Oxidative dehydrogenation of C₂H₆ and CO₂ mediated by Rh_xNb_y⁻ (x + y = 5) clusters

Abstract

Oxidative dehydrogenation (ODHE) of C₂H₆ and CO₂ to generate C₂H₄ and CO is industrially important but remains a long-standing challenge due to the complexity of this co-conversion and the thermodynamically stable and kinetically inert nature of both reactants. Herein, we theoretically demonstrated that the Rh_xNb_y⁻ (x + y = 5) bimetallic clusters can drive the ODHE of C₂H₆ and CO₂ to produce C₂H₄, CO, and H₂O. The results indicated that the desorption of C₂H₄ and CO takes place under mild conditions, and the increased number of Rh atoms in Rh_xNb_y⁻ leads to progressively more difficult C₂H₄ desorption. In contrast, the formation and evaporation of H₂O represent the kinetically and thermodynamically demanding pathway to govern the overall efficiency of ODHE. This finding provides an integrated picture to understand the fundamental mechanisms of the ODHE of C₂H₆ and CO₂. The selective release of C₂H₄ and the rate-determining behaviour of H₂O generation were rationalized.

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Introduction

Carbon dioxide (CO₂) represents the most significant greenhouse gas in the Earth's atmosphere, surpassing methane (CH₄) and nitrous oxide and becoming the principal contributor to global warming.^1–3 To reduce CO₂ emissions and mitigate greenhouse effect,^4–6 countries worldwide are actively exploring novel strategies for the resource utilization of CO₂.^7–11 However, the achievement of CO₂ activation and subsequent conversion under mild conditions poses serious challenges owing to the thermodynamic stability and kinetic inertness of the O–CO bond (5.48 eV).^12,13 Nowadays, we are in the midst of the third revolution in the oil and gas industry owing to the emergence of shale gas chemistry.^14–16 The primary components of shale gas are low-carbon alkanes (CH₄ and C₂H₆, ∼90%);^15,17–19 in this case, CO₂, serving as an appealing mild oxidant source, can be used in the transformation of light alkanes to synthesize industrial feedstocks and prevent over-oxidation.²⁰ Meanwhile, C₂H₆, as the second abundant component (3%–12%) after CH₄ in shale gas, is distinctly underutilized. The oxidative dehydrogenation (ODHE) of C₂H₆ and CO₂ (C₂H₆ + CO₂ → C₂H₄ + CO + H₂O, ΔH₀ = +1.86 eV)^17,21–24 is a promising route to generate C₂H₄, which represents one of the most important intermediates in the chemical industry. Considerable efforts have been made to improve the performance of related heterogeneous catalysts and drive these conversions taking place under mild conditions, such as controlling the ratio of active components,²¹ altering the composition of the reactive phase interface,^21,22,25 and modifying the catalyst support.^26,27 The central goal of these strategies lies in engineering the microenvironment of active sites that govern the catalytic conversion. However, it is a big challenge to understand the nature of active sites and get a fundamental understanding of reaction mechanisms due to the inherent complexity of real-life catalysts.²⁸

