Cooperative physisorption and chemisorption of hydrogen on vanadium-decorated benzene

Abstract

3d TM-decorated carbon composites have been proved to be a new generation of hydrogen storage materials. However, detailed hydrogen storage mechanisms are still unclear. Investigation of the H₂ dissociation and H migration on the 3d TM-decorated six-membered carbocycles is very critical for better understanding the hydrogen storage mechanism. In this paper, the processes of chemisorption and physisorption of multiple H₂ molecules on synthesized VC₆H₆ were simultaneously investigated for the first time. The Gibbs free energy calculations show that the optimal chemisorption pathway with the hydrogen storage capacity of 5.97 wt% is exothermic by 2.83 kcal mol⁻¹. Both the continuous hydrogenation giving the product of VC₆H₁₁–3H and reverse dehydrogenation could run smoothly at room temperature. The physisorption with a hydrogen storage capacity of 4.48 wt% will be exothermic by 13.49 kcal mol⁻¹. The H₂ molecules can be physisorbed at any temperature under 416 K and readily desorbed above 480 K at 1 atm. In summary, physisorption and chemisorption synergistically boost the hydrogen storage property of complex VC₆H₆. Our study provides a comprehensive picture of the interaction between hydrogen and VC₆H₆ and opens a new window for optimizing the future hydrogen storage materials.

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1. Introduction

To satisfy the increasing global energy demands and solve serious environmental problems, renewable energy sources need to be researched to replace fossil-based fuels.¹ Hydrogen energy is reversible, recyclable, and pollution-free.^2,3 With the rapid progress of energy transformation, the value of hydrogen energy is further highlighted.^4–9 However, the hydrogen energy industry chain, especially the basic research on hydrogen storage links, faces many difficulties currently. Although many hydrogen storage methods^10–12 have their advantages in some aspects, they are not enough to meet the practical requirements of hydrogen energy in transportation. Generally, hydrogen is attached by physisorption or chemisorption. In physisorption, hydrogen remains in a molecular state and is weakly bound to the surface. In chemisorption, H₂ molecules dissociate into double H atoms and even migrate to the material forming chemical bonds, which are strong.⁶ Kubas-type orbital interaction^13,14 is similar to physisorption, in which the H–H bond in an H₂ molecule is elongated but not broken. It improves the hydrogen adsorption energy of transition metals (TMs)-decorated carbon composites (0.10–0.80 eV)⁶ and makes most of the hydrogen gravimetric storage capacities satisfy the target of the U.S. Department of Energy (∼6.5 wt%).¹⁵ Then, TM-decorated carbon composites grew up to be a new generation of hydrogen storage materials.^16–19 Interestingly, the dissociation of the first H₂ was spontaneous on most of Sc/Ti/V-decorated carbon nanostructures.^20–22 The dissociation of the H₂ increases the probability of H migration. The question then arises: whether hydrogen molecules are adsorbed only or migrate to form C–H bonds? If dissociation and even migration take place and TM-H/C–H bond is formed, the adsorption of H₂ on transition-metal-decorated nanomaterials will change from physisorption to chemisorption. Investigation of the H₂ dissociation and H migration is very important for better understanding the hydrogen storage mechanism on the 3d transition metal-decorated carbon nanostructures. While physisorption was mainly focused on and chemisorptions was always neglected.

On the other hand, the spillover mechanism is another promising mechanism for enhancing the H₂ uptake in carbon-based materials.^23–25 Hydrogen spillover following three processes: (1) the dissociation of H₂ molecules on the TM sites; (2) the migration of the atomic hydrogen from TM sites to the carbon surface and (3) the diffusion of atomic hydrogen on the carbon surface eventually forming a stable C–H bond. Understanding these three key steps is necessary to fully understand the hydrogen spillover process. Most theoretical studies on the mechanism of hydrogen spillover on carbon adsorbent have been carried out on graphene.^26–30 The metal catalyst is an important factor affecting storage by hydrogen spillover. So far, the dissociation sources for hydrogen spillover have been long known for TMs such as Pt, Pd, Ru, Ni, and Ti.^31–34 The experimental progress of Kubas-type H₂-storage materials always confirmed by V-containing polymers.³⁵ Then, could monatomic V be used as a source of dissociation sources for hydrogen spillover?

