Carbon support curvature modulates CO₂ activation on molybdenum carbide clusters

Abstract

Density functional theory (DFT) is employed to investigate CO₂ adsorption and activation on a representative Mo₆C₅ cluster supported on both flat and curved graphene, with particular focus on the effects of support curvature. In the free-standing cluster, a locally metal-rich triangular Mo₃ site exhibits the strongest CO₂ binding. However, this highly reactive site anchors to the carbon support, thus becoming inaccessible to adsorbates, simultaneously conferring enhanced CO₂ activation capability to the remaining stoichiometric Mo–C sites. Support curvature provides an additional lever: MoC_y clusters in convex regions further strengthen CO₂ adsorption, whereas those in concave regions thermodynamically and kinetically favor CO₂ dissociation, thereby facilitating subsequent conversion steps. These findings reveal the dual structural and electronic roles of carbon supports, paving the way for designing more tailor-made MoC_y/C-based catalysts for CO₂ utilization.

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1. Introduction

The increasing concentration of atmospheric carbon dioxide (CO₂) has resulted in the critical environmental problem of global warming, highlighting the need for efficient strategies to capture and convert it into value-added chemicals.^1,2 However, the intrinsic stability of CO₂ makes its activation and subsequent conversion a true obstacle.^3,4 Recently, noble transition metals such as gold (Au),⁵ platinum (Pt),⁶ and palladium (Pd)⁷ have been demonstrated as capable of CO₂ activation and conversion, e.g., through hydrogenation or reduction through the reverse water–gas shift (RWGS) reaction. However, the scarcity and associated high cost of these metals underline the need and urgency to find other sustainable and earth-abundant alternatives.⁸

Transition metal carbides (TMCs) have attracted research attention over recent decades as promising, economic substitute catalysts for Pt-group metals, with enhanced poison resistances, catalytic activities, or selectivities.^9–11 Among all possible TMCs, molybdenum carbides (MoC and Mo₂C) stand out, both as catalysts themselves,¹² and as supports¹³ for metal clusters, which exhibit notable activity in key CO₂ conversion reactions, including CO₂ hydrogenation,¹⁴ the RWGS,¹⁵ or the electrochemical CO₂ reduction,^16,17 to name a few.

As observed in polycrystalline MoC catalyst samples, extended surfaces with different Miller indices exhibit distinct reactivities toward CO₂ conversion. For example, on the orthorhombic β-Mo₂C (001) polar surface, CO₂ can spontaneously dissociate into CO* and O* on the Mo-terminated surface. In contrast, on the C-terminated facet, the molecule is activated but tends to retain its C=O bonds.¹⁸ Furthermore, when studying RWGS over the hexagonal α-Mo₂C phase,¹² surface orientation has been shown to significantly influence catalytic performance. Specifically, the (201)-Mo/C, (001)-Mo, and (001)-C surfaces bind the adsorbate too strongly, thereby hindering the release of reaction products. In comparison, the (101)-Mo/C surface shows a better balance among CO₂ activation, dissociation, and desorption of surface intermediates. This finding integrates theoretical reaction energy profiles, which indicate that this surface is preferentially expressed on high-temperature Mo₂C nanoparticles.¹⁹ All these studies underscore the critical role of surface structure in determining CO₂ activation and conversion behavior.

Recent advances in controlled catalyst synthesis have enabled the preparation of well-defined MoC nanoparticles, referred to as MoC_y NPs.²⁰ These nanostructured catalysts have been shown to feature an improved catalytic performance compared to single-crystal surfaces and bulk powders.²¹ By controlling the size at the nanometer or sub-nanometer scale and adjusting MoC_y stoichiometry, the catalytic activity towards CO₂ can be tuned. For example, Mo-rich MoC_0.6 NPs supported on Au(111) were shown to exhibit a higher activity but lower stability for CO₂ conversion compared with nearly stoichiometric MoC_1.1 NPs.¹⁴ Thus, stoichiometry control serves as another lever for adjusting catalytic activity, comparable to the effect of bulk material surface orientation.¹² This is not surprising considering that carbon-vacancies on the bulk material surfaces can play a critical role, for example, in the RWGS catalyzed by VC.²²

As for size effects, smaller clusters expose a larger fraction of low-coordinated active sites, with eased structural flexibility and, in general, higher reactivity, while larger particles offer greater thermodynamic stability due to lower formation energies per formula unit.²³ Furthermore, the catalytic activity of MoC_y clusters can be modulated by the support effect, where a diversity of materials has been used, including carbon-based materials,²⁰ zeolites,²⁴ and transition metals.²⁵ Among these, carbon-based materials have received increasing attention recently. For example, Liu et al. reported that MoC_y clusters on oxygen-enriched carbon nanotubes (CNT) exhibit superior RWGS rates and selectivities towards CO.²⁶ Additionally, MoC_y clusters anchored on a core@shell hybrid made of a nano-diamond@graphene (ND@G) structure were found to catalyze the RWGS with superior performance than MoC_y clusters supported by typical substrates such as γ-Al₂O₃.²⁷ Interestingly, Baddour et al.²⁰ observed that MoC_y clusters on a so-called inert carbon support exhibited a twofold increase in both activity and selectivity toward C₂ products compared to unsupported analogues. However, carbon support assumed passive spectator role is questionable, as its interaction with MoC_y clusters appears to significantly influence the overall catalytic performance.