Gas-phase cluster study emerges as a promising approach to face this challenge because the active sites involved in the activation and transformation of reactants in condensed-phase catalysts are typically composed of a limited number of atoms.^29,30 Cluster reactions performed under isolated conditions provide prominent advantages to permeate and modify the geometrical and electronic structures of active species microscopically, thereby providing the scientific guidance to design superior catalysts.^31–35 The unique geometrical and electronic properties of Nb- and Rh-containing clusters endow them with high reactivity in C₂H₆ dehydrogenation or CO₂ reduction. The Luo group demonstrated that the pure Nb_n⁺ (n = 1–21) and Rh_n⁺ (n = 1–24) clusters can drive C₂H₆ dehydrogenation to generate Nb_nC_1–4⁺ and Rh_nC₂H₄⁺.^36,37 Ma and He identified that the Nb- and Rh-containing clusters, such as Nb₃C₄⁻,³⁸ Nb₂BN₂⁻,³⁹ RhTaC₂⁻,⁴⁰ Rh₂VO_2–3^–,⁴¹ RhTiO₂⁻,⁴² Rh_nVO_3,4⁻ (n = 3–7),⁴³ and Rh_n⁻ (n = 3–11),⁴⁴ exhibit outstanding reactivity in CO₂ reduction. These studies indicate that the Rh–Nb heteronuclear clusters can be potential candidates to drive the catalytic conversion of C₂H₆ and CO₂; however, such studies have not been reported in the gas phase. Herein, we theoretically designed and demonstrated that a series of Rh_xNb_y⁻ (x + y = 5) clusters can drive the ODHE of C₂H₆ and CO₂. This chosen cluster size represents a computationally tractable model that allows for relatively exhaustive exploration of pathways while being sufficiently large to capture the composition-dependent reactivity of Rh_xNb_y⁻ in the catalysis of CO₂-assisted dehydrogenation of C₂H₆. Note that theoretical calculations with density functional theory (DFT) have been demonstrated to be powerful enough to predict the structure and properties of a particular kind of catalysts, and some predicted species have been substantiated in experiments.^45,46 These fascinating results are of substantial importance to understand the nature of Rh–Nb-based heterogeneous catalysts in driving the ODHE of C₂H₆ and CO₂ at a strictly molecular level.

Results

The lowest-lying isomers and the electrostatic potential (ESP) maps of the Rh_xNb_y⁻ (x + y = 5) clusters are shown in Fig. 1A, and the other DFT-calculated low-lying isomers of Rh_xNb_y⁻ are shown in Fig. S1 and S2 in the SI. It is obvious that the number of Rh atoms in Rh_xNb_y⁻ significantly affects the geometrical and electronic structures of the clusters (Fig. 1A), and the negative charges accumulate gradually towards the periphery of clusters because of the larger electronegativity of Rh than that of Nb (Rh = 2.28, Nb = 1.60).²⁴ Note that the positively charged environment⁴⁷ is more favourable to polarize alkane molecules because the σ (C–H) orbital of alkane generally acts as an electron donor while the empty orbital of clusters behaves as the acceptor. Therefore, clusters surrounded by negatively charged metal atoms can be less accessible for alkane molecules.^48–50Fig. 1B displays clearly that it is more challenging for the initial approach of C₂H₆ towards ³Rh₄Nb⁻, with respect to other Rh_xNb_y⁻ clusters.

Fig. 1 ESP maps for ¹RhNb₄⁻, ³Rh₂Nb₃⁻, ¹Rh₃Nb₂⁻, and ³Rh₄Nb⁻. The superscripts represent spin multiplicities (A). Relaxed potential energy curve with the approach of C₂H₆ towards the Rh_xNb_y⁻ clusters (B).

The pathways in the reaction of ¹RhNb₄⁻ (IS01) with C₂H₆, as well as the reaction of product ³RhNb₄H₂⁻ after C₂H₄ evaporation with CO₂, are illustrated in Fig. 2 and 3 to understand the mechanisms of the ODHE of C₂H₆ and CO₂ mediated by Rh_xNb_y⁻, and other results are presented in Fig. S6–S11. Fig. 2 shows that C₂H₆ prefers to be weakly attached to a single Nb atom (Nb1) (¹I1, ΔH₀: −0.28 eV) through two H atoms. Driven by the strong Nb–C (5.43 eV) and Nb–H (2.30 eV) bonds,¹² the first C–H bond of C₂H₆ undergoes oxidative addition through a positive barrier of +0.11 eV (¹TS1). The transferred H atom is captured by two nearby Nb atoms, and the resulting intermediate is greatly stabilized (¹I2, ΔH₀: −1.31 eV). This step is generally recognized as the rate-limiting step in the initial alkane activation.⁵¹ The subsequent H atom transfer steps occur on a relatively flat pathway (¹I2 → ³I3, Fig. 2 and S3) and a spin flip process from the singlet to the triplet state is required. Activation of the second C–H bond from ³I3 is facile to proceed (³TS3: ΔH₀: −1.14 eV) to give rise to a significantly stabilized intermediate ³I4 (ΔH₀: −2.41 eV), which has enough internal energy to evaporate C₂H₄ into the gas phase and produce ³RhNb₄H₂⁻ (³P₁ + C₂H₄: ΔH₀: −0.49 eV). Moreover, an alternative pathway involving the recombination of two H atoms to generate H₂ is seemingly more favourable (¹P₂ + H₂: ΔH₀: −0.62 eV). However, H₂ desorption is entropically disfavoured (ΔG₂₉₈ = −0.38 eV) with respect to C₂H₄ evaporation (ΔG₂₉₈ = −0.52 eV) owing to the intricate and convoluted H migration and H–H coupling steps to drive H₂ generation, reinforcing that C₂H₄ desorption is an entropy-driven process. Moreover, the route to rupture the C–C bond of C₂H₄ from ³I4 to generate CH₄, a competitive product that commonly decreases the selectivity of C₂H₄, was also considered (Fig. S3). The calculations confirm that CH₄ formation is thermodynamically more favorable, but the slightly higher kinetic barrier to form the fourth C–H bond of CH₄ makes CH₄ generation kinetically hindered.