Six-membered carbocycle isan important linker in some metal organic frameworks^36,37 and covalent organic frameworks³⁸ but also a basic unit of C₆₀,^39,40 graphene,^41,42 and carbon nanotubes.^43–46 In this regard, Ti/Sc/V-benzene complexes as representative units of high-capacity hydrogen storage materials have received great attention.^47–50 In this study, based on first-principles calculations, the adsorption behavior of hydrogen on the synthesized VC₆H₆ (ref. 51–54) is focused on to further address the hydrogen storage mechanism. Previously, Weck,⁴⁷ Ajay,⁴⁸ and Li⁴⁹ reported that VC₆H₆ could adsorb three hydrogen molecules, but the only physisorption was considered. Here, a systematic study of both physisorption and chemisorption is investigated. The mechanism of dissociative adsorption and even the migration of the H atoms on VC₆H₆ is investigated. It was found that physisorption and chemisorption synergistically boost the hydrogen storage property of complex VC₆H₆. Most of our findings would have a great significance for the study of hydrogen storage on TM-decorated carbon composites.

2. Computational methods and details

All geometry optimizations were carried out by using the density functional theory (DFT) method at B3LYP⁵⁵/6-31+G(d,p) level. The whole calculations employed the Gaussian 09 suite of programs.⁵⁶ The optimization was carried out without any symmetry constraint and different spin multiplicities were considered. The optimized geometric coordinates and energies were listed in the ESI.† Frequency calculations were performed to confirm that there was no imaginary frequency in the stable structure, and one imaginary frequency in the transition states. Ab initio molecular dynamics (MD) simulations based on atom density matrix propagation (ADMP)^57–61 were performed to confirm part of the favorable dissociation paths.

Consecutive adsorption energies with ZPEs (ΔE_n) and Gibbs free energy corrections (ΔG_n) at 298.15 K were obtained using the following formula:

ΔE_n = E(VC₆H₆(H₂)_n−1) + E(H₂) − E(VC₆H₆(H₂)_n) (1)

ΔG_n = G(VC₆H₆(H₂)_n−1) + G(H₂) − G(VC₆H₆(H₂)_n) (2)

where E(X) is the sum of electronic and zero-point energy, G(X) is the sum of electronic and thermal free energy of the corresponding structure at 298.15 K, n represents the number of H₂ molecules.

In the equilibrium state, various conformations of VC₆H₆(H₂)_n have different energy and proportion. The proportion of conformation (P_i) was calculated according to the Boltzmann distribution:

where N is the number of conformation, E is the energy of conformation, T represents the temperature (Kelvin), R is the ideal gas constant, and Q is the partition function.

Spin multiplicity, vibrational frequencies, ionization energy, and electron affinity of VC₆H₆ were calculated to test the reliability of our calculations. The range-separated hybrid DFT method (wB97XD)⁵⁷ was used. The larger Pople-style orbital basis sets 6-311G++(3df,3pd) and diffuse functions in standard basis set aug-cc-pVTZ for C, H, and large-core relativistic Stuttgart–Dresden effective core potential(SDD)⁵⁸ basis set for V atom were included.

As shown in Table 1, both the results using B3LYP/6-31G+(d,p) and wB97XD/6-311G++(3df,3pd) show that VC₆H₆ is quartet state and the vibrational frequencies of VC₆H₆ are in good agreement with the experimental values.⁴⁸ The ionization energies and electron affinities of VC₆H₆ in Table 2 using B3LYP/6-31G+(d,p), B3LYP/aug-cc-pVTZ and wB97XD/6-311G++(3df,3pd) are in good agreement with the experimental values in ref. 51 and 53. The C–C bond lengths and the C–H bond lengths of VC₆H₆ using B3LYP/6-31+g(d,p) are 1.40–1.56 Å and 1.08–1.10 Å, respectively, which coincide well with the theoretical results by Duncan.⁵⁴ These values indicate the scheme of B3LYP/6-31+g(d,p) is a good compromise between accuracy and computational effort.