In this context, graphene-based carbon materials have attracted considerable attention. Pristine flat graphene (FG) exhibits an inherently low chemical reactivity due to its fully conjugated sp²-hybridized structure and highly aromatic stability. Thus, its potential effect has to be engineered, through e.g. surface modifications, heteroatom doping, and/or mechanical strain, in order to disrupt its π-conjugation and generate reactive sites.^28–30 Another shell of catalytic activity control that has attracted much attention recently is the graphene surface curvature, which originates intrinsically from thermal fluctuations or local strain.³¹ Nanoripples and curved graphene (CG) have often been linked to enhanced catalytic activity in the literature. For example, She et al.³² demonstrated that the surface curvature of oxidized CNT influences the oxygen reduction activity through charge redistribution and eventual stress of the epoxy groups. Similarly, Co₃O₄ clusters confined within CNT nanochannels were shown to exhibit better performance in contaminant removal processes compared to the counterparts located on the outer surface.³³

In a recent study by some of us,³⁴ how MoC_y clusters of different sizes and stoichiometries interact with graphene-based supports of varying curvatures was studied in detail. Non-stoichiometric Mo-rich MoC_y clusters with low-coordinated Mo atoms exhibited stronger binding to the explored carbon supports by the additional formation of Mo–C bonds, fostered by a bond compensation mechanism. Additionally, the support curvature was found to increase the adsorption strength of MoC_y clusters on concave surfaces, while decreasing it on convex surfaces, revealing a strong linear correlation of the adsorption energy with the surface curvature.

However, this previous study did not address how support curvature influences the chemical and catalytic behavior of MoC_y clusters. In this work, we investigate this effect in the context of CO₂ adsorption and activation, using density functional theory (DFT) to comparatively study CO₂ interaction with both isolated and carbon-supported MoC_y clusters. Using the Mo-rich Mo₆C₅ cluster as a case study, we find that the local Mo₃ trimer site binds to CO₂ most strongly. However, this site has the highest chemical activity and serves as the anchoring point to carbon supports. Consequently, other sites with a more stoichiometric-like behavior —having both Mo and C atoms— become the most active ones for CO₂. This indicates that the carbon support can mitigate the over-reactivity of Mo-rich clusters,¹⁴ while simultaneously promoting CO₂ activation at other available sites. Additionally, we find that the convex curvature of the support enhances CO₂ adsorption, whereas concave regions favor CO₂ dissociation, thereby promoting CO₂ catalytic conversion. These insights into the structural and electronic roles of the carbon support provide guidelines for designing more efficient and tailored MoC_y/C catalysts.

2. Computational models and methods

A strong interaction with the support is a prerequisite for studying the support effect on catalysis. Among the various possible compositions of MoC_y clusters studied earlier in their interaction with CO₂,²³ non-stoichiometric Mo-rich Mo₆C₅ was selected having its largest interfacial charge transfer and strongest adsorption when supported on FG and CG models,³⁴ and so possibly the largest catalytic activity effect (see Fig. 1). The Mo₆C₅ isomers were selected from previous works,²³ and reoptimized, confirming the most stable structure to further study its interaction with CO₂ and carbon supports.

Fig. 1 Atomic representations of the Mo₆C₅/C models used in this work, including (a) active sites of the supported Mo₆C₅ cluster, involving edge (E), corner (C), and interface (I) sites; (b) the atomic structure of the Mo₆C₅ cluster in a vacuum, with the Mo₃ site tagged; (c) side views of FG and CG supports and corresponding diameters (in nm) and curvatures (in nm⁻¹), where an infinite diameter corresponds to graphene, with concave and convex sites tagged; and (d) side images of Mo₆C₅ on FG, convex and concave regions of CG. C and Mo atoms are represented by gray and cyan spheres, respectively.

Regarding the carbon supports, the FG was modeled by a c(8 × 6) supercell consisting of 96 carbon atoms. The supercell dimensions are 17.1 Å along the armchair direction (a-axis) and 14.8 Å along the zigzag direction (b-axis). A vacuum spacing of 20 Å was introduced perpendicular to the graphene surface to minimize interactions between periodically repeated graphene sheets. To model realistic CGs, models where the FG was compressed along the a-axis were used, as this modeling method effectively captures curvature effects at an affordable computational cost.³⁴ In particular, two CG models with different degrees of curvature—corresponding to diameters of 1.42 and 2.08 nm—were used, and geometries for both convex and concave surfaces are provided (see Fig. 1).

