DFT investigation of efficient hydrogen storage utilizing Li and Na decorated co-doped graphene (B/N)

Abstract

This study investigates the hydrogen storage capacity of co-doped graphene with non-bonded B and N atoms (BC₄N) using density functional theory (DFT). The optimized structure reveals the introduction of co-doping ripples the surface, enhancing potential hydrogen storage applications. The adsorption behavior of Li and Na atoms on the BC₄N surface is examined, demonstrating a higher binding energy, surpassing their cohesive energies. Density of State (DOS), Partial Density of State (PDOS), and charge transfer analyses indicate electron donation from Li and Na to BC₄N monolayer, establishing BC₄N as an electron acceptor. The investigation extends to H₂ adsorption on Li/BC₄N and Na/BC₄N systems, revealing a non-dissociative form and a cooperative effect with increasing H₂ molecules. The hydrogen storage gravimetric density is calculated, and desorption temperatures are determined, highlighting the potential of Li/BC₄N and Na/BC₄N as promising candidates for efficient hydrogen storage.

Introduction

The focus on hydrogen as an ideal energy resource has grown due to its favorable characteristics, including high energy density, renewability, and friendly to the environment. Its potential to replace fossil fuels has led to a significant emphasis on developing a stable and cost-effective storage system^{1, 2, 3, 4, 5–6}. The US Department of Energy has a target for hydrogen storage capacity of 5.5 wt% of weight density⁷, emphasizing the importance of achieving optimal binding energy for effective hydrogen recycling at near-ambient conditions^8,9. Various carbon nanostructures, such as carbon nanotubes, and graphene have been investigated for their hydrogen adsorption capabilities, driven by their reversibility, fast kinetics, and high capacities^{10, 11, 12, 13, 14–15}. The interest in the processes of adsorption and desorption with carbon-based materials from the intrinsic advantageous properties these materials possess. These include low density, high chemical stability, and the capacity to manipulate pore structures and surface areas, rendering them compelling options for hydrogen storage technologies¹⁶. Among carbon-based materials, the focus of research has notably turned towards graphene-based carbon materials. This shift is primarily driven by the extraordinary features exhibited by graphene, such as an exceptionally high specific surface area, mechanical flexibility, robustness, and a lightweight composition. These attributes position graphene as a promising candidate for hydrogen storage devices, emphasizing its potential for practical applications¹⁷.

Furthermore, graphene an exceptional two-dimensional carbon material known for its distinctive properties has become a focal point of research interest due to recent advancements in its large-scale production¹⁸. Apart from its prevalent applications in electronics, graphene plays a pivotal role in sensor production and serves as a molecular adsorbent. While previous studies extensively explored graphene’s efficacy in adsorbing various small molecules, its potential as hydrogen (H₂) adsorbent is limited, and hydrogen passivation may even compromise the mechanical properties of graphene¹⁹. To address these challenges, sophisticated techniques are necessary for effective hydrogen uptake. Some studies have opted for innovative approaches, such as utilizing curved graphene or graphene hollows to enhance interactions with H₂/adsorbent²⁰. On the other hand, alternative strategies involve employing planar graphene sheets with doped heteroatoms. Transition metals such as titanium (Ti)²¹, iron (Fe)²², nickle (Ni)²³, palladium (Pd)²⁴, and platinum (Pt)²⁵ can be useful for this purpose.

Ao et al. explored Al-doped porous graphene by DFT study. Their investigations demonstrated the efficient adsorption of H₂ molecules by such structures with adsorption energy of − 0.41 eV¹⁵. Huo et al. employed theoretical methods to investigate Ti-decorated boron-doped porous graphene in adsorbing H₂ molecules²⁶. They investigated that boron-doped porous graphene decorated with titanium atoms can consistently capture sixteen hydrogen molecules, achieving a gravimetric hydrogen uptake of 8.58 wt%.

Researchers conducted both experimental and theoretical investigations on graphene to enhance hydrogen storage capacity. The studies revealed that modifying the electronic properties of dispersed carbon-based materials through doping with nonmetallic elements (such as B and N) or intentionally creating vacancies could be a promising strategy. This approach has been shown to enhance the adsorption performance of hydrogen according to various works^27,28. Yang et al.²⁹ demonstrated that, under conditions of 298 K and 10 Mpa, the hydrogen storage capacity increased to 1.2 wt% through hydrogen spillover on ruthenium-decorated boron-doped microporous carbon. In the study conducted by Wu and colleagues³⁰, they observed that B-doped graphene has a superior ability to adsorb hydrogen compared to pristine graphene. This increased adsorption capability is attributed to the presence of low activation barriers, particularly under ambient conditions. Furthermore, Lee et al.³¹ conducted research on the utilization of Li-decorated graphene for hydrogen storage. In this study, they introduced nitrogen defects that are experimentally feasible to enhance the overall performance of the hydrogen storage system.