Table 1 Spin multiplicity, energy differences Δ (in eV) between doublet state and quartet state, and vibrational frequencies of VC₆H₆ (in cm⁻¹)

Functional	Multi.	Δ (eV)	νo-p(CH)^a	νs(CC)	νi-p(CH)	ν(CC)
a Vibrational modes: νo-p(CH) = C–H out of plane bending; νs(CC) = symmetric C–C stretching; νi-p(CH) = C–H in-plane rocking; ν(CC) = asymmetric C–C stretching.
B3LYP/6-31G+(d,p)	2	0.07
	4	0.00	769.05	956.3	1319.34	1420.15
B3LYP/6-311G++(3df,3pd)	2	0.30
	4	0.00	734.10	924.20	1368.27	1507.34
B3LYP/aug-cc-pVTZ	2	0.11
	4	0.00	679.54	928.29	1341.32	1500.48
wB97XD/6-311G++(3df,3pd)	2	2.64
	4	0.00	760.51	947.81	1329.71	1426.20
wB97XD/aug-cc-pVTZ	2	1.61
	4	0.00	781.87	974.09	1348.03	1506.89
Experiments^54			758.00	958.00	1306.00	1460.00

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Table 2 Ionization energy (eV) and electron affinity (eV) of VC₆H₆

Functional	Ionization energy (eV)	Electron affinity (eV)
B3LYP/6-31+G(d,p)	6.44	0.62
B3LYP/6-311G++(3df,3pd)	6.46	0.40
B3LYP/aug-cc-Pvtz	6.44	0.65
wB97XD/6-311G++(3df,3pd)	6.59	0.65
wB97XD/aug-cc-pVTZ	5.98	0.70
Experiments	6.30 ± 0.50 (ref. 51)	0.62 ± 0.07 (ref. 53)

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Moreover, the adsorption processes of H₂ molecules on TM decorated carbon nanomaterials include Kubas-type bonding, H₂ dissociation, H atom migration, and even strong C–H bonds producing. Both our previous researches⁵² and other group's reports^59–61 prove that the B3LYP method is appropriate for obtaining both reliable structures and potential energy surfaces. Firstly, B3LYP functional is very valid for estimating the H₂ storage property of Ti-acetylene/ethylene compounds.^59–61 Secondly, the B3LYP method employing a 6-31+G(d,p) basis set was used to study the hydrogen storage capacity of alkali metal ion decorated boric acid.⁶² Thirdly, the investigation of the stepwise adsorption energies of hydrogen on TiC₆H₆ showed the M06-2X functional was not preferred and the B3LYP functionals with 6-31+g(d,p) basis sets gave an impressive agreement with the accurate results.

3. Results and discussion

3.1 Optimized configurations of VC₆H₆(H₂)_n (n = 1–4)

Optimized configurations of VC₆H₆(H₂)_n (n = 1–4) and relative free energies at 298.15 K and 1 atm are presented in Fig. 1, 3–5, respectively. Thermodynamic data show that the configurations in the quartet state are lower in energy than the corresponding doublet state except for 1c. The most stable structure is the 1a(Q), which is 8.25 kcal mol⁻¹ lower in energy than the doublet state. 1a with the dissociated H₂ molecule is mentioned in ref. 31 1b with the CH₂ group is more stable than the 1c with molecular H₂. It indicates hydrogen dissociation, H migration, and even formation of the C–H bond are favorable thermodynamically. Chemisorption forming C–H or V–H bonds is usually stronger than physisorption forming V–H₂ unit. Then, it's easy to understand that structure 1a with V–H bonds and 1b with a C–H bond is more stable than structure 1c. The configurations of 1d, 1e, and 1f have two CH₂ groups. The original C₆H₆ has a little deformation and the longest V–C bond length increases from 2.32 Å to 2.94 Å due to the formation of the CH₂ groups. Obviously, the forming of the C–H bond causes a great deformation of the C₆H₆ unit. The preferred site of one H atom in VC₆H₆ is determined by comparing the two structures in Fig. S2.† The binding energy of H to the V site is 2.83 eV, which is larger than that of H to the C site (1.82 eV). This indicates that the H atoms prefer to bind at the on-top V site. That's maybe why 1a with the V–H bonds is more stable than 1b with a C–H bond.

