Sustainable hydrogen production via CO₂-assisted BH₃ + BH₃ reaction: a computational analysis

Abstract

The activation and utilization of carbon dioxide (CO₂) for hydrogen production represents a central challenge in the development of sustainable and carbon-neutral energy systems. Borane (BH₃), a potent Lewis acid with high reactivity toward small molecules, has emerged as a promising candidate for CO₂ activation and hydrogen release. However, the mechanistic effects of incorporating multiple CO₂ molecules into BH₃-based systems remain poorly understood. In this study, density functional theory (DFT) calculations were conducted to explore the reaction mechanisms of a dimeric BH₃ system in the presence of zero to three CO₂ molecules. Potential energy surfaces were constructed at the M06-2X/6-311++G(3df,2p) level to identify key intermediates, transition states, reaction energies, and activation barriers. The computational results reveal a stepwise mechanism involving BH₃–CO₂ adduct formation and distinct transition states, with CO₂ playing a significant role in modulating both thermodynamic stability and kinetic accessibility. Notably, the inclusion of CO₂ stabilizes multi-component complexes and lowers activation barriers, thereby facilitating hydrogen release. These findings underscore the dual function of CO₂ as both a structural stabilizer and an energetic facilitator, offering valuable insights into CO₂ valorization and hydrogen generation in the context of sustainable energy applications.

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1 Introduction

One of the key areas of interest in organoboron chemistry¹ is the reactivity of boron hydrides, especially the interaction of borane (BH₃) and its derivatives with small molecules.^2–4 Borane, a strong Lewis acid,⁵ readily participates in a variety of chemical transformations, including hydroboration,⁶ coordination with Lewis bases, and activation of small molecules.⁷ Among these, the reaction between borane and carbon dioxide (CO₂)^8,9 has attracted considerable attention due to its potential implications in CO₂ fixation, catalysis, and hydrogen storage applications.^10–16 Borane-based reagents offer a promising strategy for CO₂ utilization through chemical–physical transformation. Borane, a strong electrophile, can react with CO₂ directly or in the presence of additional reactants, leading to various reduction and activation pathways.¹⁷ However, a comprehensive mechanistic understanding of this reaction remains incomplete in some experimental and computational studies in some experimental and computational studies.^9,10 Theoretical methods, particularly density functional theory (DFT), are valuable tools for elucidating reaction mechanisms, providing insight into electronic structures, energy landscapes, and dynamics of intermediate and transition states. The borane–CO₂ interaction involves initial adduct formation and subsequent structural rearrangements that determine the reaction pathway. Intermediate stability is influenced by electronic effects, solvation, and CO₂ stoichiometry. Experimental and computational studies show borane can reduce CO₂ under suitable conditions, yielding formate, carbonate, or methane derivatives, depending on the reaction environment and mechanism.^10,17

A fundamental question regarding this reaction is why two borane molecules are required instead of a single BH₃ reacting with multiple CO₂ molecules. This requirement arises could be from several key factors: Although BH₃ is a strong Lewis acid, a single molecule has limited capacity to coordinate with multiple CO₂ molecules, whereas the presence of two BH₃ molecules enables more efficient cooperative activation of CO₂. Additionally, the formation of multinuclear boron species plays a crucial role in stabilizing transition states and lowering reaction barriers, thereby facilitating CO₂ conversion. The interaction between two BH₃ molecules also increases the likelihood of forming cyclic of B–H atoms,^18–20 which are more stable. Furthermore, theoretical studies indicate that intermediates involving two BH₃ molecules exhibit higher stability due to boron–boron interactions,^21,22 leading to more favorable reaction pathways.

To effectively address these challenges, a comprehensive investigation into the electronic and structural changes occurring throughout the reaction is essential. In particular, the competition between a concerted single-step CO₂ insertion and stepwise, radical-mediated pathways highlights the need for in-depth theoretical analysis. Recent advancements in DFT methodologies offer a powerful framework for accurately predicting transition states, activation barriers, and the thermodynamic viability of proposed mechanisms. In this study, we utilize state-of-the-art computational techniques to systematically explore the borane–CO₂ reaction, with a focus on identifying key intermediates and transition states, as well as elucidating structure–reactivity relationships that underpin CO₂ activation. Furthermore, recent DFT-based investigations on boron hydride species such as BH₄⁻ reacting with radical HO˙²³ provide valuable complementary insights into hydrogen evolution mechanisms and radical reactivity within boron chemistry.