This study introduces an approach by suggesting a unique arrangement of graphene sheets that co-doped with boron and nitrogen and featuring Li, and Na atoms to enhance hydrogen storage. The B, and N atoms co-doped graphene are non-bonded that be more efficient catalyst when compared to bonded B-N co-doped graphene^32,33.To assess the influence of this co-doped structure on hydrogen adsorption, the study utilizes first-principle analyses based on density functional theory (DFT).

Results and discussion

Structural properties of co-doped graphene (B and N atom), decorated by li, and Na atom

To explore the hydrogen storage capacity of co-doped graphene with B, and N atom that is non-bonded, the optimized geometry of this system (BC₄N) is shown in Fig. 1, and the corresponding data are compiled in Table 1. A vibrational frequency calculation was also performed on the optimized BC4N sheet (B3LYP/6-31G(d, p)); no imaginary frequencies were found, confirming that the structure shown in Fig. 1 corresponds to a true local minimum. As seen in Table 1, the bond lengths between B-C, C-C, and C-N are 1.50 Å, 1.43 Å, and 1.41 Å respectively. The structure of pristine graphene is flat and by co-doped with B, and N atom that are non-bonded, the presence of ripples appears that is may be effective in hydrogen storage application. Initially, the study of binding of single atom decorated the surface such as Li, and Na atoms was determined. As seen in Fig. 2, the optimized Li, and Na atom on the BC₄N surface are prefer to be adsorbed on hollow center of the hexagon and Cartesian coordinates for the Li/BC₄N and Na/BC₄N are shown in Table S1 and S2. This corresponds well with the preferred site for Li atom adsorption on both pure graphene and porous graphene^2,34,35. In the optimized structures, the distance between Li/Na and nearest carbon atom is 2.17/2.53 Å, respectively as presented in Table 1. The binding energies for Li and Na atom over the surface were found to be −2.51 eV, and − 1.95 eV respectively that is higher than their cohesive energies^36,37. The results show that co-doped graphene with B, and N atom has the capacity to significantly enhance the binding energy of Li, and Na atoms, exceeding the cohesive energy of Li and Na. This intentional effect results in the suppression of Li, and Na adatom clustering on BC₄N system. Therefore, co-doped graphene with B, and N atom demonstrates significant potential for hydrogen storage due to its characteristic of maintaining geometric stability.

Fig. 1 [Images not available. See PDF.]

The optimized structure of B, and N co-doped graphene; top- (up) and side- (down) view.

Table 1. Equilibrium distance (d, Å), binding energies of li, and Na decorated BC4N monolayer and the charge.

System	d (Å)	Eb(eV)	QNBO(e)
BC4N	1.50 (B-C) 1.43 (C-C) 1.41 (N-C)
Li/BC4N	2.17 (Li-C)	−2.51	0.90 (Li)
Na/BC4N	2.53 (Na-C)	−1.95	0.95 (Na)

The interaction of the adsorbed Li, and Na atom on the BC₄N system were also studied by calculating the Density of State (DOS), Partial Density of State (PDOS), and charge transfer that obtained from natural bond orbital (NBO). The analysis reveals an electronic charge transfer from the Li, and Na adatom to the substrate, as illustrated in Table 1. Essentially, the adsorbent functions as an electron acceptor in relation to the Li, and Na adatom. Based on these results, it can be inferred that BC₄N systems exhibit a higher binding energy for Li, and Na adatoms on the surface. Despite the fact that the charge transfer from Na to BC₄N surface is greater than that from Li, the binding energy of Li on BC4N is greater. This seemingly strange finding can be explained by the fact that both Li and Na are electrostatically attracted to BC₄N π-electrons. Li atom experiences stronger electrostatic attraction than Na atom due to its smaller size and higher nuclear charge, and the smaller size of Li allows its orbitals to overlap more efficiently with BC4N π-orbitals, developing stronger covalent bonding, whereas Na atom’s larger size makes its orbital overlap with BC4N less optimal, limiting the covalent contribution to its binding. By analyzing the density of states (DOS) and projected density of states (PDOS) as seen in Fig. 3, The observation that peaks in the density of states (DOS) increase after decorating BC4N with Li, and Na atom. When Li and Na atom are deposited on BC4N surface, they interact with its π-electron system and this interaction can be understand by PDOS. The Fig. 3, when Li atom sit on hollow site, its 2s-orbital of Li atom directly overlap with the 2p orbitals of the surrounding C, B, and N atom in the BC4N surface at energies − 1.64 eV, 1.39 eV, and 3.25 eV. Also, Na decorated BC4N surface show overlap between 3s-orbital of Na atom with 2p orbitals of the C, B, nad N atom in the BC4N surface at energies 0.55 eV, at −2.24 eV and 1.99 eV there is overlap between 3s-orbital of Na atom with 2p-orbitals of N and C atom of the BC4N surface.

Fig. 2 [Images not available. See PDF.]