Fig. 1 Optimized configurations of VC₆H₆–H₂ at the B3LYP/6-31+G(d,p) level and relative free energies at 298.15 K (in kcal mol⁻¹). D and Q represent the doublet state and quartet state, respectively. The red circle means adsorbed hydrogen.

The dissociation of the first H₂ was spontaneous on most of Sc/Ti/V decorated carbon nanostructures.^35–42 To understand the dissociation process, Fig. 2 shows the partial orbital density state (PDOS) of V and adsorbed H₂ in 1c (VC₆H₆(H₂)), and 1a (VC₆H₆(2H)). Effective intermolecular bonding leads to bonding orbits have lower energies. Two parts interact strongly when electrons filling in these bonding orbits. The three principles of effective bonding include matching symmetry, energy proximity, and maximum overlap between orbits. For 1c, the orbital in the energy of −13.00 eV mainly comes from the s orbits of H₂ and the other orbitals of VC₆H₆ are almost unaffected by the hydrogen molecule. The larger energy difference between the orbitals from V and the H₂ causes weak interaction. For 1a, the localized 3d orbits of V in VC₆H₆ mix with s orbits from hydrogen atoms easily in energies of −6.00–7.50 eV. So, VC₆H₆ has a strong interaction with the H atoms rather than a hydrogen molecule.

Fig. 2 The total DOS of (a) 1c(VC₆H₆(H₂)), (b) 1a(VC₆H₆(2H)) and the PDOS of V and H₂.

The structures in Fig. 3 include the configurations with one CH₂ group (2d), two CH₂ groups (2e, 2g, 2h), and three CH₂ groups (2a, 2f, 2i). The 2b structure contains an activated hydrogen molecule and two V–H bonds, which was mentioned in previous literature.⁴⁰ 2a and 2b structures have an energy difference of only 0.14 kcal mol⁻¹ at the B3LYP level.

Fig. 3 Optimized configurations of various isomers of VC₆H₆–2H₂ at the B3LYP/6-31+G(d,p) level and relative Gibbs free energies at 298.15 K (in kcal mol⁻¹). The red circle means adsorbed hydrogen.

This little energy difference indicates 2b inclines to form more stable 2a. For the structure shown in Fig. 3, the bond length of the V–H bond is 1.67–1.74 Å for isomers with one H atom but is 1.90–1.95 Å for isomers with H₂, which is longer than the former. This means that the single H atom has a stronger interaction with metal V. The distance of C–C neighboring CH₂ is lengthened to 1.50–1.56 Å. Besides, the V–C bond adjacent to three CH₂ groups in 2a is stretched from 2.28 Å to 2.91 Å, and causing the metal V atom is tilted to one side.

The optimized VC₆H₆(H₂)₃ are displayed in Fig. 4. Notably, the 3a with not CH₂ groups is the most stable doublet isomer due to its higher symmetry (C_3V). From the perspective of overlooking, it can be seen that the position of H₂ molecules corresponds to the C–C bond in the six-membered ring. There are two configurations with one CH₂ group (3e, 3f), six configurations with two CH₂ groups (3i, 3l, 3m, 3n, 3p, 3q), five configurations with three CH₂ groups (3d, 3g, 3j, 3o, 3r), and three configurations with four CH₂ groups (3b, 3h, 3k). Thus, the structures with the adjacent CH₂ groups are more stable.