The DFT calculations were carried out using the Vienna ab initio simulation package (VASP) code.³⁵ The Perdew–Burke–Ernzerhof (PBE) functional³⁶ was chosen to describe the exchange and correlation energy terms, demonstrated to be suitable for describing Mo-based carbides.³⁷ The DFT Kohn–Sham (KS) equations were solved self-consistently by expanding the valence electron wavefunctions in a plane-wave basis set with a kinetic energy cutoff of 415 eV, which has been proven to deliver energy convergence within the chemical accuracy of 0.04 eV. The interactions between core and valence electrons were treated using the projector augmented-wave (PAW) method,³⁸ as implemented in VASP by Kresse and Joubert.³⁹ Spin polarization tests—see Section S1 in the SI—indicate that spin polarization does not influence either the adsorption mode or the energetics of CO₂ on MoC_y/C catalysts, with variations below 0.01 eV, in line with earlier results.¹⁴ Dispersive forces have been accounted for using Grimme's D3 approach.⁴⁰ The convergence thresholds for total energy and atomic forces were set to 10⁻⁵ eV and 0.01 eV Å⁻¹, respectively. For the chemical bonding analysis, Bader charges were calculated using the code developed by Henkelman et al.⁴¹ For the isolated Mo₆C₅ and the CO₂ molecule in the gas phase, calculations were carried out by placing them in a large cubic box with 20 × 20 × 20 ų dimensions, and calculations were at the Γ point only, required for non-periodic systems with no band dispersion. For Mo₆C₅ supported on the different carbon substrates, 3 × 3 × 1 Monkhorst–Pack k-points grids were employed, a choice validated by our k-point convergence test, as shown in Fig. S1 of the SI, ensuring energy convergence below chemical accuracy, vide supra.

The interaction strength of CO₂ on different Mo₆C₅/C models was quantified by first estimating the adsorption energy, E_ads. This energy was then decomposed into different contributions, including the deformation energy E_def, which describes the energy required to distort either the CO₂ molecule or the Mo₆C₅/C substrate from their respective optimized isolated structures to the configurations they adopt upon CO₂ adsorption, and the attachment energy, E_att, which accounts for the interaction energy between the deformed parts. Thus:

E_ads = E_CO2/subs − E_subs − E_CO2 (1)

E_def = E^ads_X − E^free_X (2)

where E_CO2/subs corresponds to the total energy of Mo₆C₅/C with CO₂ adsorbed; E_subs the total energy of the substrates (Mo₆C₅/C for supported cases, and Mo₆C₅ for isolated cases); E_CO2 the energy of the CO₂ molecule in the gas phase; and E^ads_X and E^free_X the total energy of a separated X entity (for substrates X is Mo₆C₅ or Mo₆C₅/C, for the adsorbate X is CO₂) in the adsorbed geometry and in its gas-phase optimized form, respectively. Finally, E^subs_def and indicate the energy cost to deform Mo₆C₅/C (Mo₆C₅ for isolated cluster cases) and the CO₂ molecule, respectively. According to these definitions, the CO₂ adsorption is thermodynamically favorable when E_ads is negative, indicating an exothermic process. Likewise, a negative E_att reflects a favorable interaction between the CO₂ and the catalyst; in contrast, E_def values are necessarily positive.

To describe the sites and bonding mode of CO₂ on the different models, we use a notation used in previous works⁴² derived from coordination chemistry. For example, η³-CO₂-μ³-C_BO_MO_M indicates the coordination of three atoms of the CO₂ molecule (η³) with three atoms of the MoC_y cluster (μ³), in such a way that the C atom of the CO₂ molecule is on a bridge site (C_B), either Mo–C, or Mo–Mo, while each of the CO₂ O atoms is located atop two metal atoms of the cluster (O_MO_M). Finally, to gather information on the chemical reactivity of the supported Mo₆C₅ cluster, the dissociation barrier of the adsorbed CO₂ into CO and O was evaluated by acquiring the transition state (TS) using the climbing-image nudged elastic band (CI-NEB) method,⁴³ with four intermediate images. The TS and minima were confirmed by vibrational frequency analysis, with TSs exhibiting a single imaginary frequency along the reaction coordinate. These vibrational frequencies were obtained by diagonalizing the appropriate block of the Hessian matrix, whose elements were computed as finite differences of analytical gradients, calculated only for the CO₂ molecule, i.e., decoupled from substrate phonons.

3. Results and discussion

To facilitate the following discussion, we first present the results of CO₂ interacting with the bare Mo₆C₅ cluster, serving as a reference for the intrinsic adsorption behavior. Then, we examine the interaction of CO₂ with Mo₆C₅ supported on FG, which allows us to evaluate the effect of the carbon-based support. Finally, to reveal the effect of carbon support curvature, the CO₂ adsorption on Mo₆C₅ supported on CG models is presented.