To gain deeper insights into the electronic nature of the reaction, we incorporated quantum chemical analyses, such as the electron localization function (ELF) to examine the bonding characteristics of critical species, offering valuable insights into the electronic rearrangements governing the reaction. Additionally, potential energy surface (PES) calculations were performed to delineate viable reaction pathways and characterize transition states, providing a comprehensive picture of borane–CO₂ interactions at the molecular level.

Infrared (IR) spectral simulations were also conducted to compare theoretical vibrational frequencies with experimental data, aiding in the identification of reaction intermediates and key transition states.

Kinetic modeling complemented our mechanistic investigation by estimating reaction rate constants and activation parameters along the preferred reaction pathways. By integrating PES mapping with kinetic analysis, we constructed a detailed reaction model that accounts for both thermodynamic and kinetic considerations, ultimately providing a predictive framework for borane-mediated CO₂ activation. The findings of this study contributed to a more profound understanding of boron-based CO₂ transformation processes, paving the way for the rational design of boron-containing catalysts and reagents. A deeper comprehension of these fundamental reaction mechanisms facilitated the development of efficient CO₂ conversion strategies, thereby supporting broader efforts in sustainable carbon utilization. Furthermore, the insights gained from this research extended to other borane-mediated small molecule activations, expanding the scope of organoboron chemistry beyond traditional hydroboration and synthetic applications. The computational methodology employed in this work served as a valuable reference for future experimental validation and further advancements in borane–CO₂ chemistry.

2 Computational methods

All electronic structure calculations were carried out using the Gaussian 09 (ref. 24) suite of programs. The geometries of reactants, products, intermediates, and transition states involved in the reactions of BH₃ + BH₃ + nCO₂ (n = 0–3) were optimized by employing the Minnesota functional (M06-2X) in combination with the 6-311++G(3df,2p) basis set.²⁵ This methodological framework enabled the precise optimization of BH₃ structure in the presence of CO₂, providing valuable insights into molecular interactions and structural characteristics.

Subsequent to geometry optimization, a detailed vibrational frequency analysis was conducted to characterize each stationary point. These computed vibrational frequencies were instrumental in confirming the nature of stationary points and applying zero-point energy (ZPE) corrections. Such calculations were essential for evaluating the stability and energetic properties of molecular species, thereby deepening our comprehension of their fundamental behavior. For open-shell species, the restricted formalism (M06-2X) was adopted to ensure accuracy.

Transition states were located using the Synchronous Transit-Guided Quasi-Newton (STQN) methodology, specifically employing the Quadratic Synchronous Transit (QST2 & QST3) approach when necessary. To validate the connectivity between transition states and their respective reactants and products, intrinsic reaction coordinate (IRC) analyses were performed.

The influence of CO₂ was systematically explored by progressively varying the number of CO₂ molecules (n = 0–3) within the system. For each configuration, geometry optimization, vibrational analysis, and electronic energy calculations were performed to evaluate the influence of CO₂ on reaction mechanisms, energy barriers, and product distribution. The Electron Localization Function (ELF)²⁶ approach was employed to determine the localization of excess electrons by partitioning the total electron density into distinct basins. Complementary to ELF analysis, the Atoms-in-Molecule (AIM) framework²⁷ utilized to investigate electron density distribution, with both analyses were conducted using the Multiwfn program.²⁸

A crucial aspect of this study was the determination of the rate constant (k), which serves as a key parameter in quantifying reaction kinetics. Using transition state theory (TST) under standard conditions (1 M concentration at 298.15 K), rate constants were computed via eqn (1).^29–36 All kinetic parameters were estimated in the gas phase using conventional TST, incorporating the partition functions of the reactants (BH₃, BH₃, CO₂) and transition states. The ChemRate software³⁷ was employed for all kinetic calculations.

In this expression, σ denotes the reaction symmetry number,^38,39 while κ accounts for tunneling corrections,⁴⁰ determined using the Eckart barrier. The constants k_B and h correspond to the Boltzmann and Planck constants, respectively, whereas, ΔG^≠ represents the Gibbs free energy of activation.

3 Results and disscusions

3.1 Gas-phase hydrogen release: the BH₃ + BH₃ → BH₂BH₂ + H₂ reaction

The BH₃ + BH₃ dehydrogenation mechanism was re-examined using M06-2X/6-311++G(3df,2p), with a focus on benchmarking against existing literature.

In the initial stage, BH₃ interacts with BH₃, leading to the formation of an intermediate complex, designated as IM0. This species subsequently progresses to a transition state, TS0, which corresponds to the highest energy point along the reaction coordinate, where hydrogen dissociation is actively occurring. The optimized structures of IM0 and TS0, along with key geometric parameters, are illustrated in Fig. 1. The corresponding relative energies, referenced to the isolated reactants, are depicted in the potential energy surface shown in Fig. 2 (green curve, where n = 0 denotes the absence of CO₂ molecules).

