First principles study of alkali metal-decorated bismuth selenide for hydrogen storage applications

Abstract

The identification of novel two-dimensional materials is often highly valued because of their extraordinary characteristics and prospective uses. This study presents a new bismuth selenide (Bi₂Se₃) monolayer based on density functional theory (DFT). Its bandgap, state density, and mobilities are determined and examined. This study investigates hydrogen storage in Bi₂Se₃ adorned with alkali metal (Li/Na and K) atoms. The optimal adsorption site for alkali metal (AM) atoms on the Bi₂Se₃ monolayer is located above an Se atom. The AM atoms are physically adsorbed on Bi₂Se₃, and the electronic charge shifts from these to the Bi₂Se₃ monolayer. In all scenarios examined, hydrogen molecules are physically adsorbed onto AM–Bi₂Se₃ complexes, suggesting that these systems could be employed for hydrogen storage. The K–Bi₂Se₃ monolayer shows the highest hydrogen storage capacity, with one potassium atom adsorbing up to 19 hydrogen molecules, while both Na–Bi₂Se₃ and Li–Bi₂Se₃ could adsorb 18 hydrogen molecules. It is estimated that the hydrogen-storage gravimetric capacities of AM–Bi₂Se₃ are within the US-DOE criteria, where the adatom coverage reaches about 6.71 wt% for K, 6.52 wt% for Na, and 6.66 wt% for Li.

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1 Introduction

Energy crisis is a significant concern for humanity. Particularly in the aftermath of the epidemic, the global scenario is experiencing profound transformations that could directly or indirectly affect the energy market, potentially leading to risks in global energy collaboration.¹ Moreover, mankind’s requirement for energy has increased, exacerbating the depletion of conventional fossil energy sources.^2,3 Conventional high-pressure and cryogenic liquid hydrogen storage methods are expensive, inconvenient to transport, and pose explosion risks.⁴ Therefore, scientists have concentrated on solid-state hydrogen storage owing to its large capacity, better safety, and efficient hydrogen uptake and discharge processes.^5–7

The use of 2D materials for physical adsorption in hydrogen storage has attracted significant attention as an emerging technology. Powerful hydrogen storage entails the adsorption of H₂ molecules on the surface of a 2D material via intermolecular forces.⁷ A material used for productive hydrogen storage must satisfy the criteria of energy and weight density. The H₂ adsorption energy on the substrate must range from −0.20 to −0.70 eV to promote integration/extraction processes under optimal operational conditions.^8–10 Moreover, the gravimetric density of H₂ should reach a minimum of 6.5% by weight, following the measures established by the U.S. DOE. More recently, scientists have explored the potential of 2D materials as ideal choices for hydrogen storage.^11,12 2D materials have extensive surface regions, remarkable thermal resilience, exceptional conductivity, and resilience and are a preferred choice over alternative options. Various 2D materials have been applied in gas sensing,^13,14 lithium-ion batteries,¹⁴ and hydrogen storage.¹⁵

The reversible H₂ storage system necessitates optimal binding of H₂ that is neither too strong nor too weak but falls in the physisorption range of 0.20–0.60 eV per H₂.¹⁶ Metal atoms, such as alkali metals, alkaline earth metals, and transition metals, are used to modify 2D materials to enhance their H₂ storage capacity,^17–23 The enhanced hydrogen storage performance of boron hydride monolayers functionalized with light metal atoms has been demonstrated through theoretical investigations. Introducing structural defects into the boron hydride monolayer leads to metallization, which significantly increases its hydrogen adsorption capacity. These defect-engineered metal-dispersed boron hydride systems represent promising platforms for high-efficiency hydrogen storage applications, offering improved binding energies and reversible adsorption characteristics suitable for next-generation energy technologies.^24,25