Fig. 4 Various configurations of VC₆H₆–3H₂ at the B3LYP/6-31+G(d,p) level and relative Gibbs free energies at 298.15 K (in kcal mol⁻¹). The red circle means adsorbed hydrogen.

A complex containing dissociated H₂ molecules (with V–H bond) is always more stable than the corresponding complex with activated H₂ molecules. For example, 1a with the dissociated H₂ molecule is more stable than the 1c with molecular H₂; the 2b structure contains an activated hydrogen molecule and two V–H bonds is more stable than the 2c with two molecular H₂ and so on. However, the reverse appears in the VC₆H₆(H₂)₃ isomers. Firstly, calculations at different theoretical levels confirm our results. As shown in Table S2,† both the results using B3LYP/6-31G+(d,p), B3LYP/6-311G++(3df,3pd), B3LYP/aug-cc-pVTZ, wB97XD/6-311G++(3df,3pd) and wB97XD/6-311G++(3df,3pd) show that 3a with three molecular H₂ molecules is more stable than the 3c with the dissociated H₂ molecule. Secondly, detailed analyses of the symmetry and energy of deformation are carried out to comment on why this is the case. The symmetry of optimized VC₆H₆(D) is C_6V. As shown in Table S2,† the VC₆H₆ unit in structure 3a is C_6V symmetry while that in structure 3c is C₂ symmetry. That's mean, after adsorbing 3H₂, the VC₆H₆ unit in structure 3a is nearly no change. Therefore, the energy of deformation (ΔG_R) of VC₆H₆ and hydrogen binding energy between the VC₆H₆ unit and 3H₂ unit in 3a and 3c (ΔG_H) are defined.

ΔG_R = G(VC₆H₆ unit in 3a/3c) − G(VC₆H₆)

ΔG_H = [G(VC₆H₆ unit in 3a/3c) + G (3H₂ unit in 3a/3c) − G(3a/3c)]/3

The values of ΔG_R and ΔG_H are listed in Table S3.† The deformation energy of 3c is 0.28 eV, which is greater than that of 3a (0.23 eV). When deformation energy is not taken into account, the hydrogen binding energy between the VC₆H₆ unit in 3c and 2H₂–2H unit is 2.52 eV, which is greater than that between the VC₆H₆ unit in 3a and 3H₂(0.72 eV). This is consistent with the common understanding.

Similarly, Fig. 5 lists several optimized isomers of VC₆H₆–4H₂ complexes. Notably, the structure with four activated hydrogen molecules is very unstable. The most stable configuration 4a is composed of four adjacent CH₂ groups with an activated hydrogen molecule and two H atoms. Among many other configurations, 4c, 4d, and 4f have one CH₂ group are, 4e, 4i, 4k, 4m, and 4p have two CH₂ groups, 4b, 4g, 4h, 4n, 4o, and 4s have three CH₂ groups, 4a, 4l, and 4r have four CH₂ groups, 4j has five CH₂ groups, and 4q has six CH₂ groups. The energy difference between 4g and 4h is 3.05 kcal mol⁻¹, though both have three CH₂ groups and two activated hydrogen molecules. It indicates that the energy of structures also depends on the direction of the activated hydrogen molecule. 4q and 4j have six and five consecutive CH₂ groups, respectively, but their energy is not the lowest. This may be due to the steric hindrance effect formed by the consecutive CH₂ groups. For VC₆H₆–nH₂ (n = 1, 3), the most stable isomers have no CH₂ group. For VC₆H₆–nH₂ (n = 2,4), the most stable isomers have CH₂ groups, and in which CH₂ groups are adjacent. These prompt us to think strongly about whether the C–H bond could be formed easily.

Fig. 5 Optimized configurations of various isomers of VC₆H₆–4H₂ at the B3LYP/6-31+G(d,p) level and relative Gibbs free energies at 298.15 K (in kcal mol⁻¹). The red circle means adsorbed hydrogen.