Fig. 2 DFT-calculated potential energy profile for the reaction ¹RhNb₄⁻ + C₂H₆. Relative energies (ΔH₀/eV and ΔG₂₉₈/eV) for intermediates (Is) and transition states (TSs) are shown. The superscripts represent spin multiplicities. Bond lengths are given in pm. See details in Fig. S3.

Fig. 3 DFT-calculated potential energy profile for the reaction ³RhNb₄H₂⁻ (³P₁) + CO₂. Relative energies (ΔH₀/eV) for Is and TSs are shown. The superscripts represent spin multiplicities. Bond lengths are given in pm. See details in Fig. S4.

The resulting product, ³RhNb₄H₂⁻, can capture a CO₂ molecule. Fig. 3 shows that CO₂ can be anchored by two Nb atoms with a large binding energy of 2.53 eV (¹I7), during a process in which CO₂ is highly activated with the O–C–O angle changing from 180° in the free state to 135° in ¹I7. In the next step, the O–CO bond is ruptured to form a more stable intermediate ³I8 (ΔH₀: −3.14 eV), from which two distinct pathways emerge to close the catalytic cycle. The key difference between the two pathways is whether H₂O generation occurs with (path I) or without (path II) CO attached to the cluster. In path I, the couplings of two O–H bonds (¹TS7 and ¹TS8) to form the attached H₂O molecule (³I12) represent the rate-determining steps, followed by consecutive desorption of CO and H₂O from the system. Note that these desorption processes are energetically demanding, and elevated temperatures are required. Although yielding the same thermodynamic products, the O–H coupling processes in path II that occur without CO attachment must overcome substantially higher kinetic barriers (³TS9 and ¹TS10). Concurrently, CO could desorb prior to H₂O formation because of the thermodynamically feasible process (ΔH₀: −1.21 eV). A comprehensive survey on this ODHE process of C₂H₆ and CO₂ mediated by ¹RhNb₄⁻ highlights that the generation of C₂H₄ and desorption of CO occur under near-ambient conditions (Fig. 2), while the final formation and evaporation of H₂O into the gas phase is thermodynamically and kinetically challenging to limit the overall efficiency of the catalysis (Fig. 3). A similar trend is observed in driving the catalysis of ODHE of C₂H₆ and CO₂ mediated by other Rh_xNb_y⁻ clusters (Fig. S6–S11), and the increased number of Rh atoms (x > 1) in Rh_xNb_y⁻ makes C₂H₄ generation kinetically or thermodynamically more difficult compared to the pathway mediated by RhNb₄⁻ (Fig. 2 and S6, S8, S10). In summary, with the increase in Rh atoms in the Rh_xNb_y⁻ clusters, the desorption of C₂H₄ or H₂ happens from the Nb site towards the Rh site (Fig. S10). Note that the Rh–C (6.01 eV) and Rh–H (2.50 eV) bonds are stronger than Nb–C (5.43 eV) and Nb–H (2.30 eV) bonds,¹² respectively; therefore, the desorption of both products becomes more challenging. This conclusion parallels extensive experimental observations that Rh can facilitate C–H activation and induce coke deposition at the same time.^52,53 To get a comprehensive understanding of these catalytic reactions mediated by Rh_xNb_y⁻, the rate-determining steps are summarized in Table 1.