Motivated by the recent successful synthesis of the Dirac material BeN₄, Mahamiya et al. explored the interaction of dihydrogen molecules with both pristine and scandium-functionalized BeN₄ monolayers using dispersion-corrected density functional theory (DFT) and ab initio molecular dynamics simulations. This study demonstrates that the adsorption strength of hydrogen can be significantly enhanced by metal atom decoration. Scandium, the lightest transition metal with the highest number of unoccupied d-orbitals in the 3d series, exhibits a strong affinity for hydrogen via Kubas interactions, enabling it to accommodate multiple hydrogen molecules. Consequently, Sc atoms were introduced onto the BeN₄ surface to enhance hydrogen binding energy and increase the desorption temperature, thereby improving the material's potential for efficient hydrogen storage.²⁶ Panigrahi et al. employed first-principles density functional theory (DFT) calculations to investigate the potential of BCN monolayers as effective hydrogen (H₂) storage materials. The inclusion of van der Waals corrections revealed that light metal dopants, such as Li, Na, K, Mg, and Ca, exhibit strong binding affinities to defective BCN, with binding energies of −3.41, −2.52, −2.93, −2.27, and −4.24 eV, respectively. These substantial binding energies effectively suppress the tendency of metal atoms to aggregate on the BCN surface, promoting uniform dispersion.²⁷

Lithium enhances hydrogen adsorption on 2D material surfaces and significantly increases the gravimetric hydrogen storage density.^28–30 In 2016, Das et al. investigated hydrogen storage by replacing one hydrogen atom with lithium on both the boron and nitrogen sides of a hydrogenated hexagonal boron nitride sheet.³¹ Solimannejad et al. discovered that a Li-decorated double-sided B₂N₂ nanosheet can adsorb 8 H₂ molecules, reaching a storage capacity of 12.4 wt% with dehydrogenation possible at 288 K and 1 atm.³² In 2022, Yong et al. studied H₂ adsorption on Ca-decorated graphitic nanoporous CN monolayers, finding an average adsorption energy of −0.16 to −0.23 eV and a storage capacity of 10.1 wt%.³³ In 2023, Zhang et al. reported that double-sided Li-decorated 2D Irida-graphene adsorbed 24 H₂ molecules with an adsorption energy of −0.27 eV per H₂ and a storage density of 7.1 wt%.³⁴ All these substances exhibit exceptional hydrogen storage performance.

For over five decades, A₂B₃ compounds, where A represents Bi and Sb, and B denotes Se and Te, have been renowned for their outstanding thermoelectric characteristics.^35–37 Bi₂Se₃ is a good thermoelectric material owing to its exceptional thermoelectric performance and distinctive electronic structure proximate to the band gap. Bi₂Se₃ exhibits potential applications for cooling at room temperature.³⁸ Bi₂Se₃ plays a crucial role in environmentally efficient solid-state cooling systems. These systems efficiently convert waste heat into electrical energy and are likewise suitable for optoelectronic technologies. They are used in the manufacturing of devices for various purposes, including heat regeneration and moisture detection,³⁹ solid-phase thermoelectric power sources,⁴⁰ emission detectors,⁴¹ transistors utilizing band-to-band tunneling,⁴² and magneto electronic and photoelectrochemical devices.⁴³ In recent studies, scientists have identified topological insulator behavior in Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃. Certain experimental procedures are used to prepare 2D A₂B₃ structures. As an illustration, Kong et al.⁴⁴ achieved ultrathin nanoplates of Bi₂Te₃ and Bi₂Se₃ consisting of three quintuple layers through vapor–solid growth, eliminating the need for a catalyst. Liu et al.⁴⁵ synthesized Bi₂Se₃ nanobelts using van der Waals epistaxis without catalysts and used these nanobelts to manufacture a near-infrared photodetector. Buha et al.⁴⁶ investigated the thermal robustness and anisotropic vaporization of nanocrystals made from Bismuth telluride (Bi₂Te₃) and Bi₂Se₃ using localized transmission electron microscopy. Utilizing a fast resolution-based technique, Min et al.⁴⁷ successfully produced ultra-thin monocrystalline nanodiscs and nanosheets of Bi₂Se₃. In 2018, Wang et al.⁴⁸ conducted a theoretical investigation of the monolayer structures of Bi₂Te₂S and Bi₂Te₂Se, revealing their high electron conductivities. Lu et al.⁴⁹ discovered that the Bi₂TeSe₂ monolayer behaves as a direct semiconductor and that strain engineering can produce exceptionally high electron mobility for the monolayer.