Fig. 1 Presents the optimized geometries of all species participating in the BH₃ + BH₃ reaction in the gas phase, including selected bond lengths (in Å) and bond angles (in degrees), obtained at the M06-2X/6-311++G(3df,2p) level of theory.

Fig. 2 The reaction energy profile for BH₃ + BH₃ + nCO₂ (denoted as B + B + nC) in the gas phase, presented as relative electronic energies (ΔE + ZPE) in kcal mol⁻¹, computed at the M06-2X/6-311++G(3df,2p) level.

The interaction between two BH₃ molecules leads to the formation of diborane(6) (B₂H₆). Structural parameters shown in Fig. 1 indicate that the two BH₃ units are bridged via B–H bonds with calculated bond lengths of 1.310 Å, and a B–B distance of 1.751 Å, obtained at the M06-2X/6-311++G(3df,2p) level. These values are in close agreement with the data reported by D. Sethio et al.,²⁰ who employed the CCSD(T)/cc-pVTZ method, reporting 1.315 Å and 1.763 Å, respectively. Moreover, the computed bond lengths also show strong consistency with the experimental values of 1.314 Å and 1.747 Å obtained by J. L. Duncan,⁴¹ further demonstrating the reliability and accuracy of the selected computational model. As shown in Fig. 2, the binding energy for dimer formation leading to B₂H₆ (IM0) is calculated to be −36.96 kcal mol⁻¹, representing a pre-transition state complex. This process proceeds via the transition state TS0, which features an activation barrier of 2.63 kcal mol⁻¹ relative to the isolated reactants. Analysis of the vibrational modes at TS0 reveals a key imaginary frequency of −340.19 cm⁻¹, corresponding to a concerted H₂ elimination mechanism. In this step, each BH₃ unit contributes a single hydrogen atom to form the H₂ molecule, while the two BH₃ units move closer together, shortening the B–B distance to 1.649 Å. In the TS0, the hydrogen atom from the upper BH₃ (in Fig. 2) separates, with a B⋯H distance of 2.050 Å, while the lower BH₃ provides a hydrogen atom with a B⋯H distance of 1.324 Å. These two hydrogen atoms combine to form molecular H₂, which dissociates from the remaining B₂H₄ fragment. The final relative energy of this product is 0.47 kcal mol⁻¹. This mechanism highlights that the H₂ release from B₂H₆ proceeds via a much lower activation energy pathway compared to direct cleavage of two hydrogen atoms from a single BH₃ unit, which requires a significantly higher energy input of 89.14 kcal mol⁻¹, as reported by Q. Ge et al.⁴² This finding underscores the cooperative role of the BH₃ dimer in facilitating efficient H₂ evolution, offering valuable insight into borane-based hydrogen storage and release processes.

3.2 Influence of single CO₂ molecule on the BH₃ + BH₃ dehydrogenation mechanism

As above discussed, the H₂ release process from B₂H₆ is thermodynamically unfavorable, owing to its endothermic nature (ΔH > 0). This highlights the importance of identifying suitable co-reactants that could drive the reaction toward thermodynamic feasibility. Although species such as SiH₄, NH₃, H₂O, and CO have been investigated,^43–46 the potential influence of CO₂ has not been thoroughly explored. This motivates the present investigation into the B₂H₆ + nCO₂ reaction, aimed at understanding how CO₂ interacts with electron-deficient boranes. Such interactions are directly relevant to CO₂ activation and conversion, both of which are crucial challenges in carbon management. Furthermore, exploring the chemical behavior of B₂H₆ under CO₂ atmosphere provides valuable insight into how small molecules, particularly CO₂, influence hydrogen release from boron hydrides, ultimately linking to clean hydrogen production and carbon recycling technologies.

To assess the effect of CO₂ on the dehydrogenation pathway of BH₃ + BH₃, we conducted a computational investigation of the BH₃ + BH₃ + CO₂ reaction at the same theoretical level (Fig. 3).

Fig. 3 Calculated molecular structures of species along the gas-phase BH₃ + BH₃ + 3CO₂ reaction pathway, optimized at M06-2X/6-311++G(3df,2p), displaying key bond lengths (Å) and bond angles (°).

As presented in Fig. 2 (blue line, n = 1), the initial interaction between BH₃–BH₃ and CO₂ forms a stable complex, serving as the reference point with a relative electronic energy (ΔE + ZPE) set at 0.0 kcal mol⁻¹. Progressing along the reaction coordinate, this interaction leads to the formation of intermediate IM1, which exhibits considerable stabilization at −37.78 kcal mol⁻¹, highlighting the strong association between the reactants, particularly through the participation of CO₂. The conversion from IM1 to the corresponding transition state (TS1) requires surpassing an activation barrier of only 1.2 kcal mol⁻¹, markedly lower than the 2.63 kcal mol⁻¹ required in the absence of CO₂ (TS0). This clear reduction in barrier height underscores the catalytic-like influence of CO₂ in promoting the process.