Table 1 DFT-calculated barriers for C₂H₅–H cleavage, C₂H₄–H cleavage, H–H coupling, O–H coupling and H–OH coupling, as well as the absolute barriers to desorb C₂H₄, H₂, CO and H₂O in the ODHE process mediated by Rh_xNb_y⁻ (x + y = 5)

Clusters	RhNb4^−	Rh2Nb3^−	Rh3Nb2^−	Rh4Nb^−
Barriers (eV)
C2H5–H cleavage	+0.11	+0.44	+0.19	+0.20
C2H4–H cleavage	−1.14	−0.49	−0.77	+0.18
H–H coupling	−0.84	+0.16	−0.80	−0.80
O–H coupling	+0.67	+1.03	+0.86	+0.50
H–OH coupling	+2.22	+2.91	+2.09	+1.55
Absolute barriers (eV)
C2H4	1.92	1.53	1.33	1.66
H2	0.17	0.13	0.55	0.83
CO	1.93	1.58	2.07	2.55
H2O	0.86	0.76	0.74	0.89

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The importance of the order of reactant feed has been identified for the co-conversion of CH₄ and CO₂ in gas-phase experiments; the pre-interaction of metal clusters with CH₄ rather than CO₂ is pivotal for the formation of value-added products.^54–56 Thus, the adsorption of CO₂ prior to C₂H₆ on ¹RhNb₄⁻ was investigated and the calculated results demonstrated that the reduction of CO₂ into gas-phase CO by ¹RhNb₄⁻ is a highly exothermic process to generate the isolated product ¹RhNb₄O⁻ (ΔH₀: −1.06 eV, Fig. S5A), which can also convert C₂H₆ into gas-phase C₂H₄ under relatively mild conditions (Fig. S5B). In marked contrast, the subsequent formation and evaporation of H₂O from the system is a substantially endothermic step (ΔH₀: +3.64 eV) and higher temperatures are indispensable to regenerate the reactant cluster ¹RhNb₄⁻. Note that catalysts cannot regulate the enthalpy of a catalytic reaction; thus, the thermodynamically more favorable step of CO₂ reduction mediated by ¹RhNb₄⁻ reasonably results in a more demanding process of H₂O evaporation. This finding further underscores the significance of introducing reactants in the correct order, as the initial activation of C₂H₆ into gas-phase C₂H₄ on clusters represents an energy-efficient pathway for the ODHE of C₂H₆ and CO₂.

Discussion

Composition-dependent catalytic reactivity of Rh_xNb_y⁻ (x + y = 5) in the ODHE of C₂H₆ by CO₂

In condensed-phase systems, the co-conversion of C₂H₆ and CO₂ exhibits significant complexity due to the competing processes of C–C bond preservation (ODHE of C₂H₆ into C₂H₄) and cleavage (dry reforming of C₂H₆ and CO₂ into synthesis gas).^22,23,57,58 The structural simplicity of supported monometallic catalysts (e.g., Co,^59,60 Ni,^21,23 Ga,^61,62 and Cr^63–65) faces the challenges to balance the selectivity of this catalytic conversion. In contrast, supported bimetallic catalysts (e.g., NiMo,²³ PdCo_x,⁶⁶ Ni₁Fe₃,²¹ PtNi,^27,57 and PdFe¹⁷) can effectively mitigate C–C scission and drive dehydrogenation, benefiting from synergistic effects (such as electronic effects, geometric effects, and bifunctional mechanisms). For example, the supported bimetallic catalyst Ni₁Fe₃ ²¹ can greatly suppress side reactions (e.g., coking from thermal cracking) and enhance the selectivity of C₂H₆ and CO₂ conversion towards the direction of C₂H₄ generation (∼78%). The endothermic nature makes such catalytic conversion a thermodynamically demanding process, and it is challenging to distinguish the rate-determining steps that govern the overall effectiveness of this catalysis under real-world conditions. Gas-phase cluster studies enable precise structural identification of active species in an unperturbed environment, and the elementary steps involved in the catalysis can be explored separately. The Rh_xNb_y⁻ clusters are highly promising and well-defined models for probing the mechanisms of C₂H₆ and CO₂ co-conversion over condensed-phase bimetallic catalysts. Note that the realistic ODHE reaction typically operates under charge-neutral conditions over supported catalysts, while the active site that is composed of a limited number of atoms could be neutral or charged under working conditions (e.g., Pt^δ+/TiO₂ ⁶⁷ and Au^δ−–O_v–Ti³⁺ sites⁶⁸), originating from the frequent charge transfer interaction between the active metal components and the support. In this case, clusters with a negative or positive charge can be used as active species to reveal the reaction mechanisms of related condensed-phase reactions under isolated conditions. The present calculations demonstrate that the Rh_xNb_y⁻ clusters can mediate the ODHE of C₂H₆ to C₂H₄ at ambient conditions, while H–O coupling and H₂O desorption are kinetically and thermodynamically demanding processes and elevated temperatures are required to regenerate the cluster catalysts.