Our research focuses on the first principles study of alkali metal-decorated Bi₂Se₃ for hydrogen storage applications. DFT was utilized to explore the interaction mechanisms between hydrogen and Bi₂Se₃ when decorated with alkali metals. This approach provides insights into the potential of these materials for efficient and sustainable hydrogen storage and offers a promising alternative to conventional energy sources.

2 Computational details

All computations related to the investigation of alkali metal (Li/Na/K) modification of Bi₂Se₃ for hydrogen storage purposes, including energetic equilibrium and configurations, were conducted using the Amsterdam density functional (ADF) module BAND within the context of DFT.⁵⁰ Slater-type orbitals integrated into the ADF-BAND calculations were employed to compute the molecular orbitals of each structure. Throughout this study, double-zeta polarized (DZP) sets, characterized by regular numerical precision and a core-electron treatment method, were consistently utilized.⁵¹ GGA (generalized gradient approximation) within the PBE approximation method was used to calculate the correlation–exchange interactions among electron particles.⁵²

The numerical accuracy of ADF hinges on the k-grid, basis set, and variables in density fitting as fundamental components. These particular k-points effectively represent a sampling of the Brillouin Zone and incorporate a fuzzy partition scheme pioneered and established by Becke.⁵³ Corrections to van der Waals effects were also included to ensure the relaxation of all configurations to their optimal equilibrium structure, employing the observational Grimme dispersion technique.⁵⁴ For the relaxation of all structures, the criteria for the convergence of energy, gradient, and step were defined as 10⁻⁵ eV, 0.02 eV Å⁻¹, and 10⁻³ Å, respectively. In our previous study, we utilized computational methods to devise and elucidate the structural and electronic characteristics of Bi₂Se₃. Furthermore, detailed discussions were conducted on the configurations, adsorption locations, and state density resulting from attachment involving alkali metal (Li/Na/K) atoms upon Bi₂Se₃.⁵⁵ The adsorption energy for Bi₂Se₃ can be determined using the following formula:

E_ads = [E_Bi2Se3+A.M + nE_H2 − E_{Bi2Se3+A.M+nH2}]/n, (1)

where E_Bi2Se3+A.M represents the total energy of Bi₂Se₃ about alkali metals (Li/Na/K), E_{Bi2Se3+A.M+nH2} denotes the total energy of Bi₂Se₃ adorned with alkali metals (Li/Na/K), n denotes the number of hydrogen molecules and E_H2 denotes the energy of a lone hydrogen molecule.^56,57

van der Waals long-range dispersion correction in ADF: BAND was utilized in all computations owing to its advantageous impact on improving adsorption energy.⁵⁷

Binding energy might be determined using the following equation:

E_B = E_Bi2Si3+A.M − E_Bi2Si3 − E_A.M, (2)

where E_Bi2Si3 represents the energy of unaltered Bi₂Se₃, E_A.M denotes the energy of a solitary alkali metal atom (Li/Na/K) with varying counts of n = (1, 2, 3, 4, 5), and E_Bi2Si3+A.M denotes the combined total energy of Bi₂Se₃ decorated with A.M (Li/Na/K) atoms.^57,58

We determined the H₂ temperature desorption by applying the following van’t Hoff's equation:⁵⁹

where the Boltzmann constant K_B equals 1.38 × 10⁻²³ J K⁻¹, the variation in entropy is ΔS, the transition from hydrogen converting from gas to liquid involved is 75.44 J mol⁻¹ K⁻¹, and the gas constant (R) for H₂ is 8.314 J mol⁻¹ K⁻¹, with an equilibrium pressure (p) of 1 atm.⁵⁶ First-principles molecular dynamics (MD) simulations were conducted to confirm the structural stability of the substrate at both ambient and desorption temperatures.