At TS1 (see Fig. 3), notable structural rearrangements are observed: two B–H bonds within BH₃ extend to 1.323 Å and 2.055 Å, indicating partial bond cleavage during H₂ evolution. Simultaneously, the B–B bond contracts slightly to 1.646 Å. The CO₂ fragment interacts strongly within the complex, maintaining C=O bond lengths near 1.15 Å and a nearly linear O=C=O angle of 179.5°. These structural changes correspond to an imaginary frequency of −332.32 cm⁻¹, associated with a vibrational mode representing the concerted H₂ release and atomic rearrangement. Beyond this transition state, the pathway leads to the exergonic formation of BH₂BH₂–CO₂ and H₂, with a final relative energy of −0.83 kcal mol⁻¹. The presence of CO₂ not only lowers the activation barrier but also enhances both CO₂ capture and H₂ generation, offering a dual benefit relevant to clean energy production and carbon management.

3.3 Influence of double CO₂ molecules on the BH₃ + BH₃ dehydrogenation mechanism

In this section, the influence of two CO₂ molecules on the dehydrogenation pathway of the BH₃BH₃ complex is investigated. Calculations were conducted using the M06-2X/6-311++G(3df,2p) level of theory. The initial interaction among BH₃ + BH₃ + 2CO₂ establishes a reference electronic energy (including ZPE) of 0.0 kcal mol⁻¹. As the reaction proceeds, this interaction leads to the formation of an intermediate complex (IM2, Fig. 4) with a significantly lower energy of −38.85 kcal mol⁻¹ (see Fig. 2), indicating strong stabilization due to cooperative binding by the two CO₂ molecules. The subsequent transformation from IM2 to the product state requires overcoming a remarkably low activation barrier of −0.91 kcal mol⁻¹, which is considerably reduced compared to the barriers for TS0 (2.63 kcal mol⁻¹) and TS1 (1.20 kcal mol⁻¹). This substantial reduction highlights the pronounced catalytic effect arising from the second CO₂, further accelerating the dehydrogenation process. At the TS2 structure, significant geometric rearrangement is observed: the B–H bond contracts to 1.309 Å, while the opposite B–H bond within the lower BH₃ unit elongates to 2.013 Å, marking the onset of H₂ release. Simultaneously, the B–B bond contracts slightly to 1.646 Å. Both CO₂ molecules exhibit strong interactions with the evolving product complex, with C=O bond lengths of approximately 1.155 Å and nearly linear O=C=O angles of 179.6°. The imaginary frequency associated with TS2 is calculated as −445.71 cm⁻¹, corresponding to a vibrational mode coordinating the concerted release of H₂ and the structural adjustment of the CO₂ framework.

Fig. 4 Optimized molecular structures for all species involved in the gas-phase BH₃ + BH₃ + 2CO₂ reaction, showing key bond lengths (Å) and bond angles (deg), calculated at the M06-2X/6-311++G(3df,2p) level.

As the reaction progresses, the final products BH₂BH₂–2CO₂ and H₂ form with an overall exergonicity of −2.74 kcal mol⁻¹, demonstrating that the incorporation of a second CO₂ not only further reduces the activation energy but also enhances the efficiency of both dehydrogenation and CO₂ capture, underscoring its potential significance in combined hydrogen production and carbon utilization strategies.

3.4 Influence of triple CO₂ molecules on the BH₃ + BH₃ dehydrogenation mechanism

To gain deeper insight into the CO₂-assisted dehydrogenation process, we examined the pathway involving BH₃ + BH₃ in the presence of three CO₂ molecules. The optimized structures of the intermediate and transition state are illustrated in Fig. 5

Fig. 5 M06-2X/6-311++G(3df,2p) optimized geometries of species along the BH₃ + BH₃ + 3CO₂ gas-phase reaction pathway, with key bond lengths (Å) and bond angles (°).