3.1. CO₂ interaction with unsupported Mo₆C₅

The CO₂ interaction with the isolated Mo₆C₅ cluster in the gas phase was first evaluated considering all conceivable high-symmetry possible adsorption sites and modes. The E_ads values, shown in Fig. 2 and listed in Table 1, show that for bare Mo₆C₅, E_ads ranges from −0.83 to −2.68 eV. In particular, the strongest adsorptions, with E_ads of −2.01 and −2.68 eV, are both related to the Mo₃ hollow site (see Fig. 2), consistent with reported data.²³ This site would turn out to be inaccessible when the cluster is supported. However, the other sites that will still be available when Mo₆C₅ is adsorbed exhibit more moderate and reduced E_ads values from −0.83 to −1.55 eV. Clearly, local Mo-rich sites forming hollows are particularly active towards CO₂, as seen e.g. on similar two-dimensional Mo–carbides, the MXenes.⁴² For the remaining sites (see Fig. 2), the strongest CO₂ adsorption is for the η³-CO₂-μ³-C_CO_MO_M bonding mode with the CO₂ C atom on the topmost corner site, while the two CO₂ O atoms coordinate with seldom adjacent Mo atoms. Upon adsorption, a covalent C–C bond is generated with a length of 1.44 Å, falling within the typical range of C–C and C=C bond lengths. This CO₂ chemisorption leads to the symmetric elongation of both C–O bonds, with d(CO) from 1.17 Å in a vacuum to 1.34 Å in the adsorbed molecule (see Table 2). Simultaneously, the CO₂ bond angle, α(OCO), changes from 180° to 121.4°, with a charge transfer from MoC_y to CO₂ of 1.08e (see Table 1). Finally, even if such a conformation is not as strong as the adsorption on the Mo₃ site would be, it is still more pronounced than that on the δ-MoC (001) surface with E_ads of −1.35 eV,¹⁸ highlighting the increased activity of the cluster compared to extended surfaces.

Fig. 2 Labelled atomic structures with adsorption energies, E_ads, and relative adsorption energies, ΔE, in eV, for CO₂ adsorbed on bare Mo₆C₅. Red spheres denote O atoms, while the rest of the color coding is as in Fig. 1.

Table 1 Results for CO₂ adsorption on isolated Mo₆C₅, including adsorption configurations, E_ads, E^subs_def, , and E_att, all in eV. Q corresponds to the Bader charge of the adsorbed CO₂, in e. E_ads of CO₂ on the extended δ-MoC (001) surface is included for comparison.²⁰ For CO₂ in the gas phase, d(CO) is calculated to be 1.18 Å and α(OCO) is 180°

Config.	E ads	E ^subsdef		E att	Q
B1	−2.68	0.39	3.50	−6.57	−1.51
B2	−2.01	0.39	2.02	−4.42	−1.24
S1	−1.55	0.93	3.63	−6.11	−1.08
S2	−1.35	0.64	3.11	−5.10	−0.76
S3	−1.16	0.40	2.84	−4.40	−0.88
S4	−1.10	0.46	2.95	−4.52	−0.76
S5	−1.53	0.88	3.56	−5.97	−1.11
S6	−0.83	0.45	2.96	−4.24	−0.88
S7	−1.04	0.33	2.92	−4.29	−0.74
S8	−0.94	0.32	2.90	−4.16	−0.88
S9	−0.96	0.24	2.80	−4.00	−0.73
S10	−0.86	0.48	3.10	−4.44	−0.96
δ-MoC (001)	−1.35	—	—	—	—

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Table 2 Results for CO₂ adsorption on isolated Mo₆C₅, including the CO₂ adsorption bonding mode, bond lengths, d(CO), given in Å for each of the two bonds, and molecular angle, α(OCO), given in degrees. Values for the extended δ-MoC (001) surface are included for comparison.¹⁸ For CO₂ in the gas phase, d(CO) is calculated to be 1.18 Å and α(OCO) is 180°

Config.	Bonding mode	d(CO)	d(CO)	α(OCO)
B1	η^2-CO2-μ^3-CBOMOM	1.42	1.23	123.7
B2	η^2-CO2-μ^2-CCOM	1.29	1.26	134.1
S1	η^3-CO2-μ^3-CBOMOM	1.34	1.34	121.4
S2	η^2-CO2-μ^2-CCOM	1.38	1.22	124.7
S3	η^3-CO2-μ^3-CBOMOM	1.30	1.30	125.8
S4	η^2-CO2-μ^2-CCOM	1.37	1.22	125.5
S5	η^3-CO2-μ^3-CBOMOM	1.35	1.33	122.9
S6	η^3-CO2-μ^3-CBOMOM	1.32	1.29	125.1
S7	η^2-CO2-μ^2-CCOM	1.36	1.22	125.4
S8	η^3-CO2-μ^3-CBOMOM	1.31	1.30	125.6
S9	η^2-CO2-μ^2-CCOM	1.35	1.22	126.0
S10	η^3-CO2-μ^3-CBOMOM	1.31	1.31	124.3
δ-MoC (001)	η^1-CO2-μ^1-CC	1.29	1.29	129.0

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For most stable cases and other less strongly attached sites, the breakdown of the interaction energies is reported in Table 1 and visually shown in Fig. 3. In addition, the correlation between CO₂ adsorption and these energetic parameters, as well as relationships between the CO₂ Bader charge and α(OCO) with each of the four energy terms, are presented in Fig. S2 in the SI. Most relevant trends are shown in Fig. 3, revealing a linear trend between E_ads and the Bader charge (Q) of the adsorbed CO₂, thus underlining that stronger adsorption is accompanied by a larger electron transfer from the MoC_y cluster to the CO₂ molecule, reinforcing this charge transfer as the main driving force of CO₂ capture and activation.⁴⁴ Furthermore, an almost linear correlation is also found between the CO₂ angle, α(OCO), and the CO₂ deformation energy, implying that the energy cost of bending CO₂ is proportional to the acquired angle. So far, the interaction of CO₂ on the bare Mo₆C₅ has been fully described, and the question of the effect of flat graphene will be tackled next.