The optimized structure of Li “up”, and Na “lower” decorated BC₄N monolayer.

Hydrogen storage properties

The optimized structures of H₂ adsorbed on Li/BC₄N and Na/BC₄N systems are illustrated as seen Figs. 4 and 5. The Cartesian coordinates for H₂ adsorbed on the Li/BC₄N and Na/BC₄N are shown in Table S1 and S2. The PDOS of H₂ molecules on Li/BC₄N and Na/BC₄N are seen in Figs 6 and 7. During the optimization of the first molecule of H₂ on Li/BC₄N and Na/BC₄N systems, the H₂ adsorbed on Li, and Na with tilted orientation on a lithium and sodium atom and This initial configuration establishes a specific binding geometry. By analyzing the results that collected in Tables 2 and 3, we can find out that the adsorption energy of −0.12 eV, and, the distance of d_Li−H is 2.09 Å in H₂/Li/BC₄N, and the distance of d_Na−H is 2.49 Å in H₂/Na/BC₄N. For each configuration the H-H bond lengths of H₂ molecules are 0.75 Å, which are consistent with the calculated free H₂ molecule (0.750 Å), indicating that the adsorbed H₂ molecule is in the non-dissociative form. To further validate the physisorptive nature and reliability of our H₂ adsorption data, we re-examined the H-H bond length before and after adsorption. In our calculations (GGA-PBE + D3), the free H₂ bond length is 0.750 Å, and upon adsorption it remains 0.750 Å. This negligible change is fully consistent with the findings of Dange et al.³⁸, who report that charge polarization driven H₂ physisorption on NLi₄ decorated boron phosphide biphenylene induces an H-H elongation of only ≈ 0.003 Å. Therefore, the unchanged H-H distance in our system confirms that we are describing a true physisorption process with no spurious chemisorption artifacts. The adsorption of another hydrogen molecule on the opposite side of the Li and Na decorated BC₄N system. The adsorption energy increases to −0.27 eV for Li/BC₄N and − 0.19 eV for Na/BC₄N surface, suggesting a stronger interaction. The charge on Li is 0.85e, on Na is 0.93e and the charges of H₂ on Li and Na are 0e,0.04e, 0.04e,−0.03e respectively. This indicates potential charge redistribution within the system, impacting bonding and stability. The high dipole moment (19.86 Debye and 19.60 Debye) for the first adsorbed H₂ molecule signifies significant polarization, implying the H₂ molecule is distorted upon interaction with the Li and Na atom. The rippling of the BC₄N surface evident in Figs. 4 and 5 arises directly from the physisorption of H₂, the weak van der Waals interaction and slight charge polarization at the adsorption site pull the nearest B and N atoms out of the plane, producing the observed distortion. To ensure that these distorted geometries are true minima, we have performed full vibrational frequency calculations on each H₂ adsorbed configuration with no imaginary modes, confirming that the rippled structures are stable adsorption complexes rather than transition state artifacts .

With an increasing number of hydrogen molecules, a noteworthy trend is observed. The adsorption energy continues to increase that the two, Three, and four H₂ molecules on Li/BC₄N surface are − 0.19 eV, −0.25 eV, and − 0.27 eV respectively. Binding strength increases with the number of adsorbed H₂ molecules, reaching a maximum with four molecules (−0.27 eV). This suggests cooperative effects enhance binding as more H₂ are present. As shown in Table 2, the distance between Li decorated BC₄N surface are 2.17Å, 2.18 Å for the two H₂ molecules, 2.24Å, 2.30Å, 2.26Å for the three H₂ molecules on Li/BC4N surface, but when the four H₂ molecules we found that one H₂ is far away from the Li decorated BC₄N surface, and the charges obtained from NBO of Li atom is decreased by increasing H₂ molecules adsorbed as seen in Table 2 implying a cumulative effect of hydrogen adsorption. Simultaneously, the charge on lithium decreases. This suggests a dynamic charge transfer during the adsorption process. Li-H distances and charge transfer to H₂ molecules slightly increase with more H₂ adsorption. This indicates stronger electrostatic interactions between Li and H₂ molecules. As shown in Fig. 8, regions of electron accumulation (yellow) appear primarily around the Li and Na sites and the nearest H₂ molecules, while corresponding depletion (cyan) is observed on adjacent B and N atoms. This polarization pattern confirms that H₂ adsorption is driven by charge–induced dipole interactions at the metal centers, reinforcing the physisorptive mechanism without covalent bond formation. The increasing adsorption energy with multiple H₂ molecules and efficient utilization of Li sites are encouraging characteristics. As seen in Table 3, we observed in Na/BC₄N surface that the recorded adsorption energies of two, three, and four H₂ molecules are − 0.19 eV, −0.25 eV, and − 0.23 eV respectively. Also as seen in Table 3, the distance between Na-H are 2.52Å, 2.50Å for two H₂ molecules, 2.55Å, 2.56Å, 2.52Å, and one H₂ molecules are far away when adsorbing four H₂ molecules. The distances of H-H bond are in range 0.74Å−0.75Å. To account for dispersion interaction, DFT-D3 method, the adsorption energy of hydrogen molecules on Li and Na decorated BC₄N surface as listed in Tables 2 and 3 are lower when using the Grimme D3 dispersion correction. D3 adds an attractive dispersion term to the potential energy surface, accounting for the weak interaction between hydrogen molecules with the Li and Na decorated BC₄N surface. This stronger attractive interaction leads to a lower (more negative) adsorption energy, indicating a more stable binding.

