Theoretical investigation of carbon dioxide adsorption on MgH₂ with a cobalt catalyst

Abstract

This work presents a theoretical investigation of carbon dioxide (CO₂) adsorption on MgH₂ and its reaction (chemisorption) with cobalt doped MgH₂. The focus of this study is the properties and mechanisms involved in CO₂ adsorption on clean MgH₂ surfaces and the role of Co in enhancing the adsorption process. Density functional theory (DFT) calculations were performed to examine different CO₂ adsorption sites on the MgH₂ surface along with the adsorption distances, binding energies, and geometric parameters. The results indicate that physical adsorption of CO₂ occurs on MgH₂ with similar adsorption energies at different adsorption sites. The coverage effect of CO₂ molecules on MgH₂ was also investigated, revealing an increased affinity of CO₂ with higher surface coverage. However, excessive coverage led to a decrease in adsorption efficiency due to competing surface adsorption and intermolecular interactions. The orientation of adsorbed CO₂ molecules shifted from parallel to quasi-perpendicular arrangements upon adsorption, with notable deformations observed at higher coverage, which gives a hint of CO₂ activation. Furthermore, the study explores the CO₂ adsorption capacity of MgH₂ in comparison to other materials reported in the literature, showcasing its medium to strong affinity for CO₂. Additionally, the effectiveness of a single Co atom and Co clusters as catalysts for CO₂ adsorption on MgH₂ was examined. Overall, this theoretical investigation provides insights into the CO₂ adsorption properties of MgH₂ and highlights the potential of Co catalysts to enhance the efficiency of the methanation process.

Keywords: DFT; CO₂ conversion; Cobalt catalyst; Charge transfer.

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1 Introduction

Atmospheric carbon dioxide concentration reached 424.81 ppm (global mean) in June 2023,¹ which far exceeds the natural atmospheric carbon dioxide concentrations (280 ppm)² before the Industrial Revolution took place. This has led to severe consequences, including climate change and global warming. Carbon dioxide capture and storage, as well as carbon dioxide capture and utilisation technologies, i.e., CCSs and CCUs, respectively, have been considered a suitable approach to solve this pivotal problem.³ Among the main CO₂ capture procedures (pre-combustion, post-combustion, and oxyfuel combustion^4–6), the post-combustion process is the most engineered technology as it can be retrofitted to existing power plants.⁷ However, challenges remain, such as the requirement for high-performance materials or the demand for energy for the high sorbent regeneration process.⁸ In this process, once CO₂ gas is captured by the sorption material from industrial flue gases, it can be stored in suitable geological formations⁹ in the case of CCS or reused in different industrial processes in the case of CCUs. This may create extra operational needs (CCUs with conversion), such as fuels or polymeric materials,¹⁰ or be ready to use (CCUs without conversion), such as heat transfer fluid.¹¹

A possible route for CCU is methane production (methanation) from captured CO₂ through hydrogenation. CO₂ methanation is one of the most relevant applications for recycling carbon dioxide, owing to its high gravimetric heat (55.5 MJ kg⁻¹).¹² Different means for CO₂ methanation have been proposed, including photocatalytic,¹³ thermal catalytic,¹⁴ or metal-catalyzed processes,¹⁵ among others. Recent techno-economical analyses of the most mature technologies showed several drawbacks, with the main need being the development of more efficient sorbent/catalysts to allow scaling up to the industrial level.¹⁶ A possible route for CO₂ methanation stands on the Sabatier reaction,¹⁷i.e., the hydrogenation reaction of CO₂ to CH₄, which is thermodynamically favourable ¹⁸ but must be catalyzed due to strong kinetics limitations. Likewise, the hydrogen required for the methanation may be provided to the chemical reactor¹⁹ or it could be produced in situ. This last option could allows capturing and converting CO₂ simultaneously as well as ensuring the green origin of the hydrogen used.

Among the materials which can potentially be used as hydrogen sources, MgH₂ has shown a large hydrogen storage capacity.^20–22 Nevertheless, high hydrogenation/dehydrogenation temperatures remain technologically and economically unaffordable for large-scale application of MgH₂. However, Ni- and Co-additives have been shown to positively alter hydrogen absorption/desorption kinetics.^23,24 Cui et al.²⁵ confirmed that transition metal nanoparticles (NPs) of Ti, Nb, V, Co, Mo, and Ni enhance dehydrogenation performance due to a decrease in electronegativity. Dehydrogenation co-catalyzed with MgH₂ was reported by Gennari et al. showing hydrogen absorption/desorption temperatures dropping from 350 to 250 °C (ref. 26) and activation energies from 143 to 110 kJ mol⁻¹. Liu et al. reported improved hydrogen absorption/desorption performance in terms of H₂ temperature release (198.9 °C) and activation energies (76.66 kJ mol⁻¹) using Co/Pd@CNTs catalyst.²⁷ Therefore, taking advantage of MgH₂ material as a hydrogen source, CO₂ hydrogenation and conversion into valuable products has been assessed from an experimental point of view using MgH₂ as substrate.²⁸ Therefore, MgH₂ has been considered a substrate for H₂ supply in the CO₂ methanation process due to its natural capacity to release H₂ above 350 °C.¹⁸ Theoretical studies have already been performed in this context; Manggada et al. employed an MgH₂ substrate for the CO₂ hydrogenation using a Mo-phosphonic acid catalyst to report a great reduction in the interaction energy barriers in the presence of the catalyst.²⁹ Cu/ZrO₂ system has also been evaluated in hydrogenation of CO₂ to methanol showing potential active reaction sites.³⁰ Moreover, Chen et al. reported DFT calculations revealing an enhanced weakening of the H–Mg surface bonds by introducing Mg vacancies, thus facilitating CO₂ molecule adsorption on the MgH₂ substrate.³¹ Experimentally, Co-based catalysts for this reaction have been studied widely.^32,33 Computational studies based on theoretical models are in demand to accurately assess and evaluate active sites in materials.³⁴

CO₂ methanation assays with MgH₂ substrate as a portable hydrogen medium under thermal conditions were performed in previous work on cobalt catalysts. Results showed the mechanisms for direct CO₂ reduction to CH₄ in non-catalyzed systems, however, global mechanisms of catalyzed conversion are based on the Sabatier process that is enhanced by a Co catalyst.³⁵ In this regard, the aim of the present work is to analyze for the first time CO₂–MgH₂ interactions and adsorption mechanisms with and without adsorbed atoms of Co. We shed light on the driving forces and electronic properties in this reaction using a theoretical approach based on the density functional theory (DFT).