Fig. 3 (a) CO₂ adsorption on bare Mo₆C₅ on the different sites and modes and the energy contribution breakdown; (b) Bader charge (Q) of adsorbed CO₂vs. E_ads, showing the linear correlation and the regression coefficient, R; and (c) α(OCO) vs. the deformation energy of CO₂, with the linear equation and R value.

3.2. CO₂ interaction with Mo₆C₅ supported on FG

What would be the effect of the underlying FG support on the CO₂ interaction on an Mo₆C₅ cluster? To analyze this, it is first mandatory to understand the nature of the interaction between Mo₆C₅ and the FG substrate. As detailed in Section S1 of the SI, Mo₆C₅ interacts strongly with FG, with some electron transfer from the carbide cluster to the graphene, as detailed in a previous work.³⁴ In particular, the E_ads of Mo₆C₅ onto FG is as strong as −3.66 eV, which is almost 1 eV larger than the energy of the interaction of CO₂ on the Mo₆C₅ Mo₃ site (see Table 1 and Fig. 4), thus backing up the concept that such a site will be employed to anchor on the FG, and therefore, only other sites of the cluster will be available for CO₂. Having discarded the involvement of the Mo₃ site, all possible CO₂ adsorption configurations on the remaining sites are presented in Fig. 5, with detailed results shown in Tables 3 and 4, and a comparison of the different energy contributions is shown in Fig. 4, along with the isolated Mo₆C₅ reference. Preliminary tests confirmed that CO₂ weakly physisorbs onto pristine FG and CG supports (E_ads is approximately −0.4 eV), with no significant CO₂ activation, i.e., negligible distortion of bond length and angle, in agreement with the literature for the interaction of CO₂ on carbon nanotubes.⁴⁵ Because this interaction is much weaker than that with the MoC_y, we focused our analysis on the composite system of MoC_y/C.

Fig. 4 (a) Left: The most stable CO₂ adsorption on bare Mo₆C₅ (top) and the most stable Mo₆C₅ adsorption on FG with corresponding E_ads values. Right: The most favorable CO₂ adsorption on Mo₆C₅/FG (bottom) and the corresponding site on bare Mo₆C₅ (top). The atom colors are as in Fig. 2. (b) Comparison of adsorption energetics for ten configurations on bare Mo₆C₅ and Mo₆C₅/FG.

Fig. 5 Side view of adsorbed CO₂ structures on Mo₆C₅/FG, with E_ads and ΔE values. The color coding is as in Fig. 2.

Table 3 CO₂ adsorption on Mo₆C₅ on FG, including adsorption configuration, E_ads, E^subs_def, , and E_att, all in eV. Q corresponds to the Bader charge of the adsorbed CO₂, in e

Config.	E ads	E ^subsdef		E att	Q
S1	−2.08	1.29	3.27	−6.64	−0.95
S2	−1.95	1.14	3.06	−6.15	−0.76
S3	−1.72	1.49	3.25	−6.46	−1.01
S4	−1.72	1.39	3.02	−6.14	−0.78
S5	−1.30	1.48	3.59	−6.37	−1.08
S6	−1.29	1.20	3.31	−5.81	−0.95
S7	−1.31	1.40	3.04	−6.14	−0.74
S8	−0.77	1.55	3.05	−5.37	−0.91
S9	−0.66	1.66	2.87	−5.19	−0.70
S10	−0.56	1.48	3.15	−5.20	−0.97

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Table 4 Results for CO₂ adsorption on Mo₆C₅ on FG, including the CO₂ adsorption bond sites, lengths, d(CO), given in Å for each of the two bonds, and molecular angle, α(OCO), given in degrees

Config.	Bonding mode	d(CO)	d(CO)	α(OCO)
S1	η^3-CO2-μ^3-CBOMOM	−2.08	1.32	1.32
S2	η^2-CO2-μ^2-CCOM	−1.95	1.38	1.22
S3	η^3-CO2-μ^3-CBOMOM	−1.72	1.32	1.32
S4	η^2-CO2-μ^2-CCOM	−1.72	1.38	1.22
S5	η^3-CO2-μ^3-CBOMOM	−1.30	1.33	1.35
S6	η^3-CO2-μ^3-CBOMOM	−1.29	1.31	1.33
S7	η^2-CO2-μ^2-CCOM	−1.31	1.37	1.22
S8	η^3-CO2-μ^3-CBOMOM	−0.77	1.32	1.31
S9	η^2-CO2-μ^2-CCOM	−0.66	1.35	1.22
S10	η^3-CO2-μ^3-CBOMOM	−0.56	1.30	1.32