Table 2. Structural and energetic properties for the hydrogen molecule adsorbed on Li/BC4N on one and two sided. The smaller Li-H distance (d_Li−H), the bond length of H-H, charge transfer (Q), dipole moment (µ).

System	dLi−H(Å)	dH−H(Å)	Eads(eV)	QLi(e)	QH(e)	µ (Debye)
1H2$Li/BC4N	2.09	0.75	−0.12 (−0.21)	0.82	0.03, 0.01	19.86
2H2$Li/BC4N	2.18, 2.17	0.75	−0.19 (−0.36)	0.74	0.02, 0.03, 0.04, 0.01	12.87
3H2$Li/BC4N	2.24, 2.30, 2.26	0.75	−0.25 (−0.48)	0.66	0.04, 0.01, 0.01, 0.04, 0.06, −0.00	12.91
4H2$Li/BC4N	6.04, 2.24, 2.31, 2.26	0.74, 0.75	−0.27 (−0.59)	0.66	0.04, 0.01, 0.01, 0.04, 0.06, −0.00, 0.01, −0.01	13.57
2H2$Li2/BC4N	2.10, 2.10	0.75	−0.27	0.85, 0.85	0.04, 0.00, 0.04, 0.00	8.00
4H2$Li2/BC4N	2.18, 2.15, 2.18, 2.15	0.75	−0.45	0.77, 0.77	0.01, 0.04, 0.05, 0.00, 0.01, 0.04, 0.04, 0.00	8.29
6H2$Li2/BC4N	2.25, 2.24, 2.22, 2.23, 2.21, 2.28	0.75	−0.59	0.68, 0.68	0.05, 0.00, 0.01, 0.04, 0.05, 0.01, 0.01, 0.04, 0.05, 0.01, 0.00, 0.05	8.12
8H2$Li2/BC4N	6.53, 2.25, 2.24, 2.22, 4.60, 2.22, 2.20, 2.28	0.74, 0.75	−0.61	0.68, 0.68	0.05, 0.00, 0.01, 0.04, 0.05, 0.01, 0.01, 0.04, 0.05, 0.01, 0.00, 0.05, 0.01, −0.00, 0.01, −0.02	8.28

Table 3. Structural and energetic properties for the hydrogen molecule adsorbed on Na/BC₄N on one and two sided. The smaller Na-H distance (d_Na−H), the bond length of H-H, charge transfer (Q), dipole moment (µ).

System	dNa−H(Å)	dH−H(Å)	Eads(eV)	QNa(e)	QH(e)	µ (Debye)
1H2$Na/BC4N	2.49	0.75	−0.12 (−0.14)	0.92	0.05,−0.03	19.60
2H2$Na/BC4N	2.52,2.50	0.75	−0.19 (−0.33)	0.87	−0.01, 0.03, 0.05, −0.03	19.06
3H2$Na/BC4N	2.55,2.56,2.52	0.75	−0.25 (−0.41)	0.81	0.04,−0.01,0.00, 0.03,0.05,−0.02	12.90
4H2$Na/BC4N	2.53,2.53,2.52,6.18	0.74, 0.75	−0.23 (−0.53)	0.81	0.04,−0.01, 0.00, 0.03,0.05, −0.02, 0.01, −0.01	19.29
2H2$Na2/BC4N	2.48,2.52	0.75	−0.19	0.93, 0.93	0.04,−0.03, 0.04,−0.03	7.20
4H2$Na2/BC4N	2.52,2.49,2.50,2.53	0.75	−0.35	0.89, 0.89	−0.01,0.03,0.04, −0.02, −0.01,0.03, 0.04,−0.02	7.41
6H2$Na2/BC4N	2.54,2.54,2.54, 2.52,2.55,2.54	0.75	−0.52	0.83, 0.83	0.04,−0.02,−0.01, 0.04,0.04,−0.02, −0.01,0.03,0.04, −0.02, −0.02, 0.05	7.25
8H2$Na2/BC4N	2.54,2.54,2.54,6.39, 2.57,2.59,2.55,2.85	0.74, 0.75	−0.56	0.83, 0.78	0.04,−0.02,−0.01, 0.04,0.04,−0.02, −0.01, 0.03,0.05, −0.02,−0.02,0.05, 0.01,0.01,0.02, −0.02	7.29