The corresponding potential energy profile, including ZPE corrections, indicates that the initial BH₃ + BH₃ + 3CO₂ complex starts at 0.0 kcal mol⁻¹ (Fig. 2). The reaction proceeds through the formation of an intermediate species, IM3, which is significantly stabilized at −39.85 kcal mol⁻¹ (Fig. 5). Notably, the introduction of three CO₂ molecules further reduces the activation energy required for dehydrogenation. The computed activation barrier at the transition state TS3 is only −2.35 kcal mol⁻¹, a substantial decrease compared to the previous cases: TS0 (2.63 kcal mol⁻¹), TS1 (1.20 kcal mol⁻¹), and TS2 (−0.91 kcal mol⁻¹). This progressive reduction highlights the catalytic role of CO₂ in facilitating the H₂ release from the BH₃ + BH₃ complex. At TS3, the vibrational analysis reveals an imaginary frequency of −561.83 cm⁻¹, associated with the concerted release of H₂ and structural reorganization involving CO₂. Structural changes at this point include the contraction of the B–H bond to 1.299 Å, while the opposite BH₃ unit elongates its B–H bond to 1.990 Å, indicating active bond cleavage leading to H₂ formation. Simultaneously, the B–B distance contracts to 1.645 Å. The three CO₂ molecules maintain strong interactions with the complex, characterized by C=O bond lengths ranging from 1.152 Å to 1.156 Å and nearly linear O=C=O angles close to 179.7°. The reaction ultimately yields BH₂BH₂–3CO₂ and H₂, with an overall energy release of −5.55 kcal mol⁻¹. This systematic investigation, increasing the number of CO₂ molecules from 1 to 3, underscores the remarkable adaptability of the BH₃ + BH₃ system as both a hydrogen carrier and a CO₂ sorbent. With a single CO₂ molecule, catalytic enhancement is already observed; adding two and eventually three CO₂ molecules progressively lowers the activation barriers from TS0 (2.63 kcal mol⁻¹) to TS2 (−0.91 kcal mol⁻¹) and TS3 (−2.35 kcal mol⁻¹).

This dual reactivity hydrogen release coupled with CO₂ capture positions BH₃ + BH₃ as a promising candidate for advanced energy materials. It offers both a sustainable route for hydrogen generation, essential for clean energy technologies, and an effective platform for CO₂ sequestration, contributing to carbon management strategies. This unique synergy between hydrogen storage and carbon capture highlights the potential of borane-based systems in future catalytic and energy storage applications, aligning with global efforts toward sustainable energy and environmental remediation.

3.5 IR spectra and vibrational features of BH₃BH₃–n(CO₂) complexes (n = 0 to 3)

Fig. 6 presents the infrared (IR) spectra of four species: BH₃BH₃ (a), BH₃BH₃–CO₂ (b), BH₃BH₃–2CO₂ (c), and BH₃BH₃–3CO₂ (d) which generated based on vibrational frequency results obtained from quantum chemical calculations performed at the M06-2X/6-311++G(3df,2p) level of theory (Table S2†). These spectra reveal distinct shifts in the low-frequency region (0–500 cm⁻¹) upon sequential incorporation of CO₂ molecules into the BH₃BH₃ framework. For pristine BH₃BH₃ (spectrum a), no prominent absorption bands are observed within this range, indicating the absence of external molecular interactions. However, after coordination with a single CO₂ molecule (spectrum b), new vibrational peaks emerge, attributable to modes induced by CO₂ binding. With the addition of a second CO₂ molecule (spectrum c), these features become more prominent, reflecting enhanced interaction strength. In the case of BH₃BH₃–3CO₂ (spectrum d), the intensities of these peaks further increase, signaling more complex vibrational coupling arising from multiple CO₂ incorporations. Collectively, these spectral changes provide clear evidence of progressive CO₂ integration, which profoundly modifies the vibrational signature of the parent BH₃BH₃ species.

Fig. 6 Calculated IR spectra of: (a) BH₃–BH₃, (b) BH₃–BH₃–CO₂, (c) BH₃–BH₃–2CO₂, and (d) BH₃–BH₃–3CO₂, obtained at the M06-2X/6-311++G(3df,2p) level of theory.

3.6 Analysis of electrostatic interactions in the BH₃BH₃–nCO₂ system

Analysis of the electron localization function (ELF)²⁶ maps for the BH₃BH₃–nCO₂ complexes (shown in Fig. 7a–c) provides clear evidence of direct contact between the hydrogen atoms from the boron hydride framework and oxygen atoms from the CO₂ molecules. These interactions primarily take place at the interface between the boron-containing fragment and the adsorbed CO₂ units, where increased electron density suggests partial covalent character. Supporting this interpretation, topological analysis using atoms-in-molecules (AIM)²⁷ theory (Fig. 7d–f) reveals the presence of distinct bond critical points (BCPs) that correspond to these interaction sites. Such findings indicate that the bonding mechanism is consistent with a Lewis acid–base interaction, where the boron centers function as electron acceptors, while the oxygen atoms of CO₂ act as electron donors. Together, the ELF and AIM data provide strong confirmation that stable and cooperative bonding occurs when CO₂ interacts with the BH₃BH₃ system. To further clarify the stabilizing role of CO₂, we calculated the interaction energies (E_bd) for the formation of the BH₃BH₃·nCO₂ adducts using the expression:

E_bd = E[BH₃BH₃·nCO₂] − E[BH₃BH₃] − nE[CO₂] (kcal mol⁻¹)

Fig. 7 ELF and AIM maps of the BH₃BH₃–CO₂ (a and d); BH₃BH₃–2CO₂ (b and e), and BH₃BH₃–3CO₂ (c and f), calculated at M06-2X/6-311++G(3df,2p) level.

The resulting interaction energies are −0.81 kcal mol⁻¹ (n = 1), −1.89 kcal mol⁻¹ (n = 2), and −2.89 kcal mol⁻¹ (n = 3), confirming a progressively stronger stabilization effect as more CO₂ molecules are introduced. This trend indicates not only additive but also cooperative binding interactions between the BH₃ dimer and CO₂ molecules. Additionally, structural analysis reveals that the B–B bond length decreases from 1.751 Å (in IM₀) to 1.645 Å (in TS₃), while the B–H bonds involved in H₂ formation show slight elongation. These trends, consistent across the reaction coordinate, indicate that CO₂ not only stabilizes the complex electronically but also induces favorable geometric changes that facilitate hydrogen release. This quantitative structural and energetic evidence reinforces the dual role of CO₂ as both a structural stabilizer and a reactivity modulator in the BH₃ dimer system.

3.7 CO₂ adsorption capacity of the BH₃ + BH₃ complex and comparison with conventional adsorbents

To evaluate the CO₂ capture potential of the BH₃ + BH₃ complex, we computed its CO₂ adsorption capacity under conditions where one, two, and three CO₂ molecules are incorporated into the structure. The adsorption capacity, expressed in mmol CO₂ per gram of BH₃, was determined based on the molecular weight of the system and the stoichiometry of CO₂ binding. The calculated adsorption capacities were subsequently compared with values reported for conventional hybrid sorbents, including graphene oxide (GO)-based composites, metal–organic frameworks (MOFs), and hydrogen boride (HB) sheets. These materials, summarized in Table 1.

Table 1 Comparison of CO₂ adsorption capacities of the BH₃–BH₃ complex with with those of various conventional adsorbents

Adsorbent	CO2 adsorbent capacity (mmol g^−1)
GO-ZnO	1.94 (ref. 47)
GO-UiO-66	3.37 (ref. 48)
Fe3O4-rGO	2.5 (ref. 49)
N-doped rGO-Zn	3.31 (ref. 50)
Hydrogen boride (HB) sheets	0.24 (ref. 51)
This work: BH3–BH3–nCO2	36.14 (n = 1); 72.28 (n = 2); 108.42 (n = 3)

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Notably, the CO₂ adsorption capacity of the BH₃ + BH₃ complex far exceeds those of conventional sorbents, such as Fe₃O₄-rGO (2.50 mmol g⁻¹), GO-UiO-66 (3.37 mmol g⁻¹), GO-ZnO (1.94 mmol g⁻¹), and N-doped rGO-Zn (3.31 mmol g⁻¹). This striking enhancement can be attributed to the strong chemisorptive interactions between CO₂ and the electron-deficient boron centers within the BH₃–BH₃ system, further stabilized through cooperative binding effects arising from the flexible, adaptive nature of the dimeric boron hydride framework. In contrast, most conventional hybrid sorbents primarily rely on physisorption mechanisms, which are inherently weaker and less selective under ambient conditions. The extraordinarily high adsorption capacity observed for the BH₃–BH₃ complex can, at least in part, be attributed to the fact that this system is evaluated at the molecular level, where individual interactions between BH₃ units and CO₂ molecules are fully resolved. At this scale, the inherent chemical reactivity of the boron centers and the flexibility of the B–H framework allow for highly efficient CO₂ trapping. This result serves as a molecular-level signal indicating the strong intrinsic affinity of boron hydrides for CO₂, which could potentially be translated into larger-scale materials with engineered porosity and connectivity. This molecular insight is further supported by previous investigations into the CO₂ adsorption properties of hydrogen boride (HB) sheets, a class of metal-free two-dimensional materials composed of boron and hydrogen in a 1 : 1 stoichiometric ratio. Recent studies⁵¹ have demonstrated that pristine HB sheets exhibit negligible CO₂ adsorption under ambient conditions. However, hydrogen-deficient HB sheets in which some surface hydrogen atoms are removed demonstrate reproducible physisorption of CO₂ at 297 K, with a saturation coverage of only 2.4 × 10⁻¹ mmol g⁻¹. The exceptional CO₂ uptake of the BH₃–BH₃ complex further reinforces its potential as a dual-functional platform, capable of simultaneously acting as a high-performance CO₂ capture material and an efficient hydrogen storage medium. This combined functionality not only advances the development of integrated carbon capture and utilization (CCU) systems, but also provides a promising molecular design strategy for next-generation carbon management and clean hydrogen technologies. By leveraging its unique molecular structure and intrinsic reactivity, the BH₃–BH₃ complex exemplifies how fundamental molecular chemistry can inspire the design of innovative materials for sustainable energy and environmental applications.