3.2 The optimal chemisorption pathway of multiple H₂ molecules on the VC₆H₆

3.2.1 Chemisorption of the first H₂ molecule. As shown in Fig. 6, VC₆H₆ adsorb the first H₂ in molecular form firstly. The single H₂ dissociates into two H atoms via the TS 1c/1a. For the quartet state, the dissociation is exothermic by 13.22 kcal mol⁻¹, and its barrier is only 2.72 kcal mol⁻¹. For the doublet state, the dissociation is endothermic by 0.02 kcal mol⁻¹, and its barrier is 6.53 kcal mol⁻¹. It indicates that the H₂ dissociation in 1c(Q) is more favorable than that in 1c(D), which is also confirmed by the first-principles molecular-dynamics MD simulations up to 0.3 fs. The time evolution trajectories of H–H in VC₆H₆(H₂) at 300 K are presented in Fig. 7. After 0.04 fs, the H–H bond in 1c(Q) elongates from 0.824 Å to 2.621 Å (the length of the H–H bond in 1a(Q)). While H–H bond in 1c(D)is shortened firstly and then elongates from 0.869 Å to 2.876 Å (the length of H–H bond in 1a(D)) until 0.12 fs.

Fig. 6 The Gibbs free energy profiles of the first H₂ molecule adsorbed on VC₆H₆. The red and black lines represent doublet (D) and quartet (Q) states, respectively. The energy barriers are highlighted in red for the forward reaction and blue for the backward reaction.

Fig. 7 Time evolution trajectories of the H–H in VC₆H₆(H₂) at 300 K. The bond lengths are given in Å.

One of the dissociated H atoms in 1a(Q) will migrate to form CH₂ group with a barrier of 21.79 kcal mol⁻¹, which is endothermic by 2.91 kcal mol⁻¹ and slow. At 298.15 K, the overall conformation analysis shows that the 1a(Q) and 1b(Q) of VC₆H₆–H₂ are 99.3% and 0.70%, respectively. IR stability calculations ensure that the structures 1a(Q) and 1b(Q) are energy minima without imaginary frequency (see Fig. S4 of the ESI†). Two main H modes for 1a(Q) are symmetric and antisymmetric stretching vibrations, respectively corresponding frequencies of 1606.48 and 1645.80 cm⁻¹. One main H mode vibration frequency for 1b(S) is 1582.26 cm⁻¹. The three unique modes should be present in the Raman/IR spectra of a successfully synthesized material.

3.2.2 Chemisorption of the second H₂ molecule. The intermediate 1a(Q) is the precursor of the second H₂ molecule adsorption (Fig. 8). 2b(Q) dihydrogen complex is formed by the H₂ molecule adsorption on V atom in 1a(Q). H atom in 2b(Q) migrates to C atom through TS 2b/2d(Q) with a barrier of 14.42 kcal mol⁻¹. Another H atom on 2d(Q) continues to migrate to form the other CH₂ group in 2e(Q). The reaction barrier of 2e(Q) → 2a(Q) is 4.07 kcal mol⁻¹. The energy difference between 2a(Q) and 2b(Q) is 0.14 kcal mol⁻¹, which is very small. Similarly, conformations population analysis at 298.15 K shows that 2a(Q) and 2b(Q) account for 55.83% and 44.17%, respectively, which indicates they can coexist. The formations of 2g, 2h, and 2f are unfavorable due to they are endothermic.

Fig. 8 The Gibbs free energy profiles of the second H₂ molecule adsorption on the VC₆H₆ complex. The energy barriers are highlighted in red for the forward reaction and blue for the backward reaction.

