Empowering hydrogen storage properties of haeckelite monolayers via metal atom functionalization

Using hydrogen as an energy carrier requires new technological solutions for its onboard storage. The exploration of two-dimensional (2D) materials for hydrogen storage technologies has been motivated by their open structures, which facilitates fast hydrogen kinetics. Herein, the hydrogen storage properties of lightweight metal functionalized r57 haeckelite sheets are studied using density functional theory (DFT) calculations. H2 molecules are adsorbed on pristine r57 via physisorption. The hydrogen storage capacity of r57 is improved by decorating it with alkali and alkaline-earth metals. In addition, the in-plane substitution of r57 carbons with boron atoms (B@r57) both prevents the clustering of metals on the surface of 2D material and increases the hydrogen storage capacity by improving the adsorption thermodynamics of hydrogen molecules. Among the studied compounds, B@r57-Li4, with its 10.0 wt% H2 content and 0.16 eV/H2 hydrogen binding energy, is a promising candidate for hydrogen storage applications. A further investigation, as based on the calculated electron localization functions, atomic charges, and electronic density of states, confirm the electrostatic nature of interactions between the H2 molecules and the protruding metal atoms on 2D haeckelite sheets. All in all, this work contributes to a better understanding of pure carbon and B-doped haeckelites for hydrogen storage.


Introduction
The mounting demands of energy due to increase in population and urbanization have put significant stress on conventional energy sources. Additionally, an increasing use of the fossil fuel-based energy sources has a devastating impact on the environment [1]. This situation calls for clean, renewable, and economically viable energy alternatives that would replace fossil fuels. Hydrogen stands out as a highly promising option due to its high energy density by mass, moreover its abundance, clean and renewable production [2,3]. However, the efficient storage of hydrogen molecules (H 2 ) is a major bottleneck for the practical use of this, otherwise ideal energy carrier. Conventional H 2 storage methods, such as the pressurized gas and liquefaction, are associated with safety concerns and large energy consumption, respectively [4,5]. Hydrogen can be stored in the lattice or at the surface of host storage materials [6][7][8][9][10][11]. However, it's an ongoing challenge to find good materials that are capable of storing practically meaningful volumetric and gravimetric amounts of hydrogens and releasing them on demand.
Among the various available options, carbonous materials possess a great potential for H 2 storage applications due to their salient features like stability, cost-effectiveness, and porosity. H 2 storage capacities of the host carbonous materials are further enhanced by increasing their surface areas such as via nanostructuring [12]. However, a downside of carbonous nanostructures is their weak, van der Waals type interactions with the incident H 2 molecules, which allows for molecule storage only at very low temperatures [13][14][15]. For ambient condition storage applications, the binding energies of H 2 to the host material should be close to 0.16 eV/H 2 [16,17]. To enhance the interactions between H 2 and the host carbonous nanostructures, among the different strategies, the introduction of dopant atoms has been applied with promise [18][19][20][21][22].
In literature, several studies have been devoted to the study of H 2 storage properties of the metalized carbonous nanostructures, particularly the 2D monolayers [23][24][25][26]. A recent study explored the potential of metal-doped nitrogenated holey graphene (C 2 N) as H 2 storage material [27]. The authors employed dispersion-corrected DFT simulations to study the adsorption of H 2 molecules on C 2 N in its pristine and metal-decorated (e.g. Mg, Ca, Ti, V, Mn, Fe, Co, Ni, and Zn) forms. It was found that the pristine C 2 N's weak hydrogen binding energy (0.10 eV/H 2 ) is enhanced significantly after its decoration with metals. In another study, Chen et al. employed first-principles DFT calculations for the study of lithium functionalized graphitic carbon nitride (g-CN) monolayers for H 2 storage [16]. They found that the Li atoms are strongly bonded to g-CN sheets without being clustered, therefore facilitating a rather uniform distribution of metal cations over the host material. Each Li + cation interacted with multiple H 2 molecules and that resulted in a H 2 storage capacity of 10.8 wt% Hydrogen, which is larger than is possible for many other 2D systems, such as phosphorene and MoS 2 . Similarly, Faye et al. has recently reported the H 2 storage properties of 2D carbon nitride, C 3 N, sheets through spin-polarized DFT simulations [28]. The structural and H 2 adsorption properties of Si-and Ti-doped C 3 N nanosheets were studied in the context of ambient condition H 2 storage. They found that the metal-doped C 3 N nanosheets were able to reach a high H 2 storage capacity of 9.0 wt% Hydrogen. In addition to the above-mentioned theoretical reports, several experimental groups studied the potential of use different nanomaterials for H 2 storage applications. In this regard, porous carbon-based structures [29,30], multilayered graphene [31] and Ti 2 CT x [32] have recently been explored.
Motivated by the promise of peculiar carbonous nanostructures as discussed in the above studies, we employed DFT calculations to study the structural features and H 2 storage properties of lightweight metal functionalized haeckelites (r 57 ). We found that, the graphene-like open structure, but with 5-and 7-membered rings of carbon atoms, of the haeckelites enable strong interactions with metal adatoms, and they consequently attain good H 2 storage properties.