Note that the desorption of products (e.g., C₂H₄, CO or H₂O) in the ODHE of C₂H₆ and CO₂ is highly composition-dependent on Rh_xNb_y⁻ (Fig. 4A and B). Fig. 4A clearly shows that the increased number of Rh atoms in Rh_xNb_y⁻ gradually switches the evaporation of C₂H₄ and/or H₂ from exothermic to endothermic. In the two competitive pathways, the desorption of C₂H₄ is always an enthalpy-favourable process with respect to H₂ release; thus, the two H atoms can be tightly anchored on the product Rh_xNb_yH₂⁻ and enable the subsequent reaction with CO₂ to form H₂O. For the reaction Rh_xNb_yH₂⁻ + CO₂ (Fig. 4B), although the desorption of CO and H₂O also exhibits composition-sensitive behavior, the release of CO is consistently exothermic (ΔH₀: −1.21 to −0.76 eV), whereas H₂O escape remains thermodynamically demanding (ΔH₀: +0.18 to +1.23 eV) across all Rh_xNb_y⁻ compositions. These results demonstrate unambiguously that the formation and desorption of H₂O is the rate-determining step to limit the overall efficiency of C₂H₆ and CO₂ co-conversion catalyzed by Rh_xNb_y⁻. Consequently, elevated temperatures are required to overcome the significant kinetic and thermodynamic barriers associated with these steps (Fig. 2 and 3 and S6–S11). The geometrical and electronic structures of crucial intermediates that govern C₂H₄ or H₂ desorption were specifically analysed to rationalize this component-sensitive behaviour. Pathway calculations on reactions Rh_xNb_y⁻ + C₂H₆ (Fig. 2 and S6, S8, S10) demonstrated that in the intermediate before C₂H₄ desorption (e.g., ³I4, Fig. 2), the formed C₂H₄ molecule stands stably on a single Nb [for Rh_xNb_y⁻ (x = 1–3) + C₂H₆] or Rh atom (for Rh₄Nb⁻ + C₂H₆). Thus, the charge environment of such a metal atom directly controls C₂H₄ desorption. Natural charge analysis (Fig. 4C) shows that the charged state of the Nb atom that is responsible for C₂H₄ adsorption in Rh_xNb_y⁻ (x = 1–3) changes from negatively to positively charged with the increase in Rh atoms, while the charged state of C₂H₄ suffers from negligible perturbation, indicating the gradually strengthened Nb–C₂H₄ interaction. The negative Rh atom for the reaction Rh₄Nb⁻ + C₂H₆ (−0.29 e in ³I90, Fig. S10) and the C₂H₄ (−0.20 e) moiety can seemingly give rise to weakened Rh–C₂H₄ bonding, while the laborious desorption of C₂H₄ can be attributed dominantly to the stronger Rh–C (6.01 eV) than the Nb–C (5.43 eV) bond.¹² This observation parallels condensed-phase experiments that Rh-containing catalysts typically induce deeper dehydrogenation of light alkanes; for example, the four C–H bonds of CH₄ tend to dissociate successively on the Rh surface because of the strong Rh–C bond.^69–71 These analyses are in reasonably good agreement with the change in thermodynamic data of C₂H₄ release (Fig. 4A). Note that the absolute barriers to desorb H₂ from the system are relatively small (0.13 eV–0.83 eV, Fig. 4D) with respect to that of C₂H₄ desorption, and the difficulty can be attributed to the substantial kinetic barriers for H₂ formation induced by the negative nature of both H adsorbates (Fig. S12).^13,72–76 Thus, the energy levels associated with H₂ escape were raised substantially and the gradual shift of the desorption site from Nb (x = 1 and 2 in Rh_xNb_y⁻) to Rh (x = 3 and 4 in Rh_xNb_y⁻) renders H₂ desorption energetically less favorable (Rh–H: 2.50 eV, Nb–H: 2.30 eV).¹² These extensive calculations demonstrated that the metal compositions of Rh_xNb_y⁻ predominantly govern the reaction enthalpy of elementary steps (Fig. 4A and B) and then the ability of product (C₂H₄, H₂, CO, and H₂O) desorption from the system can be regulated accordingly. An overview of the product desorption process shows clearly that, in addition to the energy-intensive process of H₂O evaporation, C₂H₄ desorption is most sensitive to the Rh/Nb ratio in the early state of catalytic reactions (Fig. 4A and B) because the thermodynamics of C₂H₄ desorption varies gradually from an exothermic to an endothermic process. In contrast, the release of CO and H₂ from the cluster exhibits irregular fluctuations with the variation of metal composition.