3.8 Kinetic study

This section investigates the hydrogen release kinetics from the BH₃ dimer in the presence of increasing numbers of CO₂ molecules. Key parameters, including equilibrium constants (K_eq) and unimolecular rate constants (k_u), were determined to assess how CO₂ influences both thermodynamic and kinetic aspects of the process.

3.9 Equilibrium constants

The equilibrium constants for the association between BH₃ + BH₃ and BH₃ + BH₃ + nCO₂ (with n = 0, 1, 2, 3) are summarized in Table 2. The data reveal a systematic decline in equilibrium constants as more CO₂ molecules are incorporated into the system. Without CO₂, the equilibrium constant reaches 1.10 × 10²⁰, indicative of an extremely favorable formation of the BH₃ dimer. When a single CO₂ is introduced, the equilibrium constant drops to 5.96 × 10¹⁵, followed by 3.17 × 10¹⁰ for the two CO₂ system, and finally 4.14 × 10⁵ when three CO₂ molecules are present. This decreasing trend reflects the competitive stabilization provided by CO₂ coordination, which shifts the equilibrium away from simple dimer formation toward the formation of CO₂-stabilized adducts. Despite this gradual reduction in K_eq, the values remain sufficiently large to indicate a strong thermodynamic driving force toward product formation in all cases. This implies that, while CO₂ reduces the preference for direct BH₃ dimerization, it promotes formation of more complex BH₃–BH₃–CO₂ adducts, ensuring that CO₂ incorporation does not hinder the overall hydrogen release process. Instead, CO₂ contributes to restructuring the pathway to favor products where both hydrogen evolution and CO₂ capture occur simultaneously.

Table 2 Equilibrium constants (K_eq) for the reaction between BH₃, BH₃, and varying numbers of CO₂ molecules

Reaction	Keq
BH3 + BH3 ⇌ BH3–BH3	1.10 × 10^20
BH3 + BH3 + CO2 ⇌ BH3–BH3–CO2	5.96 × 10^15
BH3 + BH3 + 2CO2 ⇌ BH3–BH3–2CO2	3.17 × 10^10
BH3 + BH3 + 3CO2 ⇌ BH3–BH3–3CO2	4.14 × 10^5

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3.10 Rate constants for hydrogen release

The unimolecular rate constants (k_u) associated with hydrogen release from each intermediate complex (IM_n) to its corresponding transition state (TS_n) are presented in Table 3. The results indicate a clear increasing trend in rate constants as the number of CO₂ molecules rises. For the reaction involving only BH₃ + BH₃, the rate constant is 3.3 × 10⁻¹⁶ s⁻¹. When one CO₂ molecule is introduced, the rate decreases slightly to 2.4 × 10⁻¹⁶ s⁻¹, while the system with two CO₂ molecules accelerates to 1.7 × 10⁻¹⁵ s⁻¹. The fastest hydrogen release occurs when three CO₂ molecules are present, reaching 1.2 × 10⁻¹⁴ s⁻¹. This enhancement in k_u highlights the catalytic role of CO₂, where increasing CO₂ coordination stabilizes the intermediates through favorable electrostatic and Lewis acid–base interactions. This stabilization reduces activation barriers, enabling a more efficient transition to the hydrogen release step. This trend reflects that CO₂ coordination alters the reaction pathway, creating a smoother and more thermodynamically favored transition from reactants to products. Interestingly, the simultaneous decrease in equilibrium constants (K_eq) and increase in rate constants (k_u) with growing CO₂ content reflects a mechanistic shift in the reaction. In the absence of CO₂, dimer formation is exceptionally favored thermodynamically, but hydrogen release is relatively slow. As more CO₂ is incorporated, the system shifts from direct dimerization to forming multi-component adducts, which, while slightly less stable, allow for faster hydrogen evolution. This transition highlights a CO₂-induced catalytic enhancement, where CO₂ plays a dual role: facilitating hydrogen release while simultaneously being captured into the product complex. This dual functionality makes the BH₃–BH₃–CO₂ system particularly attractive for applications in clean energy and carbon management. It not only enables controlled hydrogen release, but also contributes to efficient CO₂ capture, offering a promising integrated solution for hydrogen storage and carbon mitigation technologies.