3.2.3 Chemisorption of the third and the fourth H₂ molecules. There are a series of processes including hydrogen molecules adsorption, hydrogen molecules dissociate, and H atomic migration. It was observed in Fig. 9 that the process from 2b(Q) to 3b(Q) has energy barriers of 25.82 kcal mol⁻¹. There is another easier pathway from 2a(Q), in which the H₂ molecule can be absorbed on the V atom to form 3d(Q). Compared with 2b(Q) + H₂ → 3c(Q), 2a(Q) + H₂ → 3d(Q) is more favorable. The H₂ molecule in 3d(Q) can be dissociated. At the same time, one H atom of the H₂ molecule migrates with the barrier of 15.21 kcal mol⁻¹.

Fig. 9 The Gibbs free energy profiles of the third H₂ molecule adsorption on the VC₆H₆ complex. The energy barriers are highlighted in red for the forward reaction and blue for the backward reaction.

When the fourth H₂ molecule continues to approach the structure 3b(Q), the consecutive adsorption energies (ΔE_n-ZPE) is 2.18 kcal mol⁻¹ (0.09 eV). The 4a(Q) forms 4j(D) through a spin crossover. When 4j(D) is used as a reactant, it is unfavorable to generate 4q(D) (Fig. 10).

Fig. 10 The Gibbs free energy profiles of the fourth H₂ molecule adsorption on VC₆H₆. The energy barriers are highlighted in red for the forward reaction and blue for the backward reaction.

The optimal chemisorption pathways of H₂ molecules on VC₆H₆ are shown in Fig. 11. (More detailed information regarding optimized cartesian coordinates and computed sum of electronic and thermal free energies of mentioned structures see the ESI†). When the pressure of hydrogen increases, H₂ molecules adhering to VC₆H₆ can migrate continuously to form CH₂ groups, and finally VC₆H₁₁–3H (4j) is formed. Gibbs free energy calculations show that the whole reaction is exothermic by 2.83 kcal mol⁻¹ at 298.15 K. The generation of 4q(D) is endothermic by 11.14 kcal mol⁻¹, which is unfavorable in thermodynamics. The dissociation and migration of the second H₂ is the rate-determining step in the whole reaction with a barrier of 19.66 kcal mol⁻¹. In turn, the complex VC₆H₁₁–3H will dehydrogenate continuously until VC₆H₆ when the hydrogen pressure decreases. The energy barrier of the critical speed step (the migration of H atom in 3d(Q)) is 17.11 kcal mol⁻¹. Hence the hydrogen chemisorption adsorption and desorption on the VC₆H₆ complex could run smoothly with the hydrogen storage of 5.97 wt%, simply regulated by increasing/decreasing the hydrogen pressure.

Fig. 11 The optimal chemisorption and physisorption pathways of H₂ molecules on VC₆H₆ at 298.15 K and 0 K. The energy barriers are highlighted in red for the forward reaction and blue for the backward reaction. The red line corresponds to the physisorption structures.

As the discussion above, the chemisorptions pathway of H₂ molecules on VC₆H₆ at 298.15 K indicates that: (1) H₂ molecules attached to VC₆H₆ can be dissociated, and H atoms migrate continuously to form CH₂ groups. (2) Spin crossover mainly occurs in the pathway of adsorption of the first and fourth hydrogen molecules. (3) The optimal chemisorption pathway should be VC₆H₆(Q) → 1c(D) → 1a(Q) → 2b(Q) → 2d(Q) → 2e(Q) → 2a(Q)→ 3d(Q) → 3b(Q)→ 4a(Q) → 4j(D) (VC₆H₁₁–3H). (4) Gibbs free energy calculations show that the overall reaction to give the hydrogenation product 4j (VC₆H₁₁–3H) is exothermic by 2.83 kcal mol⁻¹ and has an energy barrier of 19.66 kcal mol⁻¹.

3.3 Physisorption of multiple H₂ molecules on the VC₆H₆

Fig. 12a shows the optimal physical adsorption path of multiple H₂ molecules on the VC₆H₆ complex. The free energy profile is shown in Fig. S5.† For n = 1, H₂ dissociates into two H atoms via the transition state TS. Though the single H₂ dissociation on VC₆H₆ is exothermic, the dissociation barrier is 6.34 kcal mol⁻¹. Moreover, 3a is more stable than 3c. So, the adsorption pathway along VC₆H₆ → 1c(D) → 2c(Q) → 3a(Q) pathway will be more favorable thermodynamically.