The calculation involved determining the gravimetric storage capacity (GC).⁶⁰

where n_H, n_Bi, n_Se and n_A.M represent the quantities of H₂ molecules and Bi, Se, and A.M atoms, respectively, while w_H, w_Bi, w_Se and w_A.M denotes the weights of H₂ molecules and Bi, Se, and A.M atoms, respectively.

3 Results and discussion

3.1 Structural and electronic properties of Bi₂Se₃

Fig. 1(a) presents the optimized structure of Bi₂Se₃, which is shown from both the z-axis and x-axis perspectives. It consists of bismuth (Bi) and selenium (Se) atoms. It is categorized within the group of materials referred to as topological insulators. Bi₂Se₃ is a compound with notable structural properties that make it suitable for various applications, including electronic and thermoelectric devices. It is famous owing to its distinctive layer structure. Each quintuple layer consists of five atomic layers arranged in a specific sequence: Se–Bi–Se–Bi–Se. These quintuple layers are weakly bonded to each other by van der Waals forces, allowing for easy cleavage along the layers. The Bi atoms are bonded with Se atoms in a trigonal planar arrangement. The lattice parameters for the Bi₂Se₃ hexagonal crystal structure are a = 4.137 Å and c = 28.64 Å. The bonding within the quintuple layers is covalent, while the interaction between the layers is primarily van der Waals. This material has already been studied for topological insulators and spintronics. The distances between bismuth and selenium atoms in Bi₂Se₃ range from 2.86 Å to −3.10 Å. The angles formed between adjacent atoms in the crystal structure are in the range of 46°–91°.

Fig. 1 (a) Z and X-views of the optimized structure of pure Bi₂Se₃. (b) Partial density of states (PDOS), (c) band structure, and (d) phonon dispersion curves.

The phonon dispersion is shown in Fig. 1(d), and the results are consistent with the study. According to Zhan et al.,⁶¹ phonon dispersion confirms the stability of the monolayer. Imaginary frequency is absent within the first reciprocal lattice cell, indicating dynamic durability of the Bi₂Se₃ monolayer. The electronic properties are derived from the optimized geometric structure of Bi₂Se₃ single layers. The Bi₂Se₃ monolayer exhibits a 0.75 eV indirect energy bandgap, as illustrated in Fig. 1(b) and (c). Detailed examination of atomic components in the density of states (DOS) is shown in Fig. 1(b). It is evident that the conduction band minimum (CBM) of the Bi₂Se₃ single atomic layer is primarily composed of p orbitals associated with Bi, with a small impact from the p orbitals of the Se atoms. However, the valence band maximum (VBM) is observed to be composed solely of p orbitals of Se atoms, with no significant charge distribution on the Bi atoms.

3.3 Adsorption of hydrogen on pristine Bi₂Se₃

Here, we examined the interaction of a solitary H₂ molecule characterized by an unmodified Bi₂Se₃ interface. Three distinct adsorption sites, namely (i) Se, (ii) Bi, and (iii) bridge within the Bi₂Se₃ structure, were selected for investigation. We explored the associated binding energies for these potential sites, considering both with and without London dispersion forces. The illustration depicts hydrogen binding on an unmodified Bi₂Se₃ surface. Subsequently, we delve into the stability characteristics of pure Bi₂Se₃ upon hydrogen adsorption. The geometric distances between the adsorption site and the H₂ molecules vary, ranging from the Bi site (5.09–5.85 Å) to the Se site (2.90–3.82 Å). The horizontal alignment with Bi and Se involves an H₂ molecule at each of two potential binding positions to compute the interaction energy. It is clear that the H₂ molecule has maintained its bonding and bond length of 0.75 Å and has not split into two distinct H atoms.⁴⁴

The binding energy of the H₂ molecule over pure Bi₂Se₃ can be calculated as follows:⁶²

where E_Bi2Se3+nH2, E_Bi2Se3 and E_nH2 represent the energy of adsorption of hydrogen on Bi₂Se₃, the energy of pure Bi₂Se₃, and the energy of the hydrogen molecule, respectively. The binding energies are listed in Table 1.