Fig. 4 Reaction heat (ΔH₀) of C₂H₄ and H₂ desorption for Rh_xNb_y⁻ + C₂H₆ (x + y = 5) (A). Reaction heat (ΔH₀) of CO and H₂O desorption for Rh_xNb_yH₂⁻ + CO₂ (x + y = 5) (B). Nb/Rh charge at the adsorption sites, and the charge of C₂H₄ desorption for Rh_xNb_yC₂H₆⁻ clusters (C). DFT-calculated absolute barrier for C₂H₄ and H₂ desorption for Rh_xNb_y⁻ + C₂H₆ (x + y = 5) (D). DFT-calculated natural charge (e) on the CO unit, O, H1, and H2 atoms along the pathways of CO₂ reduction mediated by ³RhNb₄H₂⁻, [path I (E) or path II (F)].

To achieve high olefin selectivity and avoid over-oxidation of light alkanes into CO_x and H₂O is an important issue, especially in O₂-assisted oxidative dehydrogenation because of the highly exothermic nature of these reactions.⁷⁷ In contrast, CO₂ functions as a soft oxidant and can greatly inhibit over-oxidation and improve olefin selectivity by removing hydrogen through reverse water–gas shift.^78,79 Our predicted cluster behavior aligns with available observations on real catalysts. Condensed-phase experiments also demonstrated that a catalyst should bond the oxygen atom from CO₂ dissociation strongly enough to facilitate C–H bond cleavage and achieve high C₂H₄ selectivity.⁶⁶ Herein, the reaction of C₂H₆ with product RhNb₄O⁻ after CO₂ reduction (Fig. S5) parallels this result that C₂H₄ can also be released readily without the formation of the intermediate CH₃CH₂O, from which the C–C scission takes place frequently.