As seen in Table 2 dipole moment of Li-decorated graphene increases with the number of adsorbed H₂ molecules (from 12.87 Debye for two H₂ to 13.57 Debye for four H₂) is an interesting phenomenon with potential implications for hydrogen storage and other applications. When H₂ interacts with Li or Na on BC4N surface, charge transfer occurs. H₂ slightly donates some electron density to the Li, and Na atom, creating a small individual dipole moment around each H₂-Li, and H₂-Na pair. When the H₂ adsorbs on the opposite side of Li or Na atom decorated BC₄N surface, its individual dipole moment might partially cancel out the dipole moment created by the H₂ molecules that adsorbed on one side. This could occur if the two H₂ molecules are oriented in a specific way, with their positive and negative ends pointing towards each other.

Fig. 3 [Images not available. See PDF.]

Total DOS and PDOS of BC₄N and Li, Na atom decorated BC₄N surfaces.

The partial density of states (PDOS) provides valuable insights into the electronic interactions between adsorbed H₂ molecules and the Li- and Na- decorated BC₄N surface, as shown in Figs. 6 and 7. The third hydrogen molecule’s adsorption energy on Li, Na atom decorated BC₄N surface is slightly higher than the initial two, as depicted in Tables 2 and 3. This behavior is elucidated by examining the Partial Density of States (PDOS). The energy bands associated with absorbed H₂ molecules exhibit splitting below the Fermi.

Fig. 4 [Images not available. See PDF.]

Optimized structures of H₂ molecules on Li/BC₄N monolayer.

Fig. 5 [Images not available. See PDF.]

Optimized structures of H₂ molecules on Na/BC₄N monolayer.

level when increasing hydrogen molecules at −14 eV. This observation implies interplay between the absorbed hydrogen molecules, indicating a potential interaction between them and proposed to enhance the adsorption strength of the third hydrogen molecule, resulting in the elevated adsorption energy. Additionally, the overlap of H₂ orbitals with Li-2s in specific energy intervals from − 1 eV to 5 eV, and from − 2 eV to 4 eV for the overlap H₂−1s orbitals with Na-3s orbitals signifies electrostatic interactions.

In determining the maximum hydrogen storage gravimetric density (GD) of Li and Na decorated BC₄N monolayers, a systematic addition of both metal atoms and H₂ molecules is required. For the Li and Na atom decorated BC₄N monolayer, it was observed that three H₂ molecules on the upper layer represent the maximum capacity, as adding an extra H₂ molecule is too distant from the decorated atom. In the case of decorating both sides with Li and Na on the BC4N monolayer, the maximum storage capacity increased to six H₂ molecules. The gravimetric capacity is calculated by the following equation:

1

Where , and are the mass of H₂ molecules and mass of adsorbent respectively. n is the number of hydrogen molecules. By using the above equation, Li/BC₄N storage 12.2 of hydrogen molecules, and Na/BC₄N has 9.2 storage capacities.

Desorption temperature represents the temperature at which hydrogen molecules, previously adsorbed onto a storage material, are released from the material, making the stored hydrogen available for use. The desorption temperature is a critical parameter in hydrogen storage systems, influencing the efficiency and practicality of the release process. Understanding and optimizing desorption temperatures is essential for designing.

Fig. 6 [Images not available. See PDF.]

PDOS of H₂ molecules on Li/BC₄N monolayer.

effective storage materials. The hydrogen desorption temperature (TD) in a hydrogen storage system can be approximated using the Van’t Hoff formula³⁹:

2

Where is Boltzmann constant, is the entropy change from gas to liquid phase of H2 molecule, R is the universal gas constant, and p are standard atmospheric pressure (1 atm) and equilibrium pressure respectively^{40, 41–42}. The for 6H₂$2Li/BC₄N, and 6H₂$2Na/BC₄N are 745 K and 664 K respectively. The connection between the desorption temperature of H₂ molecule and the applied pressure, noting that a decrease in pressure leads to a lower T_D. This trend is explained by the proportional association between the chemical potential of H₂ gas and pressure. Utilizing this insight, it becomes possible in practical scenarios to achieve the release of all stored H₂ molecules at temperatures considered acceptable by effectively modulating the pressure.

Fig. 7 [Images not available. See PDF.]

PDOS of H₂ molecules on Na/BC₄N monolayer.

Fig. 8 [Images not available. See PDF.]

The Charge density difference of 3H₂ on Li, and Na decorated BC₄N.

AIMD computations

To assess the thermal and structural stability of the H₂ adsorbed complexes at finite temperature, we performed ab initio molecular dynamics (AIMD) simulations (300 K, and Berendsen thermostat) on the 3H₂$Li/BC₄N and 3H₂$Na/BC₄N systems. Figure 9 shows that the temperature remains well controlled around 300 K, and Fig. 9 illustrates that the total energies of both systems fluctuate within a narrow window of ± 0.02 eV, with no drift towards positive energies. Visual inspection of snapshots throughout the 10 ps trajectory revealed no bond breaking or surface reconstructions. These results confirm that the Li- and Na- decorated BC₄N monolayers can stably host up to three H₂ molecules at ambient conditions, with both structural integrity and adsorption reversibility maintained.