2 Results and discussion

2.1 CO₂ adsorption on clean MgH₂

Different sites for CO₂ molecule adsorption were considered on a clean MgH₂ (0 0 1) surface (Fig. 1) in accordance with the position of the molecule along with different orientations. Gas molecules were placed on top of Mg atoms, on top of H atoms, and over the interatomic cavities. In this third configuration, CO₂ molecules were parallel to the surface (XY plane) with two different orientations with the aim of studying all possible interactions (Fig. S1a, ESI†). Therefore, we have considered a slab model of 8.88 × 8.88 Å; seven different DFT calculations corresponding to seven initial structures for the adsorption of a single CO₂ molecule were performed. Optimised geometries for all the considered systems are shown in Fig. 2, where CO₂ bending angles and CO₂–surface distances are also reported, while binding energies and further geometric parameters are presented in Table 1. Binding energies for all the considered systems are rather similar, ranging from −0.38 to −0.43 eV, except for the P4 structure, which shows the weakest interaction energy (−0.20 eV) by far. These energies are directly related to the adsorption distances, where intervals of 2.01 to 2.34 Å were observed for P1, P2, P3, P5, P6, and P7 structures and 3.11 Å for the weak P4 adsorption site. This effect may be influenced by the electronegativity difference between O–H and O–Mg atoms. The O–H electronegativity difference is smaller than that between O–Mg, leading to weaker E_ads. For all the cases, CO₂ intramolecular bond lengths are maintained as before the adsorption (Fig. S1c, ESI†) except for minor alterations (±0.02 Å) in P2 and P7 structures. The angle, φ_O1–C–O2, shows negligible bending. The bending molecule with the largest deviation from the CO₂ linear isolated molecule (179.97°, Fig. S1c, ESI†) is found in the P3 structure (168.38°). After DFT geometric optimisation, the CO₂ molecule on sites P1 and P6 underwent a reorientation, and it moved to the P2 adsorption site and showed adsorption energies (−0.38 and −0.40, respectively), molecule–surface distance (2.34 and 2.26 Å, respectively), and geometrical parameters similar to the P2 structure (E_ads = −0.41 eV and r_CO2-slab = 2.09 Å). In this adsorption position, the C atom of the CO₂ is located in a small cavity located on top of a Mg atom on the second layer on the surface, and in the middle of two H atoms on the surface. The two O atoms of the CO₂ molecule point to the Mg surface atoms perpendicular to the H atoms. The final geometry of CO₂ at P7 is also equivalent to the P2 adsorption site, but in this case, the CO₂ molecule is not fully parallel to the surface, and the binding energy is slightly larger (−0.43 eV). Therefore, P2, P3, and P5 were found to be the most active sites for CO₂ adsorption. Furthermore, CO₂ molecules starting at P3 and P5 evolve to a final position, where the C atoms are placed between two H atoms on the surface and the O atoms point again toward two Mg atoms on the surface; this CO₂ is, however, placed over the interatomic cavity (in contrast to P1, P2, P6, and P7 structures). For the latter, binding energies, CO₂–surface distances, and CO₂ geometric parameters are similar to those reported in previous systems, where the shortest CO₂–surface distance was found for the P3 structure (i.e., 2.00 Å). Based on the binding energy strengths, the adsorption distances, and negligible changes in CO₂ geometry, physical adsorption of the CO₂ molecule on the MgH₂ surface can be inferred for all the proposed adsorption sites. Results agree with those reported by Chen et al. who explained the viability of CO₂ hydrogenation through ionic lattice hydrogen atoms.³¹

Fig. 1 Top- and two-side-view representations of the system used in the simulations. The (0 0 1) surface energy and total volume of the optimized slab after calculation are depicted. Atom colour code: (white) hydrogen, (pink) magnesium.

Fig. 2 Top- and side-view of the CO₂ adsorption structures for the P1–P7 sites, where CO₂ bending angles and CO₂–slab distances are shown. Atom colour code: (white) hydrogen, (pink) magnesium, (red) oxygen, (blue) carbon.

Table 1 Adsorption energies and geometric parameters for CO₂ adsorption on different surface sites (P1–P7) on MgH₂. The values for the configurations with the highest energy (P2 and P7) are reported in bold

	E ads (eV)	r C–O1 (Å)	r C–O2 (Å)	φ CO2 (deg)	r CO2-slab (Å)
P1	−0.38	1.17	1.17	176.73	2.34
P2	−0.41	1.17	1.17	175.49	2.09
P3	−0.38	1.17	1.19	168.38	2.01
P4	−0.20	1.17	1.17	179.77	3.11
P5	−0.39	1.17	1.17	177.83	2.24
P6	−0.40	1.17	1.17	176.46	2.26
P7	−0.43	1.16	1.17	174.25	2.10

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To better understand the adsorption mechanism for CO₂ gas, the effect of coverage of different CO₂ molecules was considered. The full coverage limit (1 ML) was defined as 4 CO₂ molecules (12 atoms) on top of 12 slab surface atoms (8 hydrogen + 4 magnesium atoms). Hence, an increasing number of CO₂ molecules corresponding to 0.25 ML, 0.5 ML, 0.75 ML, 1 ML, and saturated 1.25 ML were added to the MgH₂ surface (1, 2, 3, 4, and 5 molecules, respectively) according to Fig. S1b, ESI.† Surface saturation was used to evaluate the eventual reorientation of the CO₂ molecules on the MgH₂ surface. Optimized structures are shown in Fig. S2, ESI,† and the adsorption energies (per CO₂ molecule) and geometric properties of each of the adsorbed CO₂ are reported in Table 2. An increasing affinity of CO₂ molecules to the MgH₂ surface is inferred whenever enlarging surface coverage as E_ads scale from −0.3 to −0.4 eV (2 to 4 adsorbed molecules). This means that each molecule adsorbs more easily with an increase in coverage. Moreover, E_ads values agree with the ones reported for a single CO₂ molecule (P1, P2, P3, P5, P6, and P7), leading to efficient adsorption mechanisms upon coverage. However, this behaviour is not reproduced by CO₂ exceeding coverage structure (1.25 ML), where the E_ads drops to −0.25 eV (per CO₂ molecule). The lowering of the adsorption efficiency might be caused by the competing effects of the surface adsorption and the CO₂ intermolecular interactions imposed by the structural design constraints together with the non-availability of the most suitable surface adsorption sites (P1–P3 and P5–P7), and the surplus molecules interact at a less energetically favoured site (P4). Regarding the orientation of the adsorbed molecules, despite the initial position of the CO₂ being parallel to the surface, molecules tend to reorient after geometric optimisation toward quasi-perpendicular arrangements. This is more notable with the coverage effect. In contrast to adsorption structures with single CO₂ molecules, CO₂ bending angles and bond distances for all the structures vary upon adsorption (Table 2) and with CO₂ addition. CO₂ (1) molecules located on the strongest adsorption site, i.e., P2, especially deform when coverage is increased, reaching a bending angle of 123.94°, bond distances of 1.28 Å, 1.24 Å, and 1.06 Å distance to the MgH₂ surface hydrogens, when n = 5 in the coverage (Fig. 3a). At this adsorption site, slab deformation is also noticeable, especially in the ω₂ angle, which changes from 157.78° in the clean slab to 149.94° after the interaction (Table S1, ESI†). Indeed, it can be inferred that a weak H-bond might be present between H₄ (MgH₂ surface) and the C atom of CO₂ (1) because of the bond distance (1.06 Å) and interacting angle (140.61°), although electronic charge transfer could also give rise to an adsorption mechanism that also explains chemical adsorption (Fig. 3b). A comparable situation is observed at the opposite side: MgH₂ H5 atom with a C–H length of 2.41 Å and contact angle of 134.34°; a slab deformation of ω₃ changing from 157.78° to 174.35° was observed in this case (Table S1, ESI†). Alternate orientation of CO₂ molecules forming spatially perpendicular entities (non-parallel arrangement) were observed. This conformation may be adopted to avoid CO₂ quadrupole–quadrupole interactions, benefiting CO₂-slab interactions.³⁶ The reported effect, i.e., a stronger E_ads when coverage with n CO₂ molecules increases, has already been described in previous literature for the CO₂ adsorption on rutile TiO₂ (1 1 0) sorbent.³⁷ This phenomenon will be further analysed in an upcoming section using the charge transfer phenomenon.