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Upon supporting Mo₆C₅ on FG, note that the Mo₃ site anchors the cluster on FG, and Mo₆C₅ atoms are classified as corner, edge, and interface sites, as shown in Fig. 1, with progressively higher coordination numbers. Notably, corner sites of Mo/C are more positively/negatively charged than other sites (see Fig. S3), enabling stronger interactions with CO₂, a point validated later. Additionally, a notable increase in the electronic states near the Fermi level, E_F, is observed (see the spin-polarized density of states (DOS) in Fig. S4 of the SI), which also includes the isolated Mo₆C₅ cluster and pristine FG. This can be an indication of enhanced electronic activity due to the interaction between the cluster and support. This is better appreciated in the differential DOS (see Fig. S4 of the SI) gained after subtracting the sum of the isolated components from the composite material, i.e., Mo₆C₅ and FG. This resulting redistribution of electronic density provides direct evidence of electronic coupling and charge delocalization at the interface.

Another general trend observed is that the presence of the FG support enhances CO₂ adsorption, particularly on most attachment sites, as seen in Fig. 4, where in a series of cases, CO₂ binds more strongly to the Mo₆C₅/FG than to the unsupported Mo₆C₅, i.e., with more negative E_ads values. In particular, the enhancement is more remarkable on the first four sites, S1 to S4, belonging to the four lowest-coordinated atoms (see Fig. 1), i.e., corner Mo atoms, and corner C atoms either far from or close to the support. These four atoms form a quadrilateral region that exhibits significantly stronger CO₂ adsorption than other sites. On average, the E_ads of sites S1 to S4 increase by approximately 0.58 eV compared with the corresponding sites on the unsupported Mo₆C₅ cluster.

As far as the coordination effect is concerned, it is worth stating that the S1 and S3 configurations adopt the η³-CO₂-μ³-C_CO_MO_M binding mode. A clear tip effect is observed, also present in the bare cluster: CO₂ binds farthest from the carbon support, as in configuration S1, with stronger adsorption (∼0.36 eV) than at the carbon site closer to the support, as in configuration S3. Furthermore, S1 shows stronger adsorption than configuration S2, highlighting that the η³-CO₂-μ³-C_CO_MO_M mode is more favorable than the η²-CO₂-μ²-C_CO_M mode, having three contact points instead of two, in line with trends observed on the unsupported cluster. Notably, by comparing configurations S1 and S5 on Mo₆C₅/FG, both featuring the same binding mode, it can be seen that the substitution of one corner Mo with an edge Mo (see Fig. 5) results in a significant weakening of CO₂ adsorption, with E_ads reduced by ∼0.78 eV. However, the same comparison on the bare Mo₆C₅ cluster shows only a negligible difference of ∼0.02 eV. This suggests that the carbon substrate polarizes the electronic structure of Mo₆C₅, enhancing the reactivity of interface and tip sites while suppressing the activity of middle-region sites toward CO₂ activation. Following this logic, the observed decrease of E_ads for configurations S8 to S10 on Mo₆C₅/FG relative to the bare cluster case can be reasonably attributed to the involvement of middle-region sites (see the Mo and C edge sites in Fig. 1).

Interestingly, it appears that for all CO₂ adsorption configurations on Mo₆C₅/FG, the E^subs_def values are significantly higher than those of the bare cluster (see the energy contributions in Fig. 4). To understand the structural difference between supported and bare clusters, we analyzed the geometrical root-mean-square displacement (RMSD) values for all studied configurations reported in see Table S1. Taking the CO₂ adsorption configuration S1 as a reference, the RMSD of bare Mo₆C₅ decreases from 0.15 Å to 0.09 Å upon support on FG. This, together with the higher deformation energy of the Mo₆C₅/FG composite and the smaller distortion of the cluster, highlights the significant deformation occurring in the graphene support. Although the RMSD of the support is modest (∼0.013 Å, see Table S1), the large number of carbon atoms (96) confirms its intrinsic flexibility.

This analysis supports a kind of support-mediated fluxional mechanism, where the redistribution of strain contributes to both enhanced stability and improved catalytic performance, without compromising the integrity of the cluster's active sites. As the carbon support undergoes significant structural relaxation in response to CO₂ adsorption on the supported cluster, the correlation between E_ads and the Bader charge is weakened, as shown in Fig. S5 of the SI. Instead, as shown in Fig. S6, another clear correlation emerges between the deformation energy of the CO₂ molecule and its Bader charge, Q. Regarding the CO₂ deformation energy, no consistent trend is observed upon adsorption at the FG-supported Mo₆C₅ (see Fig. 4). The extent of CO₂ bending varies depending on specific adsorption configurations. However, due to the markedly larger deformation energies of the support, the calculated E_att values are generally more negative for Mo₆C₅/FG than for the bare clusters across all configurations (see Fig. 4). This indicates that, despite the additional structural cost from deformation, the overall attachment between CO₂ and the supported cluster is thermodynamically more favorable than on the bare cluster.