Fig. 9 [Images not available. See PDF.]

Temperature and Energy profiles from AIMD simulations of 3H2 on Li, and Na decorated BC4N.

Conclusion

Co-doped graphene (BC₄N) exhibits favorable characteristics for hydrogen storage applications. The co-doping introduces structural ripples, enhancing binding energies for Li and Na atoms, preventing clustering. Results reveal that charge transfer from Li and Na to BC₄N surface. H₂ adsorption on Li/BC₄N and Na/BC₄N systems shows non-dissociative behavior. The calculated hydrogen storage gravimetric density suggests significant storage capacities for both Li/BC₄N and Na/BC₄N. Desorption temperatures are determined, providing insights for practical applications. Overall, co-doped graphene BC₄N emerges as a promising material for efficient and practical hydrogen storage.

Computational details

The study involves a comprehensive geometry optimization of various structures, conducted using the B3LYP/6–31 g(d, p) level of theory. The calculations are executed through the Gaussian 09 code⁴³. The study also incorporates the dispersion correction method known as DFT-D3, based on the Grimme scheme⁴⁴. This method is employed to accurately account for weak van der Waals interactions occurring between H₂ molecules and the substrates under consideration.

The focus of the investigation is on co-doped graphene, where non-bonded B and N atoms (BC₄N) are present, and these structures are terminated with hydrogen atoms. The binding energy (E_b) between lithium and sodium decorated BC4N monolayers calculated are shown as following:-

3

Where , are the total energies of Li, Na decorated BC₄N, energy of BC₄N, and energy of the isolated decorated-atom respectively.

The calculation of hydrogen adsorption energy (E_ads) on a Li, and Na over the stable position was calculated using equation:

4

Where are referred to the H₂ molecules adsorbed on decorated atom, and the energy of the free H₂ molecules respectively.

Charge density difference (CDD) plots were utilized to investigate the electron rearrangement accompanying H₂ adsorption. The CDD was computed as³⁸.

5

Where is the total charge density of the Li, and Na decorated BC₄N sheet with three adsorbed H₂ molecules, and and are those of the Li, and Na decorated BC4N sheet and gas phase H₂ cluster, respectively.

Author contributions

N. N. Mostafa: Methodology, Validation, Formal analysis, Investigation, Data Curation, Visualization, Writing - Original Draft; Kamal A. Soliman: Conceptualization, Methodology, Writing - Review & Editing; S.M. Abd El Haleem: Conceptualization, Supervision, Writing - Review & Editing; W.S. Abdel Halim: Conceptualization, Validation, Supervision, Writing - Review & Editing.

Funding

Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Data availability

No datasets were generated or analysed during the current study.

Declarations

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

1. Zhou, Y et al. Enhanced hydrogen storage on Li-doped defective graphene with B substitution: A DFT study. Appl. Surf. Sci.; 2017; 410, pp. 166-176.2017ApSS.410.166Z1:CAS:528:DC%2BC2sXkslSht78%3D

2. Zheng, N et al. A DFT study of the enhanced hydrogen storage performance of the Li-decorated graphene nanoribbons. Vacuum; 2020; 171, 109011.2020Vacuu.171j9011Z1:CAS:528:DC%2BC1MXitVeqsb%2FJ

3. Choudhary, A et al. First principles calculations of hydrogen storage on Cu and Pd-decorated graphene. Int. J. Hydrog. Energy; 2016; 41, 39 pp. 17652-17656.2016IJHE..4117652C1:CAS:528:DC%2BC28Xht1OktbjJ

4. van den Berg, A. W. C. & Areán, C. O. Materials for hydrogen storage: current research trends and perspectives. Chem. Commun., 6, 668–681 (2008).

5. Jiang, M. et al. Light metal decorated graphene-like Si2BN monolayers as hydrogen storage media: A DFT investigation. Int. J. Hydrog. Energy., 50, 865-878 (2023).

6. Reshak, AH et al. First-principles calculations of structural, elastic, electronic, and optical properties of perovskite-type KMgH3 crystals: novel hydrogen storage material. J. Phys. Chem. B; 2011; 115, 12 pp. 2836-2841.1:CAS:528:DC%2BC3MXivVSisL4%3D [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/21375346]

7. Parkar, P; Chaudhari, A. Reversible hydrogen storage on multiple Ti-doped B12C6N6 nanocage. J. Energy Storage; 2023; 62, 106910.