Table 2 Adsorption energy (per molecule) and geometric parameters for the adsorption of n CO₂ molecules (n = 2 to 5) on MgH₂. The values for the configuration with the highest energy (4 × CO₂) are reported in bold

	n CO2	E ads (eV)	r C–O1 (Å)	r C–O2 (Å)	φ CO2 (deg)	r CO2–H (Å)
2 × CO2	1	−0.30	1.21	1.19	155.75	1.97
	2		1.16	1.17	179.18
3 × CO2	1	−0.36	1.28	1.23	131.50	1.18
	2		1.16	1.17	177.39
	3		1.19	1.16	177.54
4 × CO 2	1	−0.40	1.26	1.23	130.91	1.17
	2		1.16	1.18	174.02
	3		1.18	1.17	171.8
	4		1.16	1.17	178.15
5 × CO2	1	−0.25	1.28	1.25	123.94	1.06
	2		1.17	1.18	174.76
	3		1.20	1.17	175.40
	4		1.18	1.17	173.54
	5		1.17	1.17	173.20

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Fig. 3 Details of the geometric parameters of (a) adsorbed CO₂ bending angle and C–H4 distance and (b) Mg2–H4–C contact angle related to the CO₂ (n = 1) molecule behaviour in the structure of 5 adsorbed CO₂ molecules.

In summary, although the P7 position is the most stable adsorption site, adsorption energies ranging from −0.38 to −0.43 eV (except for the P4 position) indicate that the MgH₂ causes suitable physical adsorption of CO₂ molecules. The coverage effect enhances CO₂–MgH₂ surface interactions until full coverage is achieved. CO₂ molecular structure distortion and slab deformation upon CO₂ adsorption unveil possible chemical interaction between the CO₂ gas molecules and the MgH₂ sorbent. Hence, activation of the CO₂ molecule is demonstrated by the bending angle and bond distances of molecules and the CO₂–MgH₂ slab adsorption distances.

The CO₂ adsorption capacity of MgH₂ has been compared with that of diverse sorbent materials in the literature (Table 3). Clean MgH₂ slab surface shows medium to strong affinity for CO₂ molecules, and therefore, noteworthy CO₂ adsorption capacity. However, the adsorption capacities of MgH₂ are far from those provided by other kinds of materials, such as decorated metal–organic frameworks³⁸ (MOFs), doped monolayers,³⁹ γ-Al₂O₃ (1 0 0),⁴⁰ or CuO₂ (110),⁴¹ as depicted in Table 3. Binding energies for the adsorption of a single CO₂ molecule on different materials reported in the literature, along with the DFT functional employed here, are given in Table 3.

Table 3 Adsorption energies and computational methodology of the adsorption of one CO₂ molecule on the non-catalyzed surface of different materials found in the literature

Methodology	Material	E ads (eV)	Ref.
DFT-D3, PBE	MgH 2	−0.41	This work
DFT, PBE	MgH2	−0.09	20
DFT-D3, PBE	Calcite (1 0 4)	−0.38	42
DFT, B3LYP	AlN monolayer	−0.15	43
DFT, PBE	TiO2 Brookite (2 1 0)	−0.16	44
DFT, PBE	TiO2 Anatase (1 0 1)	−0.20	45
DFT, PBE	γ-Al2O3 (1 1 0)	−0.43	46
DFT, PBE	γ-Al2O3 (1 0 0)	−0.80	32
DFT-D2, PBE	Ni (1 1 0)	−0.29	47
DFT-TS, PBE	TiO2 anatase (1 0 1)	−0.42	48
DFT, PBE	CeO2 (1 1 0)	−0.24	49
DFT, PBE	CuO2 (1 1 0)	−1.22	50
DFT-vdW-DF2, PBE	V-MOF-74s	−0.55	30
DFT-D, PBE	MoS2@GeSe monolayer	−0.96	31
DFT-D, PBE	TiO2 rutile (1 1 0)	−0.09	29
DFT-D, PBE	BC3 monolayer	−0.11	51
DFT-D, PBE	Cu-MOF	−0.82	52

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2.2 Co-doped MgH₂

To improve CO₂ affinity to MgH₂ sorbent, the Co single-atom catalyst (SAC) and Co cluster have been proposed as catalysts for CO₂ adsorption.³³ Adsorption energies for the different interacting sites of SAC (Fig. S1, ESI†) and Co–surface distances are reported in Table 4. For the 5 possible adsorption sites considered along the MgH₂ surface, C1 and C2 structures showed larger E_ads values (−6.47 and −7.93 eV, respectively) than C3, C4, and C5 (−3.55 to −4.49 eV) (Table 4). Regarding geometry, the initial Co SAC position on C1 converged to the C2 position of Co as inferred through geometric parameters reported in Fig. 4 and Table 4. Thus, C1 and C2 sites can be considered equivalent, although the greater stability of the C2 SAC structure should be noted, which reflects the Co atom embracement by H1 and H2 atoms of the MgH₂ surface (Fig. 4). Despite the C1 Co–surface distances being very similar to those in C2 (Table 4), ω₂ and ω₃ surface angles deformation (Table S1, ESI†) from 157.78 to 132.37° and 133.91°, respectively, manifest the insertion of the Co atom in the MgH₂ surface structure. In contrast, for the C1 structure, ω₂ and ω₃ surface angles present negligible deformation (from 157.78 to 158.00° and 160.82° respectively) (Table S1, ESI†). For this reason, the C2 Co SAC structure was considered in the following section for CO₂ adsorption studies.

Table 4 Adsorption energy and geometric parameters for Co atoms (SAC) at different MgH₂ surface sites (C1–C5). The values for the configuration with the highest energy (C2) are reported in bold

	E ads (eV)	r Co–H1 (Å)	r Co–H2 (Å)
C1	−6.47	1.52	1.50
C2	−7.93	1.57	1.57
C3	−4.49	2.34	2.17
C4	−3.55	1.56	1.56
C5	−4.49	1.56	1.56

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Fig. 4 Top- and side-view of the Co SAC structures for the C1–C5 sites and Co–Mg distances. Atom colour code: (white) hydrogen, (pink) magnesium, (green) cobalt.

When considering multiple Co atom catalysts, stronger adsorption energies were observed on MgH₂ compared to SAC. E_ads (per Co atom) range from −3.09 to −10.55 eV and from −7.18 to −9.43 eV for one-by-one Co atom addition and 1/4 to full surface coverage, respectively (Tables S2 and S3, ESI†). Interatomic Co distances, which vary from 2.16 to 4.15 Å, for the one-by-one clusterization and full coverage systems (Tables S4 and S5, ESI,† respectively), agree with Co clusterization atom distances reported in the literature.⁵³ Catalyst adsorption on the MgH₂ surface causes geometric disruption of the first and second layers of MgH₂, and the Co embracement effect observed for the SAC structures is also reproduced for the structures with multiple Co atoms (Fig. S3 and S4, ESI†). A structure with seven Co atoms is the most energetically stable system (−10.55 eV) for n Co clusterization on catalyzed MgH₂. The geometric parameters (Table S1, ESI†) of the converged structure indicate that H4 and H5 atoms were displaced along the x-direction (Fig. S3, ESI†) and closely (1.64 and 1.62 Å) interacted with the central Co atom (Fig. S5, ESI†), while Mg2–H4 and Mg3–H5 distances extended from 1.82 Å to 2.05 and 2.51 Å, respectively (Table S1, ESI†). For the structure with full coverage of Co (4/4, Fig. S4, ESI†), the E_ads were slightly weaker (−9.43 eV) than that for the cluster with 7 Co atoms (Table S3, ESI†). However, the geometric disorder of the first MgH₂ layer is larger, exhibiting considerable displacement of atoms and disruption of the H–Mg–H angles (Table S1, ESI†), triggering initial structural decomposition and Co atoms integration on the MgH₂ solid surface.

For all the reported Co catalyzing structures, large adsorption energies and non-negligible changes in surface structure were found. Therefore, the Co catalyst is intended to be capable of weakening substrate bond forces, and thus, the mechanisms of interaction between CO₂ molecule and MgH₂ surface are expected to be enhanced.