Fig. 12 (a) The consecutive adsorption energies ΔE_n (ΔG_n) of multiple H₂ molecules on the VC₆H₆ (in eV), (b) temperature dependence of ΔG_n at p = 1 atm.

When all the three hydrogen molecules are adsorbed in molecular form, the consecutive adsorption energies are 0.50, 0.56, 0.45 eV, respectively. And the average hydrogen adsorption energy for VC₆H₆(H₂)₃ is 0.50 eV, which is between physisorption and chemisorption (0.20–0.60 eV). As shown in Fig. 11, the physisorption of the three hydrogen molecules is exothermic by 13.49 kcal mol⁻¹ at 298.15 K, and need no energy barrier. The hydrogen storage capacity of VC₆H₆ is 4.48 wt%. Based on the van't Hoff equation: TD= (E_a/k_B)(ΔS/R − ln P)⁻¹,⁶³ the three H₂ can be adsorbed at any temperature under 421 K and 1 atm. Notably, spin multiplicity and the Gibbs free energy correction fully considered here. The temperatures at which ΔG = 0 eV/H₂ for 1c(Q), 2c(Q), 3a(D) are 480 K, 462 K, and 416 K, respectively (Fig. 12b). It also indicates that three H₂ molecules can be spontaneously adsorbed on VC₆H₆ forming 3a below 416 K. And three H₂ can be readily desorbed above 480 K under atmospheric pressure.

4. Conclusions

TM-decorated carbon composites grew up to be a new generation of hydrogen storage materials. Most of these researches reported that the dissociation of the first H₂ was spontaneous on most of Sc/Ti/V-decorated carbon nanostructures. As known that H migration easily occurs on metal sites. Then hydrogenation reaction would also occur during the hydrogen storage on 3d TM-decorated organic complexes. To further address this issue, the process of hydrogen adsorption on synthesized VC₆H₆ is focused on answering the question that whether hydrogen molecules are absorbed only or migrate to form C–H bonds.

Optimized configurations of VC₆H₆(H₂)_n (n = 1–4) and relative Gibbs free energies at 298.15 K and 1 atm were presented. For VC₆H₆–nH₂ (n = 1, 3), the most stable isomers have no CH₂ group. For VC₆H₆–nH₂ (n = 2,4), the most stable isomers have adjacent CH₂ groups. The chemisorptions pathway of H₂ molecules on VC₆H₆ at 298.15 K indicates that H₂ molecules attached to VC₆H₆ can be dissociated, and H atoms migrate continuously to form CH₂ groups. Gibbs free energy calculations show that the overall reaction giving the hydrogenation product 4j (D) (VC₆H₁₁–3H) is exothermic by 2.83 kcal mol⁻¹ and has an energy barrier of 19.66 kcal mol⁻¹. Hence the hydrogen chemisorption adsorption and desorption on the VC₆H₆ complex could run smoothly with the hydrogen storage of 5.97 wt%, simply regulated by increasing/decreasing the hydrogen pressure. The physisorption along VC₆H₆ → 1c(D) → 2c(Q) → 3a(Q) will be exothermic by 13.49 kcal mol⁻¹. The three H₂ can be adsorbed at any temperature under 416 K and readily desorbed above 480 K at 1 atm. The corresponding hydrogen storage capacity is 4.48 wt%. In summary, both physisorption and chemisorption tend to occur in certain circumstances.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (21805176), the 1331 Engineering, and Education Reform Project (J2019098) and Youth Science and Technology Research Foundation (201901D211394) of Shanxi Province of China, the Doctor Fund (0505/02070359) of Shanxi Normal University.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra06057g

‡ These authors contributed equally to this work and should be considered co-first authors.

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