8. Lee, H et al. Ab initio study of dihydrogen binding in metal-decorated polyacetylene for hydrogen storage. Phys. Rev. B; 2007; 76, 19 195110.2007PhRvB.76s5110L

9. Fair, KM et al. Hydrogen adsorption capacity of Adatoms on double carbon vacancies of graphene: A trend study from first principles. Phys. Rev. B; 2013; 87, 1 014102.2013PhRvB.87a4102F

10. Xu, WC et al. Investigation of hydrogen storage capacity of various carbon materials. Int. J. Hydrog. Energy; 2007; 32, 13 pp. 2504-2512.2007IJHE..32.2504X1:CAS:528:DC%2BD2sXpvVOku7s%3D

11. Ozturk, Z et al. Hydrogen storage in heat welded random CNT network structures. Int. J. Hydrog. Energy; 2015; 40, 1 pp. 403-411.2015IJHE..40.403O13289811:CAS:528:DC%2BC2cXhvF2hurbI

12. Liang, H et al. Manipulating active sites on carbon nanotube materials for highly efficient hydrogen storage. Appl. Surf. Sci.; 2023; 619, 156740.1:CAS:528:DC%2BB3sXjsV2qs7o%3D

13. Liu, M et al. Novel 1D carbon nanotubes uniformly wrapped nanoscale MgH2 for efficient hydrogen storage cycling performances with extreme high gravimetric and volumetric capacities. Nano Energy; 2019; 61, pp. 540-549.2019NatEn..4.540L1:CAS:528:DC%2BC1MXpslGgtLg%3D

14. Tang, L et al. A DFT study on defects and N doping to enhance hydrogen storage in Mg-decorated graphene. Appl. Surf. Sci.; 2024; 648, 159078.1:CAS:528:DC%2BB3sXisFyit7vJ

15. Ao, Z et al. Hydrogen storage in porous graphene with al decoration. Int. J. Hydrog. Energy; 2014; 39, 28 pp. 16244-16251.2014IJHE..3916244A1:CAS:528:DC%2BC2cXitVyksL4%3D

16. Zheng, Q; Wang, X; Gao, S. Adsorption equilibrium of hydrogen on graphene sheets and activated carbon. Cryogenics; 2014; 61, pp. 143-148.1:CAS:528:DC%2BC2cXjt1Wnt7o%3D

17. Zheng, Q et al. Analysis of adsorption equilibrium of hydrogen on graphene sheets. Int. J. Hydrog. Energy; 2013; 38, 25 pp. 10896-10902.2013IJHE..3810896Z1:CAS:528:DC%2BC3sXitlahu7k%3D

18. Bonaccorso, F et al. Production and processing of graphene and 2d crystals. Mater. Today; 2012; 15, 12 pp. 564-589.1:CAS:528:DC%2BC3sXhvFaqtLY%3D

19. Chu, Y et al. Mechanical properties of hydrogen Edge–Passivated chiral graphene nanoribbons. J. Nanomechanics Micromechanics; 2015; 5, 4 04015001.

20. Ashna, GE et al. Hydrogen adsorption on vacancy-bent graphene nanosheets: A DFT study. Mater. Today Commun.; 2023; 37, 107319.1:CAS:528:DC%2BB3sXitlaqsrnE

21. Chakraborty, B et al. High capacity reversible hydrogen storage in titanium doped 2D carbon allotrope Ψ-graphene: density functional theory investigations. Int. J. Hydrog. Energy; 2021; 46, 5 pp. 4154-4167.2021IJHE..46.4154C1:CAS:528:DC%2BB3cXit1yjtrjE

22. Sterlin Leo Hudson, M et al. Hydrogen uptake of reduced graphene oxide and graphene sheets decorated with Fe nanoclusters. Int. J. Hydrog. Energy; 2014; 39, 16 pp. 8311-8320.2014IJHE..39.8311S1:CAS:528:DC%2BC2cXmtlWqsrk%3D

23. Ismail, N; Madian, M; El-Shall, MS. Reduced graphene oxide doped with ni/pd nanoparticles for hydrogen storage application. J. Ind. Eng. Chem.; 2015; 30, pp. 328-335.1:CAS:528:DC%2BC2MXhtVOhtbrK

24. Parambhath, VB et al. Investigation of spillover mechanism in palladium decorated hydrogen exfoliated functionalized graphene. J. Phys. Chem. C; 2011; 115, 31 pp. 15679-15685.1:CAS:528:DC%2BC3MXovFKmsLY%3D

25. Jung, H et al. Bio-inspired graphene foam decorated with Pt nanoparticles for hydrogen storage at room temperature. Int. J. Hydrog. Energy; 2016; 41, 9 pp. 5019-5027.2016IJHE..41.5019J1:CAS:528:DC%2BC28XhtlOgs7k%3D

26. Huo, Y et al. Boron-doping effect on the enhanced hydrogen storage of titanium-decorated porous graphene: A first-principles study. Int. J. Hydrog. Energy; 2021; 46, 80 pp. 40301-40311.2021IJHE..4640301H1:CAS:528:DC%2BB3MXit1Kmt7vN