2.3 CO₂ adsorption on Co/MgH₂

In this section, CO₂ and CO₂ + 2/4 H₂ adsorption on Co/MgH₂ systems are discussed. First, one CO₂ molecule adsorption on Co SAC/MgH₂ was analyzed for all the SAC structures reported in the previous section. In the case of C1 and C2 structures, only the C2 SAC position was considered as Co SAC spatial location is equivalent, and the energetic stability is stronger. Both the dispositions of the CO₂ molecule considered initially, i.e., parallel and perpendicular to the surface on top of the SAC atom, manifested large CO₂E_ads in the range of −6.61 to −12.43 eV (Table 5). In the case of the C2 adsorption site, CO₂ adsorption energy for the parallel disposition became smaller compared to the perpendicular disposition. However, for C3, C4, and C5 structures, parallel CO₂ disposition showed larger interacting energies with respect to the surface. In general, larger adsorption energies (more negative values) rely on stronger interactions and greater disruption of CO₂ geometric parameters (Table 5). Whereas in CO₂ perpendicular disposition, no changes were noticed in the geometry of the gas molecules, while significant structural changes were found for the parallel disposition molecule, except for CO₂ adsorption on the C2 structure. CO₂–Co SAC distances are similar for all the structures (1.81 to 1.98 Å). The C3, C4, and C5 structures featured intense disruption of the CO₂ bending angles (134.94 to 140.19°) (Table 5). Therefore, despite detecting C1 and C2 as the most stable SAC structures, CO₂ adsorption turned out to be biased for C3, C4, and C5 (in that order), as depicted through reported E_ads (Table 5). Adsorption on the C3 structure provides stronger interaction energy (−12.43 eV), but also the most disordered MgH₂ first layer.

Table 5 Adsorption energy and geometric parameters for CO₂ adsorption for all the Co SAC sites on MgH₂ considered here. Both parallel (∥) and perpendicular (⊥) dispositions of the CO₂ molecule were considered. The values for the configuration with the highest energy (C3 CO₂ ∥) are reported in bold

	E ads (eV)	r C–O1 (Å)	r C–O2 (Å)	φ CO2 (deg)	r C–Co (Å)	r O1–Co (Å)
C2 CO2 ∥	−6.61	1.20	1.20	180	1.98
C2 CO2 ⊥	−9.71	1.18	1.19	179.66		1.93
C3 CO 2 ∥	−12.43	1.27	1.27	136.99	1.82
C3 CO2 ⊥	−8.86	1.19	1.18	178.23		1.85
C4 CO2 ∥	−10.17	1.23	1.29	140.19	1.81
C4 CO2 ⊥	−9.38	1.18	1.19	179.37		1.94
C5 CO2 ∥	−8.42	1.28	1.24	134.94	1.98
C5 CO2 ⊥	−7.98	1.17	1.18	179.85		3.24

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Two adsorption mechanisms are inferred from this analysis: the first one and the most likely to occur (stronger interacting energy) is adsorption through the C atom of the CO₂ molecules. The second one, which is energetically weaker, is adsorption via the O atom with a molecular disposition perpendicular to the surface (Fig. S6, ESI†). From the former mechanism, chemical adsorption manifestation is proposed to occur based on the CO₂ and MgH₂ surface structure perturbation (Table S1, ESI†), whilst physisorption is inferred for the latter adsorption mechanism. Hence, CO₂ chemical activation through carbon atoms is observed as an effect that should be attributed to the Co catalyst.

CO₂ adsorption on a catalyst with two Co atoms on the MgH₂ surface presented much weaker adsorption energies for both parallel and perpendicular disposition of the gas molecule (−2.71 and −2.69 eV, respectively), which ended up converging in the same geometrical position (Fig. S7, ESI†). Although the distortion in the CO₂ molecular structure in the two-Co structure is slightly stronger (Table 6), the adsorption mechanisms of both the SAC and two-Co catalyst seem to behave similarly. Moderate surface deformation was observed (Table S1, ESI†).

Table 6 Adsorption energy and geometric parameters for CO₂ adsorption on MgH₂ for the C2 Co SAC and the two Co atom structures. Both parallel (∥) and perpendicular (⊥) dispositions of the CO₂ molecule were considered. The values for the configuration with the highest energy (C3 CO₂ ∥ and 2 Co CO₂ ∥) are reported in bold

	E ads (eV)	r C–O1 (Å)	r C–O2 (Å)	φ CO2 (deg)	r C–Co1 (Å)	r C–Co2 (Å)	r Co1–Co2 (Å)
	Co SAC/C3
CO 2 ∥	−12.43	1.27	1.27	136.99	1.82
CO2 ⊥	−8.86	1.19	1.18	178.23		1.85

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	2 Co
CO 2 ∥	−2.71	1.24	1.34	129.37	1.84	2.24	2.71
CO2 ⊥	−2.69	1.25	1.33	130.59	1.83	2.2	2.81

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Further investigation was carried out on the CO₂ adsorption mechanism on MgH₂ by taking into consideration H₂ molecules that mimic H₂ release from a distinct hydrogen storage substrate. Thus, 4 and 2 H₂ molecules, according to different experimentally reported methanation mechanisms (Sabatier process and direct CO₂ reduction),²⁶ were considered, along with one CO₂ molecule for the C2 SAC and two Co atoms catalyzing MgH₂ structures. Geometrically optimized systems displayed in Fig. S8 (ESI†) yield adsorption energies in the range of −2.61 to −3.43 eV with similar CO₂ molecule distortion geometries (Table 7). CO₂ molecule deformation is found to be in line with the previously reported adsorbed molecules, whereas H₂ molecules do not interact within the system as no structural changes occur on the molecules themselves and there are no significant interactions that could be observed within the MgH₂ surface or the CO₂ molecule either (Fig. S8, ESI†). It might be highlighted that for the C2 SAC structure interaction with 1 CO₂ and 4 H₂ molecules, the CO₂ molecule is turned parallel to the surface leading to CO₂–MgH₂ full contact, in contrast to the remaining structures (Fig. S8, ESI†). Unremarkable slab surface deformation was observed for these structures (Table S1, ESI†).

Table 7 Adsorption energy (total) and geometric parameters for CO₂ and H₂ adsorption on MgH₂ for the C2 Co SAC and the two Co atom structures. System with 1 × CO₂ molecule and 2 × H₂ molecules or 1 × CO₂ molecule and 4 × H₂ molecules were considered. The values for the configuration with the highest energy (1 CO₂ + 4 H₂) are reported in bold

	E ads (eV)	r C–O1 (Å)	r C–O2 (Å)	φ CO2 (deg)	r C–Co1 (Å)	r C–Co2 (Å)	r Co1–Co2 (Å)	r H1–H2 (Å)
	Co SAC/C2
1 CO2 + 2 H2	−2.61	1.26	1.26	136.72	1.83	—	—	0.75
1 CO 2 + 4 H 2	−3.43	1.32	1.25	129.73	1.80	—	—	0.75

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	2 Co
1 CO2 + 2 H2	−3.10	1.28	1.28	136.36	1.90	1.90	2.66	0.75
1 CO 2 + 4 H 2	−3.43	1.28	1.29	136.36	1.90	1.89	2.66	0.75

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2.4 Insights into the charge transfer analysis and adsorption mechanisms