Mechanisms of H₂O generation

An overall survey verifies that the products C₂H₄ and CO in the ODHE of C₂H₆ and CO₂ mediated by Rh_xNb_y⁻ can be released readily under ambient conditions (Fig. 2 and 3 and S6–S11), whereas external energy is required to generate gas-phase H₂O because of the substantial kinetic barriers of O–H bond coupling and the thermodynamically demanding process of H₂O desorption. It has been frequently identified that CO adhesion on clusters can play vital roles to regulate a reaction from endothermic to exothermic and then make it a thermodynamically and kinetically more feasible process.^80–82 Herein, though CO attachment can significantly suppress the energies of crucial intermediate species during H₂O formation (Fig. 3 and S7, S9, S11), the endothermic nature of the final products (e.g., ³RhNb₄CO⁻ + H₂O, ΔH₀: +0.70 eV, Fig. 3) compared to the exothermicity of CO desorption (¹RhNb₄OH₂⁻ + CO, ΔH₀: −1.21 eV) drives CO desorption prior to H₂O formation. Natural charge analysis reveals that the two attached H atoms carry negative charges prior to O–H coupling (Fig. 4E and F and S13), resulting in electrostatic repulsion with the oxygen atom and pronounced kinetic barriers have to be surpassed. The tight CO–Nb or CO–Rh bonding greatly stabilizes related intermediates or transition states in the pathway, while the charged states of H atoms and the oxygen atom involved in H₂O formation were negligibly perturbed (Fig. 4E and F). The leading result is that the absolute barriers of H–O coupling were only slightly affected. These results underscore that the endothermic nature of ODHE between C₂H₆ and CO₂ is primarily due to the energy required to regenerate the catalyst, namely, removing the residual H atoms and O atom, following C₂H₆ dehydrogenation and CO₂ reduction. Niobium oxide exhibits strong oxidation ability because of the existence of a unique Lewis/Brønsted acid Nb site to anchor the oxygen atom tightly.⁸³ Our predicted results also show clearly that after CO₂ dissociation, the leaving oxygen atom was always captured by one Nb atom (Fig. 3 and S7, S9, S11). This may be the dominant factor in making H₂O formation a challenging step of ODHE. This finding parallels the CO₂-assisted dehydrogenation of light alkanes on condensed-phase catalysts, in which the reaction endothermicity is accounted for by the subsequent reverse water–gas shift step following alkene desorption,^77,79,84 and the hydrogenation of lattice oxygen by residual H adsorbates was identified as the rate-determining step. Note that catalysts can only regulate the kinetic barriers and not disturb the reaction enthalpy. Consequently, a more evenly distributed reaction enthalpy across the elementary steps will result in a less endothermic process of the overall reaction. This finding provides an integrated and clear picture to capture the pivotal step that governs the overall efficiency of C₂H₆ and CO₂ co-conversion. Gas-phase clusters cannot fully represent the nature of active sites on heterogeneous catalysts and cannot model exactly the dynamic range of oxidation states found on realistic catalysts. Meanwhile, the well-defined oxidation states and electronic structures in gas-phase clusters are of significant importance to establish clear and molecular-level structure–activity relationships, which can serve as a foundational benchmark and a source of mechanistic hypotheses for studies of more complex and realistic systems.

Conclusion

In summary, we theoretically demonstrated that a series of Rh_xNb_y⁻ (x + y = 5) clusters can mediate the oxidative dehydrogenation (ODHE) of C₂H₆ and CO₂ to give rise to C₂H₄, CO and H₂O, and composition-dependent reactivity of Rh_xNb_y⁻ in regulating product desorption was identified. It was found that desorption of products C₂H₄ and CO occurs under ambient conditions, and the increased number of Rh atoms in Rh_xNb_y⁻ results in enhanced barriers for C₂H₄ desorption. The reasons behind this selective desorption of C₂H₄ from C₂H₆ rather than CH₄ or H₂ were rationalized. Meanwhile, the final formation and escape of H₂O to regenerate Rh_xNb_y⁻ catalysts represent the rate-determining steps that govern the overall efficiency of ODHE. This finding decouples the individual elemental steps from the complex catalytic process of C₂H₆ and CO₂ co-conversion and identifies unanimously the energetically demanding step of H₂O generation that leads to the highly endothermic nature of this ODHE.

Author contributions

H. Z. performed the theoretical calculations and organized the raw data. H. Z. and X.-Y. S. analyzed the calculation results. H. Z. and X.-N. L. wrote the manuscript. ORCID: https://orcid.org/0000-0002-0316-5762.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. Details of additional theoretical results (DFT-calculated structures and reaction mechanisms, and natural charge analysis). See DOI: https://doi.org/10.1039/d5dt02594j.

Acknowledgements

This work was financially supported by the National Key R&D Program of China (2021YFA1500704) and the National Natural Science Foundation of China (22473012 and 92461313).

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