Table 1 Binding energies (in eV per H₂) of H₂ on pristine Bi₂Se₃ at various locations

Adsorption site	Se	Bi	Bridge
E b (eV)	−0.18	−0.17	−0.19

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This indicates which H₂ molecules could interact with Bi₂Se₃via London dispersion forces. This sequence of molecular adsorption energies indicates pristine Bi₂Se₃.⁶⁰

The calculated results indicate that the Br site exhibits the highest adsorption energy, identifying it as the most favorable site for H₂ adsorption in the pristine Bi₂Se₃ monolayer. However, although adsorption occurs successfully, the corresponding energy values do not meet the benchmark established by the U.S. Department of Energy (US-DOE) for efficient hydrogen storage. To address this limitation and enhance the binding energy within the DOE-specified range, alkali metal decoration is proposed as a strategy to improve hydrogen storage performance.

3.3 Adsorption and electronic properties of AM on Bi₂Se₃

Initially, the investigation focused on the interaction between Li/Na/K atoms and the Bi₂Se₃ monolayer. With this consideration in mind, lightweight alkali metals were adsorbed onto Bi₂Se₃. By exploring various adsorption sites on the Bi₂Se₃ base, we identified the optimal adsorption site for a lone Li/Na/K atom in the monolayer. The adsorption characteristics concerning a single Li, Na, or K atom at three different sites (Bi, Se, and Br) on the Bi₂Se₃ surface were calculated, as illustrated in Fig. 2. Metal tends to create stable compounds above the Se atom of Bi₂Se₃. The energetic stability of metal-decorated Bi₂Se₃ was explored by investigating the binding energy using eqn (2).

Fig. 2 Views of optimized configurations of (a) Li-, (b) Na- and (c) K-modified Bi₂Se₃.

The binding energy for each metal species in Li/Na/K–Bi₂Se₃ is measured to be −1.72 eV, −1.44 eV, and −1.99 eV, respectively. The feasibility of metal adherence as a process is indicated by the negative values of E_b per metal adsorbent. The binding energy (E_b) of Li at Bi₂Se₃ is observed to be greater than its cohesive energy in bulk, which is 1.63 eV.⁶³ Likewise, binding energy (E_b) values for Na–Bi₂Se₃ and K–Bi₂Se₃ complexes are also greater than those of bulk metals, where Na exhibits a cohesive energy of −1.13 eV and bulk K exhibits a cohesive energy of −0.93 eV. Higher binding energy (E_b) values for metal adsorbents Li, Na, and K, compared to their respective lattice energies, suggest that metal collection is unlikely within the system. After adsorption, the Bi₂Se₃ monolayer shows a Se–Li bond distance of 2.54 Å, while the Bi–Li distance is 3.58 Å. The Se–Na bond distance in the Bi₂Se₃ monolayer is 2.89 Å, while the Bi–Na distance is 4.05 Å. In the Bi₂Se₃ monolayer following adsorption, the Se–K bond distance is 3.23 Å, while the distance between Bi and K is 4.46 Å.