Charge density difference – or spatial charge redistribution – maps for the most stable aforementioned systems are shown in Fig. 5. Panel (a) represents the charge density for the clean slab; panels (b) to (d) depict the charge density difference of carbon dioxide on MgH₂; panels (e) to (f) show the charge density difference of Co atoms on MgH₂; and panels (h) to (k) show the charge density difference of CO₂ and H₂ on Co/MgH₂. Blue and yellow surfaces represent charge density depletion and accumulation, respectively. The difference plot slices prepared for complementary charge density in relevant regions of the system aid in comprehending the charge density transfer effect (Fig. 6), where red and blue colours represent maximum and minimum charge density accumulation, respectively. In panels (b) to (d) of Fig. 5, charge accumulation around oxygen and surface hydrogen atoms is outlined, whereas atomic charge depletion is observed for central carbon atoms, justifying the physisorption effect. Moderate charge transfer between CO₂ molecules and MgH₂ is shown, except for the CO₂ (2) molecules in panel (d), Fig. 5. Contrarily, large charge density transfer can be observed along with Co adsorption on the MgH₂ surface. The chemisorption of Co SAC on the MgH₂ surface is confirmed through strong charge interactions. An analogous effect is observed for the subsequent addition of Co atoms (Fig. 5f and g). More complex charge transfer patterns are observed in panels h to k. Combining panels (h) to (k) of Fig. 5 and 6, we can observe a double charge transfer effect: first, from the Co atoms adsorbed to the H atoms on the MgH₂ surface, and second, from the carbon of the CO₂ molecule adsorbed to the Co catalyst atoms. Hydrogen molecules do not seem to interchange charge density either with catalyzing surface or CO₂ molecules as no surfaces are associated with H₂ molecules.

Fig. 5 Charge density difference maps (ρ_system − ρ_slab − ρ_Co − ρ_gas) for the most stable structures (a–k) with the isosurface value of 0.005e. The yellow region represents charge density accumulation, while the blue region represents charge depletion.

Fig. 6 Charge density difference slice for the most stable structures (a–k) considering an isosurface value of 0.005e. Red-like colours represent charge density accumulation, while the region leaning to blue shades represents charge depletion.

Lastly, to gain insight into the CO₂ adsorption mechanisms, charge density transfer was investigated via valence Bader charges analysis. Valence electronic charges for CO₂ and H₂ molecules, first and second layers of MgH₂ and Co atoms were considered before and after the adsorption of the corresponding atoms/molecules (Tables S6–S8, ESI†). Next, charge transfer was calculated as the difference between the isolated surface/CO₂ molecule/Co atom and the valence Bader charges for the overall systems of the CO₂ molecule adsorbed on a clean MgH₂ surface, Co atom adsorbed on a clean MgH₂ surface, and CO₂/H₂ adsorbed on the catalysing systems (Tables S8–S10, ESI,† respectively). Positive and negative charge differences indicate charge uptake and charge loss, respectively. This means that an atom with a positive charge difference has electronic charge accumulation (negative ionic charge). Given the reported results, minor charge differences between CO₂ atoms and MgH₂ surface atoms confirm the physisorption mechanism at P2 and P7 sites (Table S9, ESI†). However, a significant charge difference was found within the CO₂ atoms: uptake of electronic charge by O atoms (+0.76 to +0.85) from the central C atom (which losses −1.51 and −1.67, respectively), favouring weak van der Waals interactions with the hydrogens on the MgH₂ surface (Table 1).

In the case of the four-CO₂-molecules system, physical adsorption could be inferred for CO₂ (1), CO₂ (3), and CO₂ (4) molecules on MgH₂, but chemisorption was confirmed for the CO₂ (2) molecule as significant charge transfer was observed between the H₄ and C₁ (2) atoms (Table S9, ESI†). This result is validated by the previously observed bending angle of the gas molecule, as well as adsorption distance (Table 2) and accumulation/depletion charge density map (Fig. 5d).

The charge difference reported for Co atoms on MgH₂ confirms strong interactions between the sorbent and selected catalyst as a large charge transfer was found between the hydrogen atoms on the surface and Co atoms (Table S11, ESI†). Therefore, strong adsorption of Co atoms on the MgH₂ surface was also corroborated by large adsorption energies and short interatomic distances (Tables 4, S2, and S3, ESI†). The charge difference of Co₄, Co₅, and Co₉ (Co atoms on the top of the surface H atoms), as well as Co₄, for seven Co and 4/4 systems, respectively, are particularly pronounced according to charge density maps (Fig. 5f and g).

Finally, the CO₂ and H₂ adsorption on the catalysis systems depicted moderate charge transfer between the MgH₂ surface and Co atoms combined with CO₂ adsorption on top of the Co atoms. In these structures, partial charge transfer from the C central CO₂ atom developed toward the O atoms, in parallel to partial charge transfer to the Co catalyst, leading to large ionic charge accumulation on the Co atoms. Thus, strong interactive forces between the CO₂ gas molecules and the catalysis surface are confirmed. Along with large E_ads and short adsorption distances, these findings corroborate the chemical nature of the adsorption mechanism. Additionally, considerable charge density is distributed along the CO₂ oxygen atoms, which may lead to possible interactive sites for H₂ adhesion. However, despite that, low reactivity was found for H₂ molecules according to the reported charge transfer and charge density plots.

Based on the reported results, two main conclusions can be reached: i) high CO₂ adsorption capacity of MgH₂ was confirmed with a preferential physisorption mechanism for the clean surface and a chemisorption route for the Co-catalysed surface, and ii) no interaction could be detected between the adsorbed CO₂ and H₂ molecules.

3 Conclusions

In this theoretical inquiry, we systematically investigated the properties and mechanisms governing carbon dioxide (CO₂) adsorption on magnesium hydride (MgH₂) surfaces augmented with Co atoms. The focal point of our analysis was an unaltered MgH₂ surface and the impact of Co species on the CO₂ adsorption process. The findings unveiled the physical manifestation of the adsorption phenomena on the MgH₂ surface, whereby disparate adsorption sites are present indicating uniform adsorption energies. The influence of CO₂ molecular coverage on MgH₂ demonstrated increased affinity at enhanced surface coverage, reaching an optimal saturation point after which excessive coverage occurred and induced a decline in adsorption efficiency. Following adsorption, the orientational configuration of CO₂ molecules transitioned from parallel to quasi-perpendicular arrangements, accompanied by discernible deformations at heightened coverage.

In the context of comparative analyses with alternative materials, MgH₂ emerged as a noteworthy medium with a strong affinity for CO₂. Furthermore, our scrutiny of the efficacy of Co single atoms or clusters for CO₂ adsorption on MgH₂ indicated the superiority of Co single atoms for adsorption at specific sites that were reflected in heightened adsorption energies. This mechanism entails the activation of CO₂ molecules through perturbation of molecular properties, characterisation of CO₂–MgH₂ slab interactions, and facilitation of electronic charge transfer.

These observations collectively contribute to a deep comprehension of the underlying properties and mechanisms of CO₂ adsorption on MgH₂ in the presence of Co. Importantly, they provide pivotal insights into the initial reaction step, thereby guiding the rational design of more efficient CO₂ conversion technologies.

4 Computational methods

Quantum Espresso 6.5 software⁵⁴ with the PW package was used for DFT spin-polarised calculations. For all the atoms involved in simulations, projector augmented wave (PAW) pseudopotentials were used,^55,56 together with the revised version⁵⁷ of the PBE exchange–correlation functional.^50,58,59 Periodic boundary conditions (PBC) were applied, and dispersion forces were also included via the semi-empirical correction by Grimme, DFT-D3.⁶⁰ The Burai graphical user interface of Quantum Espresso was used to build the systems. The DMol3 package from the BIOVIA materials studio environment was also employed for geometry pre-optimisation and initial systems equilibration (DFT-PBE).