3.3. CO₂ interaction with Mo₆C₅ supported on CG surfaces

Finally, the introduction of substrate curvature may further affect the electronic properties of the supported metal carbide, and, in turn, affect its chemistry. This is clear from the adsorption energy of the Mo₆C₅ cluster on concave and convex regions of CG. For a given curvature (κ = 1.41 nm⁻¹, see Fig. S7 of the SI), Mo₆C₅ binds more strongly on the concave region of the support than on FG, with an enhanced adsorption of the Mo₆C₅ from −3.66 eV to −3.94 eV. This is accompanied by a larger electron transfer from the carbide to the substrate, 1.85e vs. 1.66e for FG, as estimated from Bader analysis of the electron density. In contrast, for the same curvature, the interaction in convex regions is weaker (E_ads of −2.87 eV), with a reduced charge transfer (1.50e). This trend is consistent with previous findings, where a concave surface enhances carbide–carbon support interaction and charge redistribution, while the opposite occurs for convex regions.³⁴ Furthermore, even if the Mo₆C₅ cluster displays a discrete spectrum of energy levels, we found it convenient to consider the equivalent of the d-band center of Mo₆C₅ on FG, which is shown in Fig. S8. The d-band center shifts from −0.96 eV for support on FG to −0.83 and −0.58 eV when supported in the concave and convex regions, respectively. This modulation of the d-band center by substrate curvature partly governs the different activities toward CO₂ adsorption and activation, as discussed in the following parts.

To further analyze the effect of curvature of the C support on the Mo₆C₅/CG model systems, all possible CO₂ adsorption configurations on Mo₆C₅ supported on both concave and convex regions of CG were systematically explored, as illustrated in Fig. 6. The configuration indices were kept consistent with those used in bare and FG-supported cases to facilitate direct comparison. Detailed energetics and structural information can be found in Fig. S9, S10 and Tables S2, S3 in the SI. In Fig. 7, the CO₂ adsorption energies for Mo₆C₅ supported on carbon substrates with concave and convex geometries are systematically compared across all configurations.

Fig. 6 Structures for CO₂ adsorption in concave regions (top) and convex regions (bottom) of Mo₆C₅/CG, with E_ads and ΔE values. The color coding is as in Fig. 2.

Fig. 7 Adsorption energy breakdown contributions of CO₂ on Mo₆C₅ clusters supported by FG and CG.

Regardless of whether the Mo₆C₅ cluster is supported in concave or convex regions, configuration S1 remains the most stable available site for CO₂ adsorption. For this binding mode, the CO₂ adsorption strength follows the order convex > FG > concave, with E_ads values of −2.29 eV, −2.08 eV, and −2.02 eV, respectively (see Fig. 7). This indicates that the local curvature modulates the carbide–support interaction and, consequently, the CO₂ adsorption strength. Convex-supported Mo₆C₅ exhibits the strongest adsorption and thus the most favorable activation potential. For all S1 configurations, CO₂ adsorption on carbon-supported Mo₆C₅ is consistently stronger than on the bare cluster; even the weakest case on the concave-supported surface still outperforms the corresponding site on bare Mo₆C₅ (−1.55 eV), highlighting the overall promotional effect of the carbon support. These results underline that, in addition to MoC_y stoichiometry and surface sites, substrate curvature is another tuning parameter for MoC_y chemical activity.

Next, we briefly discuss the rest of the CO₂ adsorption configurations. Across all curvatures, S2 follows the trend already observed for S1, with binding of CO₂ on the topmost active sites with the η²-CO₂-μ²-C_CO_M binding mode having generally weaker bonds than the η³-CO₂-μ³-C_CO_MO_M mode. Interestingly, a comparison between S1 and S3 on both concave and convex surfaces reveals that the sites farther from substrate exhibit stronger CO₂ activation capacity compared to closer sites, once again confirming the already mentioned tip effect as identified above in bare and FG-supported Mo₆C₅ systems. To further elucidate this behavior from an electronic structure perspective, the projected DOS (PDOS) for the two distinct carbon atoms was computed, having Mo₆C₅/FG as a reference (see Fig. S11 of the SI). The PDOS analysis shows that these farther sites exhibit a higher DOS near the E_F level compared to closer sites. This suggests a larger availability of electronic states for interaction with CO₂, which likely facilitates stronger adsorption and activation at these sites. Statistical analysis in Fig. 7 shows that nine out of ten CO₂ adsorption configurations on Mo₆C₅ supported in convex regions exhibit more negative adsorption energies than in concave regions, indicating generally stronger CO₂ adsorption on convex-supported systems. In contrast, no clear trend is observed in the deformation energies of CO₂ molecules between the two curvature types. However, within each case, CO₂ deformation energies correlate well with the Bader charges, Q, of the adsorbed molecule and the α(OCO) angle bending, as shown in Fig. S9 and S10 of the SI. Regarding substrate deformation, configurations on concave surfaces typically exhibit larger deformation energies, likely due to the stronger carbide–support interaction in these regions, an effect that ultimately results in weaker E_ads but comparable E_att across both curvatures.