Computational methods
All DFT calculations were carried out using the generalized gradient approximation (GGA) exchange-correlation functional of Perdew-Burke-Ernzerhof (PBE) [33] and the projector augmented wave (PAW) [34,35] method, as implemented in the Vienna ab initio simulation package (VASP) [36][37][38]. A plane wave basis with a kinetic energy cutoff of 600 eV was used. The H 1 s, B 2s2p, C 2s2p, Li 1s2s, Na 3s2p, K 3s3p4s, Ca 3s3p4s, Sc 3p4s3d and Ti 3p4s3d electrons were considered as valence. Spin-polarized calculations were performed within the framework of DFT and no charge or dipole correction procedures were applied [39]. The DFT-D3 scheme [40,41] was used to account for the dispersion interactions, which provides accurate results for molecule storage systems [42][43][44][45].
The original structural parameters of r 57 were obtained from literature [46] and the structure was further optimized with the above settings and a vacuum spacing of 20 Å to avoid interactions between periodic images. Using the Г-centred Monkhorst-Pack scheme [47] with a 7 × 9 × 1 k-mesh for the unit cell, the geometries were fully optimized until the total forces acting on each atom were smaller than 0.01 eV/Å. The isolated H 2 molecule was calculated by using a 20 Å edge cubic box with periodicity.
We calculated the binding energy of metal atoms to the host sheet, as follows where E M is the total energy of one metal atom in its respective metal crystal, E Host and E Host− Mn are the total energies of the host simulation cells prior and posterior to metal decoration, respectively. The average adsorption energy (E avg ) and the consecutive adsorption energy (E con ) of H 2 molecules to the host materials were defined as where E H2 is the total energy of a H 2 molecule in gas phase, E Host− H 2(n− 1) and E Host− H2n are the total energies of the host sheets with (n− 1) and n H 2 molecules, respectively.