Magnesium hydride is characterized by a tetragonal crystal system with a P4₂/mnm space group (α-MgH₂).^61,62 Experimental lattice parameters are a = b = 4.512 Å and c = 3.016 Å.⁶³ From this data, bulk lattice was relaxed with a k-point Monkhorst–Pack grid⁶⁴ of 12 × 12 × 12, which was converged before considering production runs (see Table S12 and Fig. S9, ESI†) to allow the necessary energy accuracy, along with a cut-off energy of 40 Ry (544.23 eV), according to the largest value recommended in the employed pseudopotentials.

The new lattice parameters of the relaxed system were a = b = 4.503 Å and c = 3.01 Å. To mimic the bulk crystal, a 2 × 2 supercell with 4 layers of depth was generated. A surface with (0 0 1) Miller index was considered for the slab model since it is the most suitable surface regarding vacancy formation energies, and thus, the dehydrogenation process.^48,65 A twenty-Angstrom vacuum layer was set above the model slab to avoid the interaction of neighbouring MgH₂ cells. For all the calculations, two bottom layers of the slab were fixed to maintain crystal behaviour. Fig. 1 shows the overall simulated cell of dimensions, 8.88 × 8.88 × 30.47 Å, enclosing 96 atoms.

Surface energy, E_surf, for the clean MgH₂ slab was calculated according to eqn (1) because the symmetry of the two-sided slab guarantees the double counting of the surface energy. E_bulk is the energy of the bulk MgH₂, and A_slab is the surface area of a side of the calculated supercell slab model.

In this formula, N_slab is the number of atoms on the slab, and N_bulk is the number of atoms in the bulk material.

Once the E_surf of the clean MgH₂ slab and the energy E_CO2 of the isolated CO₂ molecule were computed, CO₂ adsorption energy (E_ads) on non-catalyzing systems was also calculated for different positions of the carbon dioxide molecule (P1–P7) as well as for different numbers of the CO₂ molecules (n = 1–5) according to eqn (2):

E_ads = (E_surf+nCO2 − E_surf − nE_CO2)/n (2)

Co-doped systems were then examined; first, by considering one cobalt atom as the SAC, C1–C5, followed by n = 1–9 cobalt atoms in a growing plain cluster disposition; lastly, accounting for partial to full cobalt surface coverage layouts (1/4, 2/4, 3/4, and 4/4 of the slab surface). The energies of catalyzing systems were calculated as follows (eqn (3)):

E_{int Co/MgH2} = (E_surf+nCo − E_surf − nE_Co)/n (3)

Accordingly, CO₂ adsorption energy (E_ads) on the catalyzing systems was evaluated for different dispositions of one CO₂ molecule (parallel and perpendicular arrangement with respect to the MgH₂ surface) and for one molecule of CO₂ and 2–4 hydrogen molecules (in agreement with 1 : 2 and 1 : 4 CO₂/H₂ reaction ratio) to understand interaction mechanisms. One Co SAC and two Co-catalyzed MgH₂ systems were considered in this section. eqn (4) describes CO₂ or CO₂ + 2/4 H₂ adsorption energies:

E_ads = E_{nCo/MgH2+nCO2+nH2} − E_nCo/MgH2 − nE_CO2 − nE_H2 (4)

For the systems in which more than one carbon dioxide molecule or hydrogen molecule is considered, the calculated adsorption energy was divided by the number of molecules to estimate the adsorption energy per molecule. In Fig. S1, ESI,† top view of the considered positions for one CO₂ molecule (P1–P7, Fig. S1a, ESI†) and 1 to 5 CO₂ molecules (Fig. S1b, ESI†) over MgH₂ (0 0 1) surface are shown as well as the initial bond distances and bending angle of the optimized carbon dioxide molecule (Fig. S1c, ESI†). Accordingly, SAC positions of Co (C1–C5), Co clusterization (1 Co–9 Co), and Co coverage arrangements (1/4 Co, 2/4 Co, 3/4 Co, and 4/4 Co) are shown in Fig. 1d, S1e and f, ESI,† respectively.

To elucidate the CO₂ adsorption mechanism and CO₂ + H₂ interactions over MgH₂ (0 0 1) surface catalyzed and non-catalyzed by Co, charge density differences obtained from electron (pseudo-) charge density quantum espresso plots were evaluated. The final spatial distribution of electronic charge density upon CO₂/Co/H₂ adsorption was calculated by subtracting the charge densities of the CO₂/Co/H₂ entity (ρ_MgH2, ρ_Co, ρ_CO2, ρ_H2, respectively) from the entire final system, ρ_{Co/MgH2+CO2+H2} according to eqn (5):

ρ_final = ρ_sys − ρ_MgH2 − ρ_Co − ρ_CO2 − ρ_H2 (5)

VESTA and VMD were used to visualize charge density differences and to evaluate charge transfer results. Bader charges of the valence electrons were also evaluated for the largest energy configurations. For this purpose, the Bader code by the Henkelman group^66–69 was employed to identify single atoms inside the system and evaluate their charge density allowing the evaluation of charge transfer phenomena upon adsorption.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This investigation was funded by the CO₂ absorbing Materials Project-RISE (CO2MPRISE) which received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. H2020-MSCA-RISE-2016-CO2MPRISE-734873. We also acknowledge SCAYLE (Supercomputación Castilla y León, Spain) for providing supercomputing facilities. The statements made herein are solely the responsibility of the authors.