27. Du, A; Zhu, Z; Smith, SC. Multifunctional porous graphene for nanoelectronics and hydrogen storage: new properties revealed by first principle calculations. J. Am. Chem. Soc.; 2010; 132, 9 pp. 2876-2877.1:CAS:528:DC%2BC3cXhvFOqs7w%3D [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/20155897]

28. Beheshti, E; Nojeh, A; Servati, P. A first-principles study of calcium-decorated, boron-doped graphene for high capacity hydrogen storage. Carbon; 2011; 49, 5 pp. 1561-1567.1:CAS:528:DC%2BC3MXhsFOhurY%3D

29. Wang, L; Yang, FH; Yang, RT. Hydrogen storage properties of B- and N-doped microporous carbon. AIChE J.; 2009; 55, 7 pp. 1823-1833.2009AIChE.55.1823W1:CAS:528:DC%2BD1MXnsVOrt7s%3D

30. Wu, HY et al. DFT study of hydrogen storage by spillover on graphene with Boron substitution. J. Phys. Chem. C; 2011; 115, 18 pp. 9241-9249.1:CAS:528:DC%2BC3MXkvFGjsLg%3D

31. Lee, S et al. Effect of nitrogen induced defects in Li dispersed graphene on hydrogen storage. Int. J. Hydrog. Energy; 2013; 38, 11 pp. 4611-4617.2013IJHE..38.4611L1:CAS:528:DC%2BC3sXjsVWls7w%3D

32. Shao, Y et al. Progress in Nonmetal-Doped graphene electrocatalysts for the oxygen reduction reaction. ChemSusChem; 2019; 12, 10 pp. 2133-2146.1:CAS:528:DC%2BC1MXotl2rtL8%3D [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/30806034]

33. Zhao, Y et al. Can Boron and nitrogen Co-doping improve oxygen reduction reaction activity of carbon nanotubes??. J. Am. Chem. Soc.; 2013; 135, 4 pp. 1201-1204.1:CAS:528:DC%2BC3sXntVelug%3D%3D [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/23317479]

34. Seenithurai, S et al. Li-decorated double vacancy graphene for hydrogen storage application: A first principles study. Int. J. Hydrog. Energy; 2014; 39, 21 pp. 11016-11026.2014IJHE..3911016S1:CAS:528:DC%2BC2cXpsl2iurw%3D

35. Wang, F et al. Li-decorated porous graphene as a high-performance hydrogen storage material: A first-principles study. Int. J. Hydrog. Energy; 2017; 42, 15 pp. 10099-10108.2017IJHE..4210099W1:CAS:528:DC%2BC2sXivFehsLk%3D

36. Chan, KT; Neaton, JB; Cohen, ML. First-principles study of metal Adatom adsorption on graphene. Phys. Rev. B; 2008; 77, 23 235430.2008PhRvB.77w5430C

37. Zhang, H et al. First-principles study of sodium adsorption and diffusion on vacancies, N, S, and NS-codoped graphene. Mater. Today Commun.; 2022; 32, 103817.1:CAS:528:DC%2BB38Xhs1KnurnN

38. Dange, D; Beniwal, P; Dhilip Kumar, TJ. Efficient hydrogen storage in superalkali NLi4-Decorated Boron phosphide biphenylene. ACS Appl. Energy Mater.; 2025; 8, 11 pp. 7594-7604.1:CAS:528:DC%2BB2MXhtFyrurfN

39. Durgun, E; Ciraci, S; Yildirim, T. Functionalization of carbon-based nanostructures with light transition-metal atoms for hydrogen storage. Phys. Rev. B; 2008; 77, 8 085405.2008PhRvB.77h5405D

40. Mahamiya, V et al. Remarkable enhancement in catechol sensing by the decoration of selective transition metals in biphenylene sheet: A systematic first-principles study. J. Phys. D; 2022; 55, 50 505401.1:CAS:528:DC%2BB2cXktlektLs%3D

41. Naderizadeh, A; Baizaee, SM; Kahnouji, H. Density functional theory study of reversible hydrogen storage in monolayer beryllium hydride by decoration with Boron and lithium. Int. J. Hydrog. Energy; 2023; 48, 20 pp. 7400-7418.2023IJHE..48.7400N1:CAS:528:DC%2BB38XjtVWmsrvI

42. Faye, O; Szpunar, JA. An efficient way to suppress the competition between adsorption of H2 and desorption of nH2–Nb complex from graphene sheet: A promising approach to H2 storage. J. Phys. Chem. C; 2018; 122, 50 pp. 28506-28517.1:CAS:528:DC%2BC1cXisVarsbfK

43. Frisch, M. J. et al. Gaussian 09 Rev. D.01 (Wallingford, 2009).

44. Grimme, S et al. A consistent and accurate Ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys.; 2010; 132, 15 154104.2010JChPh.132o4104G [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/20423165]