3.4. CO₂ dissociation on Mo₆C₅ supported on CG surfaces

To further investigate the effect of the carbon support on the chemistry of the supported Mo₆C₅ cluster, we explored the CO₂ dissociation pathway on Mo₆C₅ supported on FG and on the concave and convex regions of CG. For consistency, the most stable adsorption configuration S1 mode is used for all systems. The corresponding total energy profile is shown in Fig. 8 with the corresponding energy barriers, E_b, and reaction step energy changes, ΔE, summarized in Table S4 of the SI.

Fig. 8 CO₂ dissociation energy profiles on bare Mo₆C₅ clusters and on FG, concave CG, and convex CG surface models.

Compared to the bare Mo₆C₅ cluster, which shows an E_b of 1.72 eV, all supported cases exhibit significantly lower barriers (∼1.10 eV), confirming the promoting effect of carbon supports. The concave CG-supported system presents the lowest E_b and most favorable ΔE, indicating enhanced CO₂ activation and conversion in concave regions. Although the energy barrier difference between convex and concave regions is modest (∼0.07 eV), it accounts for approximately 6.7% of the overall energy barrier, which may translate into a significantly amplified effect on reaction kinetics due to the exponential dependence of the rate on the activation energy barrier, as described by standard transition state theory (TST):

where k is the reaction rate, Q^# and Q^react are the partition functions at the transition state and reactant configurations, respectively, k_B is the Boltzmann constant, h is Planck's constant, and T is the reaction temperature. To estimate the kinetic impact of a 0.07 eV difference in the activation barrier between convex and concave configurations, a rough estimate can be obtained by simply assuming that the preexponential factor is approximately the same for the reaction at concave and convex regions. Therefore, at room temperature, one would get:
indicating that the modest difference in E_b implies a 15-fold increase in the reaction rate, underscoring the so far unknown but significant role of support curvature in tuning the catalytic activity of supported MoC_y clusters toward CO₂ conversion.

To conclude the analysis, we computed the vibrational frequencies of CO₂ adsorbed on Mo₆C₅ for the S1 configuration as a representative example across the above systems, with results summarized in Table S5 of the SI. The results show that the vibrational frequencies of adsorbed CO₂ are significantly different from those of the gas phase molecule. However, the values for the adsorbed molecule vary by less than 10 cm⁻¹ across the different surface curvatures, indicating that such small differences may be challenging to resolve experimentally via infrared spectroscopy. The similarity in vibrational signatures suggests that the nature of the CO₂ binding remains essentially the same across the different support geometries. Therefore, the observed differences in CO₂ adsorption energies are attributed primarily to the influence of the carbon support on the electronic properties of the Mo₆C₅, as discussed in previous work.³⁴

4. Conclusions

The interaction of CO₂ with bare and carbon-supported Mo₆C₅ clusters, taken as an example, has been systematically studied using DFT calculations with the PBE-D3 functional. On bare Mo₆C₅, the highly reactive Mo₃ site strongly binds and activates CO₂. When supported on flat graphene, the carbon support coordinates with this locally metal-rich site, mitigating the potential overactivity and instability observed in previously reported Mo-rich MoC_y clusters,¹⁴ and promoting the activity of remaining near-stoichiometric active sites toward CO₂ adsorption and activation. Introducing support curvature further modulates the interaction: the convex regions enhance CO₂ adsorption, while the Mo₆C₅ anchored in concave regions shows the lowest CO₂ dissociation energy barrier, with the most favorable exothermic ΔE, implying that the support curvature is another parameter for tuning the catalytic activity of supported MoC_y clusters. These findings are likely to be general and highlight the key, yet previously disregarded, role of carbon support curvature, guiding the future rational design of MoC_y/C catalysts with improved catalytic performance toward CO₂ conversion.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

Input and output files are available from the authors upon request.

Supplementary information: The supplementary information contains the k-point convergence test; linear correlations between the CO₂ Bader charge and the molecule angle vs. energy contribution breakdowns; atomic and electronic structure analysis of Mo₆C₅/FG; Density Of States (DOS) of supported Mo₆C₅; Root-Mean-Square Displacement (RMSD) of fragments in interactions; Projected DOS (PDOS) for d-orbitals of supported Mo₆C₅; tip effect of supported Mo₆C₅ towards CO₂ adsorption; table of energy profile of CO₂ adsorption and activation on supported Mo₆C₅; vibrational frequencies of CO₂ adsorbed on isolated and supported Mo₆C₅. See DOI: https://doi.org/10.1039/d5cp02714d.

Acknowledgements

The research carried out at the Universitat de Barcelona has been supported by the Spanish MCIN/AEI/10.13039/501100011033 PID2021-126076NB-I00 and TED2021-129506B-C22 projects, partially funded by FEDER Una manera de hacer Europa, and by the María de Maeztu CEX2021-001202-M grant. The authors acknowledge partial support from COST Action CA18234 and from the Generalitat de Catalunya 2021SGR79 grant. W. C. thanks the China Scholarship Council (CSC) for financing his PhD (CSC 202308440222). F. V. thanks the ICREA Academia Award 2023 with Ref. Ac2216561.

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