References

1. Global Monitoring Laboratory, Earth System Research Laboratories, https://gml.noaa.gov/ccgg/trends/, (accessed July 2023).
2. IPCC, Climate Change 2007. The Physical Science Basis, Cambridge Univ. Press, Cambridge, 2007.
3. F. Kazemifar, A review of technologies for carbon capture, sequestration, and utilization: Cost, capacity, and technology readiness, Greenhouse Gases: Sci. Technol., 2022, 12, 200–230.
4. P. Markewitz, W. Kuckshinrichs, W. Leitner, J. Linssen, P. Zapp, R. Bongartz, A. Schreiber and T. E. Müller, Worldwide innovations in the development of carbon capture technologies and the utilization of CO2, Energy Environ. Sci., 2012, 5, 7281–7305.
5. N. S. Sifat and Y. Haseli, A critical review of CO2 capture technologies and prospects for clean power generation, Energies, 2019, 12, 4143.
6. A. Sood, A. Thakur and S. M. Ahuja, Recent advancements in ionic liquids-based carbon capture technologies, Chem. Eng. Commun., 2021, 210, 933–954.
7. B. Dutcher, M. Fan and A. G. Russell, Amine-based CO2 capture technology development from the beginning of 2013 – A review, ACS Appl. Mater. Interfaces, 2015, 7, 2137–2148.
8. A. I. Osman, M. Hefny, M. I. A. Abdel Maksoud, A. M. Elgarahy and D. W. Rooney, Recent advances in carbon capture storage and utilization technologies: A review, Environ. Chem. Lett., 2021, 19, 797–849.
9. A. Raza, R. Gholami, R. Rezaee, V. Rasouli and M. Rabiei, Significant aspects of carbon capture and storage–A review, Petroleum, 2019, 5, 335–340.
10. K. M. K. Yu, I. Curcic, J. Gabriel and S. E. Tsang, Recent advances in CO2 capture and utilization, ChemSusChem, 2008, 1, 893–899.
11. G. Cau, D. Cocco and V. Tola, Performance and cost assessment of Integrated Solar Combined Cycle Systems (ISCCSs) using CO2 as heat transfer fluid, Sol. Energy, 2012, 86, 2985–2985.
12. R. C. Weast, CRC handbook of chemistry and physics, CRC Press, Boca Raton, 1973–1974.
13. U. Ulmer, T. Dingle, P. N. Duchesne, R. H. Morris, A. Tavasoli, T. Wood and G. A. Ozin, Fundamentals and applications of photocatalytic CO2 methanation, Nat. Commun., 2019, 10, 3169.
14. Z. Liu, X. Gao, B. Liu, Q. Ma, T. S. Zhao and J. Zhang, Recent advances in thermal catalytic CO2 methanation on hydrotalcite-derived catalysts, Fuel, 2022, 321, 12411.
15. J. Ashok, S. Pati, P. Hongmanoram, Z. Tianxi and C. Junmei, A review of recent catalyst advances in CO2 methanation processes, Catal. Today, 2020, 356, 471–489.
16. Z. Lv, H. Du, S. Xu, T. Deng, J. Ruan and C. Qin, Techno-economic analysis on CO2 mitigation by integrated carbon capture and methanation, Appl. Energy, 2024, 355, 122242.
17. A. Tripodi, F. Conte and I. Rosetti, Carbon Dioxide Methanation: Design of a Fully Integrated Plant, Energy Fuels, 2020, 34, 7242–7256.
18. P. Sabatier and J. B. Senderns, Mouvelles synthese du methane, C. R. Acad. Sci., 1902, 134, 514–516.
19. K. Fakumoto, W. Zhang, R. Mizoguchi, Y. Lin, C. Chai, H. Machida and K. Narinaga, CFD simulation of CO2 methanation through the Sabatier reaction in a shell-and-tube reactor incorporating phase change on the shell side, Fuel, 2023, 349, 128126.
20. Q. Hou, X. Yang and J. Zhang, Review on Hydrogen Storage Performance of MgH2: Development and Trends, ChemistrySelect, 2021, 6, 1589–1606.
21. E. M. Dematteis, J. Barale, M. Corno, A. Sciullo, M. Baricco and P. Rizzi, Solid-state hydrogen storage systems and the relevance of a gender perspective, Energies, 2021, 14, 6158.
22. C. N. C. Hitman, M. A. A. Aziz, A. H. Ruhaimi and M. R. Taib, Magnesium-based alloys for solid-state hydrogen storage applications: A review, Int. J. Hydrogen Energy, 2021, 46, 31067–31083.
23. O. Zavorotynska, I. Saldan, S. Hino, T. D. Humphries, S. Deledda and B. C. Hauback, Hydrogen cycling in γ–Mg(BH4)2 with cobalt-based additives, J. Mater. Chem. A, 2015, 3, 6592–6602.
24. I. Saldan, S. Hino, T. D. Humphries, O. Zavorotynska, M. Chong, C. M. Jensen, S. Deledda and B. C. Hauback, Structural changes observed during the reversible hydrogenation of Mg(BH4)2 with Ni-based additives, J. Phys. Chem. C, 2014, 118, 23376–23384.
25. J. Cui, J. Liu, H. Wang, L. Ouyang, D. Sun, M. Zhu and X. Yao, Mg-TM (TM: Ti, Nb, V, Co, Mo or Ni) core-shell like nanostructures: Synthesis, hydrogen storage performance and catalytic mechanism, J. Mater. Chem. A, 2014, 2, 9645–9655.
26. M. G. Verón, H. Troiani and F. C. Gennari, Synergetic effect of Co and carbon nanotubes on MgH2 sorption properties, Carbon, 2011, 49, 2413–2423.
27. M. Liu, X. Xiao, S. Zhao, M. Chen, J. Mao, B. Luo and L. Chen, Facile synthesis of Co/Pd supported by few-walled carbon nanotubes as an efficient bidirectional catalyst for improving the low temeprature hydrogen storage properties of magnesium hydride, J. Mater. Chem. A, 2019, 7, 5277–5287.
28. M. L. Grasso, L. Fernández Albanesi, S. Garroni, G. Mulas and F. C. Gennari, Methane production by mechanochemical processing of MgH2-Li2CO3 as sources of H2 and CO2 at room temperature, J. CO2 Util., 2020, 40, 101209.
29. G. W. Manggada and S. Zhou, Phosphonic acid modification to molybdenum atom catalyst for CO2 hydrogenation on magnesium hydride surface, DISTILAT: Jurnal Teknologi Separasi, 2022, 8, 315–324.
30. S. Polierer, J. Jelic, S. Pitter and F. Studt, On the reactivity of the Cu/ZrO2 system for the hydrogenation of CO2 to methanol: A density functional theory study, J. Phys. Chem. C, 2019, 123, 26904–26911.
31. H. Chen, P. Liu, J. Li, Y. Wang, C. She, J. Liu, L. Zhang, Q. Yang, S. Zhou and X. Feng, MgH2/CuxO hydrogen storage composite with defect-rich surfaces for carbon dioxide hydrogenation, ACS Appl. Mater. Interfaces, 2019, 11, 31009–31017.
32. V. Iablokow, S. K. Beaumnt, S. Alayoglu, V. V. Pushkarev, C. Specht, J. Gao, A. P. Alivisatos, N. Kruse and G. A. Somorjai, Size-controlled model Co nanoparticle catalyst for CO2 hydrogenation: Synthesis, characterization, and catalytic reactions, Nano Lett., 2012, 12, 3091–3096.
33. G. Zhou, T. Wu, H. Xie and X. Zheng, Effect of structure on the carbon dioxide methanation performance of Co-based catalyst, Int. J. Hydrogen Energy, 2013, 38, 10012–10018.
34. A. Morales-García, F. Viñes, J. R. B. Gomes and F. Illas, Concepts, models, and methods in computational heterogeneous catalysis illustrated through CO2 conversion, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2021, 11(4), e1530.
35. M. L. Grasso, S. Rozas, P. A. Larochette, S. Aparicio and F. Gennari, Thermochemical transformation of CO2 for CH4 production using metal hydride and carbonates as portable sources, Int. J. Hydrogen Energy, 2023, 48, 21835–24849.
36. A. J. Stone, The theory of intermolecular forces, Oxford University Press, New York, 1997.
37. C. Sorescu, J. Lee, W. A. Al-Saidi and K. D. Jordan, CO2 adsorption on TiO2(110) rutile: Insight from dispersion-corrected density functional theory calculations and scanning tunneling microscopy experiments, J. Chem. Phys., 2011, 134, 104707.
38. K. Lee, J. D. Howe, L.-C. Lin, B. Smith and J. B. Neaton, Small-molecule adsorption in open-site metal–organic frameworks: A systematic density functional theory study for rational design, Chem. Mater., 2015, 27, 668–678.
39. H. Yang, C. He, L. Fu, J. Huo, C. Zhao, X. Li and Y. Song, Capture and separation of CO2 on BC3 nanosheets: A DFT study, Chin. Chem. Lett., 2021, 32, 3202–3206.
40. Y. Pan, C.-J. Liu and Q. Ge, Adsorption and protonation of CO2 on partially hydroxylated γ-Al2O3 surfaces: A density functional theory study, Langmuir, 2008, 24, 12410–12419.
41. A. K. Mishra, A. Roldan and N. H. Leeuw, A density functional theory study of the adsorption behavior of CO2 on CuO2 surfaces, J. Chem. Phys., 2016, 145, 4958804.
42. G. Carchini, I. Hussein, M. J. Al-Marri, R. Shawabkeh, M. Mahamoud and S. Aparicio, A theoretical study of gas adsorption on calcite for CO2 enhanced natural gas recovery, Appl. Surf. Sci., 2020, 504, 144575.
43. Y. Jiao, A. Du, Z. Zhu, V. Rudolph and S. C. Smith, Adsorption of carbon dioxide and nitrogen on single-layer aluminum nitride nanostructures studied by density functional theory, J. Phys. Chem. C, 2010, 114, 7846–7849.
44. M. M. Rodriguez, X. Peng, L. Liu, Y. Li and J. M. Andino, A density functional theory and experimental study of CO2 interaction with brookite TiO2, J. Phys. Chem. C, 2012, 116, 19755–19764.
45. D. C. Sorescu, W. A. Al-Saidi and K. D. Jordan, CO2 adsorption on TiO2 (1 0 1) anatase: A dispersion-corrected density functional theory study, J. Chem. Phys., 2011, 135, 124701.
46. Y. Pan, C.-J. Liu and Q. Ge, Adsorption and protonation of CO2 on partially hydroxylated γ-Al2O3 surfaces: A density functional theory study, Langmuir, 2008, 24, 12410–12419.
47. O. Mohan, Q. T. Trinh, A. Benerjee and S. H. Mushrif, Predicting CO2 adsorption and reactivity on transition metals surfaces using popular density functional theory methods, J. Exp. Nanosci., 2019, 45, 1163–1172.
48. V. Chihaia, D. A. Neacsu, V. Alexiev and D. Angelescu, Performances of the bond order interacting potentials on calculating the surface energies of MgH2 facets, Available at SSRN: https://ssrn.com/abstract=4282784.
49. N. Kumari, N. Sinha, M. A. Haider and S. Basu, CO2 reduction to methanol on CeO2 (1 1 0) surface: A density functional theory study, Electrochim. Acta, 2015, 170, 21–29.
50. J. P. Perdew, K. Bruke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, 77, 3865–3868.
51. H. Yang, C. He, L. Fu, J. Huo, C. Zhao, X. Li and Y. Song, Capture and separation of CO2 on BC3 nanosheets: A DFT study, Chin. Chem. Lett., 2021, 32, 3202–3206.
52. Q. Cui, G. Qin, W. Wang, K. R. Geethalakshmi, A. Du and Q. Sun, Novel two-dimensional MOF as promising single-atom electrocatalyst for CO2 reduction: A theoretical study, Appl. Surf. Sci., 2020, 500, 143993.
53. B. Farkas and N. H. Leeuw, Towards a morphology of cobalt nanoparticles: Size and strain effects, Nanotechnology, 2020, 31, 195711.
54. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari and R. M. Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter, 2009, 21, 395502.
55. P. E. Blöchl, Generalized separable potentials for electronic-structure calculations, Phys. Rev. B, 1990, 41, 5414–5416.
56. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1990, 59, 1758–1775.
57. Y. Zhang and W. Yang, Comment on “Generalized Gradient Approximation Made Simple”, Phys. Rev. Lett., 1998, 80, 890–890.
58. G. Prandini, A. Marrazzo, I. E. Castelli, N. Mounet and N. Marzari, Precision and efficiency in solid-state pseudopotential calculations, npj Comput. Mater., 2018, 4, 72.
59. K. Lejaeghere, G. Bihlmayer, T. Björkman, P. Blaha, S. Blügel, V. Blum, D. Caliste, I. E. Castelli, S. J. Clark, A. Dal Corso, S. de Gironcoli, T. Deutsch, J. K. Dewhurst, I. Di Marco, C. Draxl, M. Dułak, O. Eriksson, J. A. Flores-Livas, K. F. Garrity, L. Genovese, P. Giannozzi, M. Giantomassi, S. Goedecker, X. Gonze, O. Grånäs, E. K. U. Gross, A. Gulans, F. Gygi, D. R. Hamann, P. J. Hasnip, N. A. W. Holzwarth, D. Iuşan, D. B. Jochym, F. Jollet, D. Jones, G. Kresse, K. Koepernik, E. Küçükbenli, Y. O. Kvashnin, I. L. M. Locht, S. Lubeck, M. Marsman, N. Marzari, U. Nitzsche, L. Nordström, T. Ozaki, L. Paulatto, C. J. Pickard, W. Poelmans, M. I. J. Probert, K. Refson, M. Richter, G.-M. Rignanese, S. Saha, M. Scheffler, M. Schlipf, K. Schwarz, S. Sharma, F. Tavazza, P. Thunström, A. Tkatchenko, M. Torrent, D. Vanderbilt, M. J. van Setten, V. Van Speybroeck, J. M. Wills, J. R. Yates, G.-X. Zhang and S. Cottenier, Reproducibility in density functional theory calculations of solids, Science, 2016, 351, aad3000.
60. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, A consistent and accurate ab initio parametrization of density functional disersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys., 2010, 132, 15104.
61. J.-P. Bastide, B. Bonnetot, J.-M. Létoffé and P. Claudy, Polymorphisme de l'hydrure de magnesium sous haute pression, Mater. Res. Bull., 1980, 15, 1215–1224.
62. H. S. AlMatouk, V. Chihaia and V. Alexiev, Density functional study of the thermodynamic properties and phase diagram of the magnesium hydride, CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 2018, 60, 7–15.
63. M. Bortz, B. Bertheville, G. Bötter and K. Yvon, Structure of the high pressure phase γ-MgH2 by neutron powder diffraction, J. Alloys Compd., 1999, 287, L4.
64. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, 13, 5188–5192.
65. W.-Y. Chen, J.-J. Tang, Z.-W. Lu, M.-X. Huang, L. Liu, C.-C. He and Y.-J. Zhao, Theoretical investigation of the surface orientation impact on the hydrogen vacancy formation of MgH2, Surf. Sci., 2021, 710, 121850.
66. M. Yu and D. R. Trinkle, Accurate and efficient algorithm for Bader charge integration, J. Chem. Phys., 2011, 134, 064111.
67. W. Tang, E. Sanville and G. Henkelman, A grid-based Bader analysis algorithm without lattice bias, J. Phys.: Condens. Matter, 2009, 21, 084204.
68. E. Sanville, S. D. Kenny, R. Smith and G. Henkelman, Improved grid-based algorithm for Bader charge allocation, J. Comput. Chem., 2007, 28, 899–908.
69. G. Henkelman, A. Arnaldsson and H. Jónsson, A fast robust algorithm for Bader decomposition of charge density, Comput. Mater. Sci., 2006, 36, 354–360.

