)	Feunsat–O–O–Feunsat	O 1s	529.7–529.8 (P1)	Oupper
				529.81
				Olower
				531.13
(b)	O–Feunsat–O–Smono	O 1s		OFe-atop
				527.40
				OSvacs
				529.26
(c)	Feunsat–O–Ssurf–O	O 1s	531.1–531.2 (P2)	OS-atop
				529.69
				OSvacs
				529.75
(d)	Feunsat–Ssurf–Obridge	O 1s		Obridge-1
				529.22
				Obridge-2
				529.67

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To account for the observed P2 species (531.1–531.2 eV), several geometries were evaluated. As shown in Fig. 8(b), oxygen bound to a surface Fe atop site yields a significantly lower binding energy of 527.40 eV (Table 3(b) (O_Fe-atop)). By comparison, oxygen occupying S-atop sites is relatively more stable than the Fe-atop sites both on the defect-free (−0.64 eV) and defective (−0.43 eV) FeS₂(100) surfaces, as shown in Fig. S4. Therefore, the O_Fe-atop configuration can therefore be excluded as a candidate for the P2 species. In contrast, the O–O configuration at the S_vac site shown in Fig. 8(a) and Table 3(a) produces a calculated binding energy of 531.13 eV for O_lower, which is consistent with P2; on the other hand, O_upper shows 529.81 eV, matching P1.

In summary, oxygen species adsorbed at the S_vac site, the S atop site, the bridge side between Fe_unsat and S_surf, and O_upper in the O–O species contribute to P1, while O_lower in the O–O species is the probable source of P2. These assignments are supported by the progressive NO exposure experiments on high-S_vac FeS₂(100) (Fig. 5), where the P2 component ratio increases from 0.26 at the early stage to ∼0.4 at higher exposure. This trend suggests that P2 (O_lower) is linked to O–O species at S_vac sites, while P1 originates from multiple adsorption geometries, including a fraction (∼0.4 of P1 at the final stage) derived from O_upper in the O–O species and the remainder from other oxygen configurations.

3.2.2. Reaction pathways for NO dissociation and N₂ formation on defective surfaces. The calculated dissociative adsorption pathways of NO on both defect-free and defective FeS₂(100) surfaces are shown in Fig. 9(a)–(c). On the defect-free surface (black), NO adsorbs most stably with the nitrogen atom coordinated to a surface Fe site, with an adsorption energy of −2.01 eV. However, dissociation into N_ads and O_ads is thermodynamically unfavorable, with the final state lying +1.84 eV above the molecular adsorption state. In contrast, Fig. 9(a′)–(c′) illustrates the corresponding pathway on a defective surface containing the S_vac site. In this case, NO adsorption is more exothermic (−3.10 eV) and the dissociation state becomes mildly endothermic (+0.50 eV), representing a substantial reduction in energy relative to the defect-free surface. The DFT-D3 results show that the dissociated adsorption configuration of NO is energetically much more stabilized on the defective FeS₂(100) surface than on the defect-free surface. In contrast to the defect-free surface, these results indicate that sulfur-vacancy sites preferentially stabilize the dissociated N and O species. Although transition-state calculations were not carried out in this study, the substantial stabilization of the dissociated state qualitatively suggests that NO dissociation may proceed more preferably on the defective surface, in line with a Brønsted–Evans–Polanyi relationship. According to the geometry optimization, the pronounced energy difference between the dissociated final states on the defect-free FeS₂(100) surface (Fig. 9(c)) and the defective surface (Fig. 9(c′)) can be attributed to the much stronger stabilization of the dissociation fragments—especially N_ads—in the presence of the S_vac. On the defect-free surface, N and O adsorb on relatively saturated sites with limited coordination, resulting in a high-energy final state. By contrast, one S_vac creates two under-coordinated local Fe_unsat sites, enabling N_ads to form stronger Fe–N interactions, thereby stabilizing the dissociated state and lowering the dissociation energy.

Fig. 9 DFT-D3 computed energy profiles for the dissociative adsorption of NO on FeS₂(100) surfaces, comparing the defect-free model (black line) and the S-vacancy model (blue line). Gas-phase molecules not explicitly shown in the structures were treated using isolated gas-phase calculations.

In order to investigate the experimentally observed low N/O atomic ratio after prolonged NO exposure (Fig. 9(d′), (e′), (f′) and (g′)), further calculations were carried out to model the reaction between a pre-adsorbed nitrogen atom and an incoming NO molecule. Fig. 9(d′) shows the structure of an additional NO adsorption on the defective FeS₂ surface after the initial dissociative adsorption of NO. According to the calculated results, the second NO molecule that adsorbs onto the N top, forming an N–N bond, makes the energy more stable, decreasing from −2.60 eV to −4.04 eV. After N_2(g) desorbs as shown in Fig. 9(e′), the total energy becomes more thermodynamically stable, decreasing from −4.04 eV to −4.21 eV. Next, the oxygen atom interacts with a neighboring surface sulfur dimer, breaking the S–S bond and generating a new S_mono species (Fig. 9(f′)), which results in further stabilization from −4.21 eV to −4.28 eV. This is the most likely path for S_mono formation from the interaction between the adsorbed O species and the sulfur dimer during the reaction.

Finally, two plausible mechanistic pathways for N₂ formation and residual O stabilization were identified. In path 1 (Fig. 9(g′-1)), both oxygen atoms migrate toward the S_vac site, forming a new O–O bond. The computed O 1s binding energies show that the lower O atom (O_lower, 531.13 eV) corresponds to the experimental P2 species, while the upper O atom (O_upper, 529.81 eV) matches P1 and is thermodynamically stable from −4.28 eV to −4.67 eV. In the case of Path 2 (Fig. 9(g′-2)), the other oxygen atom occupies the S_vac site (Fig. 9(g′-2)). This pathway explains the observed initial S_mono increase and decrease at prolonged NO exposure in Fig. 6 during progressive NO exposure, and the final geometry is thermodynamically stable. Both oxygen atoms in this configuration yield binding energies consistent with the P1 feature and are thermodynamically stable from −4.28 eV to −6.12 eV.