Table 3 Unimolecular rate constants (k_u) for the hydrogen release process from intermediate complexes (IM_n) to transition states (TS_n) in the BH₃ + BH₃ + nCO₂ system (where n = 0,1,2,3)

Reaction	ku (s^−1)
BH3 + BH3 → BH2BH2 + H2	3.3 × 10^−16
BH3 + BH3 + CO2 → BH2BH2–CO2 + H2	2.4 × 10^−16
BH3 + BH3 + 2CO2 → BH2BH2–2CO2 + H2	1.7 × 10^−15
BH3 + BH3 + 3CO2 → BH2BH2–3CO2 + H2	1.2 × 10^−14

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4 Conclusions

This study employed Density Functional Theory (DFT) calculations and kinetic modeling to illuminate the reaction between BH₃, BH₃, and CO₂, with a specific focus on hydrogen release and CO₂ capture mechanisms. Our findings reveal a significant influence of CO₂ on the BH₃–BH₃ system:

(a) CO₂ significantly alters the hydrogen evolution pathway: as the number of CO₂ molecules increases, the reaction mechanism shifts, leading to reduced energy barriers and enhanced stabilization of intermediates.

(b) Strong CO₂–BH₃–BH₃ interactions enhance CO₂ adsorption and shift thermodynamic equilibrium: computed equilibrium constants and binding energies demonstrate a high affinity, favoring stable multi-molecular adduct formation, crucial for combined hydrogen storage and carbon capture.

(c) The BH₃–BH₃ + (CO₂)_n system functions as a dual-functional platform for clean energy: it simultaneously releases hydrogen and captures CO₂, offering a promising strategy to address both clean hydrogen generation and CO₂ reduction. The system's tunability with varying CO₂ amounts allows for optimization of both processes, showcasing its potential for energy storage and carbon management.

In essence, this work establishes the BH₃–BH₃ + nCO₂ system as a highly promising candidate for integrated hydrogen storage and carbon capture. Future research should prioritize experimental validation and system optimization to fully realize its potential for sustainable energy solutions.

4.1 Influence of CO₂ on hydrogen evolution

The introduction of CO₂ significantly reshapes the reaction pathway and modifies the energy profile of the BH₃–BH₃ system. As the number of CO₂ molecules increases from one to three, the reaction mechanism progressively shifts, reducing the energy barriers and enhancing the stabilization of intermediate species.

4.2 Equilibrium and interaction energies

The computed equilibrium constants (K_eq) and binding energies reveal strong interactions between CO₂ and the BH₃–BH₃ complex. This strong affinity not only enhances CO₂ adsorption but also impacts the thermodynamic equilibrium, with increasing CO₂ concentration favoring the formation of stable multi-molecular adducts. Such robust binding further supports the feasibility of utilizing this system for combined hydrogen storage and carbon capture.

4.3 Dual-functional platform for clean energy

The ability to simultaneously release hydrogen and capture CO₂ highlights the multifunctionality of the BH₃–BH₃ complex. This dual capability offers a promising strategy to simultaneously address two pressing challenges: clean hydrogen generation and CO₂ reduction. By adjusting the amount of available CO₂, the system can be tuned to optimize both processes, presenting valuable potential for energy storage and carbon management technologies.

In summary, this study identifies the BH₃–BH₃ + nCO₂ system as a compelling candidate for integrated hydrogen storage and carbon capture applications. Future efforts should focus on experimental validation and further fine-tuning of system conditions to fully unlock its potential for sustainable energy solutions.

Data availability

Data will be made available on request.

Author contributions

Trinh Le Huyen: conceptualization, methodology, validation, data curation, formal analysis, visualization, writing – original draft, writing – review & editing. Tran Thi Thanh Huyen and Chi Nam Cao: data curation and visualization. Pham Cam Nam: supervision, software, writing – review & editing.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Trinh Le Huyen was funded by the Postdoctoral Scholarship Programme of Vingroup Innovation Foundation (VINIF), code VINIF.2023.STS.23. This work was supported by The University of Danang – University of Science and Technology, code number of Project: T2024-02-34. During the preparation of this paper, generative AI and AI-assisted technologies were employed for grammar and spelling checks and sentence rewriting as needed. Following the use of these tools, the content was reviewed and edited to ensure accuracy, and we take full responsibility for the publication's content.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ra03449c

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