Results and discussions
The optimized structure of the r 57 monolayer is shown in Fig. 1(a). The optimized lattice constants of the unit cell are a = 7.47 and b = 5.86 Å, with the C-C bond lengths altering between 1.39 and 1.49 Å. These parameters agree well with the literature [46].
To investigate the interaction of H 2 with the r 57 sheet, four different kinds of adsorption sites were considered: top of C atoms (C T ), top of C-C bonds (C B ), top of 5-atom ring centres (F T ), and top of 7-atom ring centres (S T ). The lowest energy configuration is found to be when the H 2 molecules are positioned at S T sites, with E H2 b = 0.07 eV, which indicates a weak interaction between the 2D material and H 2 molecules. For efficient hydrogen storage, the binding interactions of hydrogen molecules on pure r 57 sheets would have to be improved, such as through the incorporation of lightweight metal atoms to the host material.
Similar to the procedure for hydrogen molecules interacting with the 2D material, for the metal atoms, we also considered different adsorption sites on the r 57 sheet. For all metals, the lowest energy adsorption site is predicted to be the S T site and the calculated binding energies of the metal atoms on r 57 are shown in Table 1. The E M b for Li, Na, and K is positive, meaning that these alkali metals adsorb stably on the r 57 sheet, whereas Ca decoration is prone to metal clustering as evident from the negative E M b . Next, we focus on the most promising alkali metal loadings of r 57 -Li 1 , r 57 -Na 1 , and r 57 -K 1 as host materials for H 2 molecules. The optimized structures prior and posterior to full hydrogen loading are shown in Fig. 2. We found that each Li, Na, and K on r 57 interact with three H 2 molecules with E H2− avg b of 0.18, 0.19, and 0.18 eV/H 2 , respectively. On r 57 -Li 1 , a fourth H 2 molecule is accommodated with a moderate E con of 0.13 eV/H 2 . However, as shown in Fig. 2(a), it is positioned relatively further away from the Li atom. Similarly, the fourth H 2 molecule binds with E con of 0.16 and 0.12 eV/H 2 on r 57 -Na 1 and r 57 -K 1 , respectively. The fifth H 2 molecule adsorbs onto the metal atoms of r 57 -Na 1 (Fig. 2(b)) and r 57 -K 1 (Fig. 2(c)), but only via weak interactions of 0.08 eV/H 2 and 0.06 eV/H 2 , respectively. For all these considered cases of alkali metal modified matrix, the maximum effective hydrogen storage capacity is 3.6 wt% H 2 (for r 57 -Na 1 H 8 ), which is lower than the 5.5 wt% storage target as set by the U. S. Department of Energy (DOE) [48].
To enhance the hydrogen storage capacity of r 57 sheets, an increased amount of dispersed metal ions is required on their surface. Earlier theoretical studies show that incorporating B atoms into graphene provides a way for immobilizing metal atoms on its surface [49]. Additionally, taking into account that B-doped graphene monolayers are experimentally realized [50], we also study here the B doping of r 57 . All the three unique C atoms of r 57 unit cell, as illustrated in Fig. 1(a), were considered in turn for the atomic substitutions with B. The most stable configuration, B@r 57 , is reached when a B atom substitutes C 1 atom, as shown in Fig. 1(b). Next, we studied the adsorption of a H 2 molecule on B@r 57 , and found that the molecule tends to reside at S T site with a binding energy of 0.07 eV/H 2 , which is both positionally and energetically very similar to the hydrogen molecule on the pure r 57 sheet.
The calculated adsorption energies of different metal atoms on B@r 57 are shown in Table 1. According to these results, when compared with r 57 , the B@r 57 has stronger interactions with the metal atoms. Interestingly, all metal atoms at any of the considered loading ratios in the current study, have positive binding energies on B@r 57 . Furthermore, according to Bader charge analysis results of the B@r 57 -M n compounds (M = Li, Na, K, and Ca; n = 1, 4, and 8), shown in Table 2, all metal atoms on B@r 57 monolayers were depleted. However, with an increase in the number of adsorbed metal atoms in the simulation cell, the average electrical charge of metal atoms decreased. Among the metals studied here, the change of charge depletion was lowest for Li, meaning that, Li atoms were electrically the least affected by an increase in metal population on B@r 57 monolayers.
Next, we discuss the hydrogen storage performances of the Mdecorated B@r 57 sheets.   (1) Li decoration: For one-, four-, and eight-Li atom decorations, the most stable geometries of the compounds are shown in Fig. 3(a)-(c), with the corresponding E Li b = 0.86, 0.20, and 0.02 eV/Li, respectively. Considering both E Li b and sterical suitability for molecular hydrogen interactions, the four-Li atom decorated B@r 57 compound, B@r 57 -Li 4 , provides a good balance of metal loading for hydrogen storage purposes. To further illustrate the stability of B@r 57 -Li 4 , we carried out ab initio molecular dynamics (AIMD) calculations [51] on the corresponding 2 × 2 × 1 supercell. Fig. 4 shows the structures at the end of 10 ps AIMD calculations that were performed at four different temperatures of 200, 300, 400, and 500 K. Although the Li atoms became more mobile with an increase in temperature, they still were attached to the 2D material even at elevated temperatures. Moreover, we studied the cases when each Li attracts one, two, and three H 2 molecules, and found that B@r 57 -Li 4 efficiently adsorbed a total The metal ions of the B@r 57 -M 1 compounds interact with only three to five H 2 molecules, whereas for the B@r 57 -M 8 compounds, the distances between neighbouring metal atoms are comparable to the respective M-M distances found in their bulk metal crystal structures. Additionally, for the latter compounds, the calculated absolute Bader charge values of metal ions were small. Thus, due to steric and electronic effects, these compounds are not the most interesting compositions for hydrogen storage. Based on these findings, the B@r 57 -Li 4 compound is the most promising candidate for molecular hydrogen storage. Therefore, to provide a versatile insight into the nature of interactions between H 2 molecules and B@r 57 -Li 4 , we further studied their electronic properties. Fig. 5 shows the optimized geometry of the fully hydrogen loaded B@r 57 -Li 4 H 24 compound and its corresponding electron localization function (ELF), both as calculated using DFT. Clearly, all Li atoms were exposed on the B@r 57 monolayer and they were electrically depleted. Moreover, Li atoms had no apparent orbital interactions with either of the B@r 57 monolayer or the H 2 molecules that were positioned around them. The localized electron clouds surrounding the H 2 molecules showed no evidence of orbital interactions with the atoms of the host material. The electronic density of states (DOS) calculations were also used to investigate the B@r 57 -Li 4 compounds. As shown in Fig. 6(a) DOS plot of the pure B@r 57 monolayer, the bonding contributions were mainly from the p orbitals of C and B atoms. When Li dopants were added onto the monolayer, their valance s electrons were transferred to the host material and no strong orbital interactions were evident between Li and monolayer C or B atoms ( Fig. 6(b)). Instead, the charge transfer from Li atoms to the 2D material results in an increased density for the occupied states of C and B atoms, which indicates ionic bonding between the metal and nonmetal atoms of B@r 57 -Li 4 . Fig. 6(c) shows the DOS for the fully hydrogenated B@r 57 -Li 4 compound. The adsorbed H 2 molecules on the monolayer populate around − 9 eV, and they showed no real influence on the valance states of C, B, and Li atoms. The calculated DOS data is consistent with the above discussed ELF and atomic charge analysis results.

Conclusions
In summary, the adsorption of H 2 molecules on lightweight metal atom decorated haeckelites was studied by first-principles DFT calculations. We found that H 2 molecules interact weakly with pristine r 57 and B-doped B@r 57 haeckelites. With the introduction of alkali and alkaline earth metals, the binding energies of hydrogen molecules were improved. When compared with pure r 57 , the B@r 57 haeckelites were more useful in immobilizing the metal atoms, and hence more successful in reaching to high hydrogen storage capacities. Of the metal decorated B@r 57 systems investigated here, the B@r 57 -Li 4 compound is the most promising candidate for practical usage, as it yielded the highest hydrogen storage capacity of 10.0 wt% H 2 at a hydrogen binding energy of 0.16 eV/H 2 . A further analysis of the electronic structures revealed that the interactions between the protruding Li atoms of the B@r 57 -Li 4 compound and the H 2 molecules were mainly electrostatic by nature.

Declaration of Competing 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.