These two pathways account for the experimentally observed oxygen species in XPS (P1 and P2) and the intensity changes of sulfur species at high NO doses. Path 1 associates P2 formation with O–O bond formation at the S_vac site, whereas Path 2 links the transient increase in S_mono to oxygen–sulfur interactions before S_vac occupation.

On the whole, in the first experiment, we compared NO adsorption on FeS₂(100) surfaces with low- and high-sulfur-vacancy (S_vac) concentrations. The results showed that Fe on the low-S_vac surface was only partially oxidized, whereas the high-S_vac surface exhibited full oxidation. These findings indicate that S_vac sites serve as active sites for NO dissociative adsorption. In addition, the low N/O atomic ratio (∼0.01) suggests that most nitrogen species desorbed as N₂ from the surface after reaction. To investigate this process in detail, we carried out a second experiment as a function of NO exposure time on the high-S_vac surface. The results confirmed the reproducibility of the reaction processes and revealed the oxidation sequence through Fe 2p spectral changes, along with semi-quantitative analysis of surface composition using S 2p, N 1s, and O 1s spectra. These results showed that the N/O atomic ratio is initially close to 1.0 (∼0.66), indicating that both nitrogen and oxygen species were present on the surface at the early stages of the reaction and that the N species desorbed upon further NO_(g) exposure, which anticipated the conversion into N_2(g). Furthermore, changes in the S 2p region suggest that the surface sulfur dimer participates in the reaction. Complementing these experimental observations, DFT-D3 calculations provided atomistic insight into the surface reactions. Using the ΔSCF method, the absolute O 1s binding energies of possible surface-bound oxygen species were computed to assist in peak assignment. We have proposed a reaction mechanism that is consistent with both the experimental trends and calculated binding energies. The present mechanism is also thermodynamically favorable, further supporting the interpretation of the observed O 1s features.

4. Conclusions

The present study elucidates the atomic-level mechanism by which S_vac promote nitric oxide (NO) dissociative adsorption on FeS₂(100) surfaces using a combined SR-XPS and DFT-D3 approach.

SR-XPS experiments reveal that high-S_vac surfaces undergo pronounced Fe oxidation, concurrent with reductions in S_surf and S_mono, the appearance of Fe–N bonding, and the formation of two distinct oxygen species. The N/O atomic ratio as a function of exposure indicates that NO initially adsorbs dissociatively at S_vac sites, followed by N₂ formation via recombinative desorption, leaving oxygen on the surface. Progressive exposure experiments further indicate that P2 (high-binding-energy O species) becomes more prominent at higher O coverage, suggesting O–O bond formation at S_vac sites.

DFT-D3 calculations indicate that NO dissociative adsorption is thermodynamically more favorable on the defective FeS₂(100) surface than on the defect-free surface. Computed O 1s binding energies match experimental values, assigning P1 primarily to oxygen at S_vac, S atop, and (Fe–S)–O sites and assigning P2 to the lower oxygen atom in an O–O species at S_vacs. Two mechanistic pathways for N₂ formation and oxygen stabilization are proposed: (1) O–O at S_vacs and (2) interaction of oxygen with the neighboring surface sulfur dimer to form S_mono. Both are consistent with the observed oxygen and sulfur species under NO exposure.

Overall, the experimental and theoretical results presented in this study reveal a strong correlation between the S_vac concentration and NO dissociation reactivity on FeS₂(100). SR-XPS measurements show that high S_vac densities markedly promote NO adsorption and facilitate dissociative reaction pathways. In addition, SR-XPS identified characteristic oxygen and nitrogen species remaining on the FeS₂ surfaces after NO exposure. DFT-D3 calculations clarified the possible surface oxygen species on FeS₂(100) by directly computing absolute binding energies using the ΔSCF method. In addition, the energy diagram provided insight into the thermodynamic and mechanistic origins of the observed processes. These findings highlight the essential role of defect engineering in controlling surface reactivity and suggest that tuning S_vac populations on FeS₂(100) surfaces offers a promising strategy for modulating catalytic behavior toward nitrogen oxides.

Author contributions

W. H.: experimental and theoretical investigation, visualization, writing – original draft and writing – review and editing; F. O.: experimental investigation, review and editing; K. M.: experimental investigation, review and editing; S. T.: experimental investigation, review and editing; D. H.: sample preparation from a natural crystal; M. F.: software and theoretical investigation; T. O.: calculational resources, software, and theoretical investigation; J. Y.: funding acquisition, supervision, investigation, writing – original draft and writing – review and editing.

Conflicts of interest

The authors declare no conflicts of interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6cp00466k.

The data will be available from the corresponding author on reasonable request.

Acknowledgements

The present study was supported by the Transformative Research Areas (A) program “Geochemistry of CO worlds” (25H01695) of the Japan Society for the Promotion of Science (JSPS). This work was also supported by SPRING-GX of the University of Tokyo, Grant Number GXA240129. The computation in this work has been done using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo (2024-P-0014 and 2025-P-0001). Synchrotron radiation experiments were performed at the BL-13B of the Photon Factory under the approval of the PF-PAC (No. 2023G096 and 2025G133). We thank Prof. Kazuhiko Mase, Prof. Kenichi Ozawa, and the staff members of the Photon Factory for their technical support.

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Footnote

† Present address: Research and Development Directorate, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Kanagawa, 2525210, Japan.

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