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Footnote

† Electronic supplementary information (ESI) available: Fig. S1 (initial dispositions of all the considered systems); Fig. S2 (optimized geometries of systems considering nCO₂ molecules); Table S1 (MgH₂ surface angle and radius deformation); Table S2 (adsorption energies for Co-catalyzed systems); Table S3 (adsorption energies for Co-catalyzed systems); Table S4 (interatomic distances between the Co atoms for the 1 to 9 cluster formation); Table S5 (interatomic distances between cobalt atoms for surface coverage); Fig. S3 (optimised geometries of Co clusters systems); Fig. S4 (optimized geometries of Co clusters systems); Fig. S5 (details of the geometric parameters of the 7Co/MgH₂ structure); Fig. S6 (optimized geometries of CO₂ on Co SAC systems); Fig. S7 (optimized geometries of CO₂ on nCo-catalyzed systems); Fig. S8 (optimized geometries of CO₂ + H₂ on Co-catalyzed systems); Table S6 (Bader ionic charges of CO₂ adsorption on clean MgH₂); Table S7 (Bader ionic charges of Co adsorption on clean MgH₂); Table S8 (Bader ionic charges of CO₂ and H₂ adsorption on Co/MgH₂); Table S9 (valence Bader charge difference for CO₂/MgH₂ systems); Table S10 (valence Bader charge difference for Co/MgH₂ systems); Table S11 (valence Bader charge difference for CO₂/Co–MgH₂ systems); Table S12 (MgH₂ surface energies for the k-point testing set); Fig. S9 (MgH₂ surface energies as a function of the selected k-points). See DOI: https://doi.org/10.1039/d3im00096f

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