The DOS plot illustrates the distribution of electron energy levels across different materials. The x-axis represents energy, while the y-axis indicates the number of available energy states at each energy level. Peaks in the plot highlight energy ranges with a high density of electron states. In DOS plots Fig. 3(a)–(c), the contributions of Li-2s/2p, Na-2s/2p, and K-2s/2p states are displayed. For each alkali metal, the distribution of states near the Fermi level sheds light on their interaction with adsorbed hydrogen. Peaks near −5 eV correspond to the 2s states, and those around −3 eV correspond to the 2p states. Moving from Li to K, the peaks shift to lower energies, indicating the decreasing ionization energy of these metals. Lithium exhibits moderate states near the Fermi level, implying weaker bonding and lower desorption energy, which makes hydrogen easily released. Sodium shows broader peaks near the Fermi level, indicating stronger adsorption with hydrogen, while potassium displays even stronger interaction, as observed from larger peaks, leading to higher desorption energy and more difficult hydrogen release.

Fig. 3 Projected density of states (PDOS) for unbound (a) pure Li, (b) Na, and (c) K and adsorbed (d) Bi₂Se₃–Li, (e) Bi₂Se₃–Na, and (f) Bi₂Se₃–K.

In lower panel Fig. 3(d)–(f), the DOS of the combined system, including the substrate atoms (likely Bi₂Se₃, with Bi-6p and Se-4p orbitals), is presented along with the alkali metals. Peaks of around −15 eV and −10 eV for Bi and Se correspond to their 6p and 4p states, respectively. The composite material features peaks associated with the 2s and 2p states of Li, Na, and K, as well as the 6p and 4p states of Bi and Se. Overlapping peaks indicate hybridization between the states of different elements, leading to the formation of new energy bands in the composite material. K shows stronger hybridization compared to Li and Na, correlating with its higher desorption energy.

3.4 Adsorption and desorption of H₂ molecules on AM-decorated Bi₂Se₃

The adsorption behavior relating to hydrogen on Li, Na, and K metal-decorated Bi₂Se₃ was further examined, as shown in Fig. 4 (z and x-axis views). Initially, an isolated hydrogen molecule was introduced into the system, and it was observed that the hydrogen molecule was inclined towards the metal atom on the substrate. This one-inclined orientation associated with the H₂ molecule increases its consistency and facilitates the adsorption of additional hydrogen molecules.⁶⁴ The distances between the hydrogen molecule and the active site of the metal atoms are 2.32 Å, 2.58 Å, and 3.09 Å. The bond length of the adsorbed hydrogen molecule is 0.75 Å. It remains the same as that of hydrogen molecules without adsorption. To determine the stability of complexes formed after H₂ binds to the surface of Li/Na/K–Bi₂Se₃, adsorption energy data were computed, as detailed in Table 2. Subsequently, successive adsorption of H₂ on the surface of Li/Na/K–Bi₂Se₃ was performed. The H₂-adsorbed Li/Na/K–Bi₂Se₃ complexes are denoted as Li/Na/K–Bi₂Se₃+ nH₂, where ‘n’ represents several molecular hydrogens. We observed that Li–Bi₂Se₃ and Na–Bi₂Se₃ can adsorb 18 H₂ molecules, while K–Bi₂Se₃ can adsorb 19 hydrogen molecules. Optimized structures Li/Na/K–Bi₂Se₃ + nH₂ are displayed in Fig. 4. The stability of the complexes formed by the adsorption of hydrogen molecules on Li/Na/K–Bi₂Se₃ was assessed using adsorption energy, as calculated in eqn (1). The adsorption energies for Li/Na/K–Bi₂Se₃+ nH₂ systems are listed in Table 2. (E_ads) values imply that binding H₂ is significantly stronger than on pristine Bi₂Se₃. Moreover, as shown in Table 2, the adsorption energy values for Li, Na, and K–Bi₂Se₃ + 2H₂ are approximately −0.53 eV, −0.48 eV, and −0.46 eV, respectively. These adsorption energy values fall effectively within the criteria set by DOE-US. This indicates that additional H₂ uptake can proceed on Li/Na/K–Bi₂Se₃.

Fig. 4 Optimized geometry of Li–Bi₂Se₃: (a) 1H₂, (b) 9H₂, (c) 18H₂, Na–Bi₂Se₃, (d) 1H₂, (e) 9H₂, (f) 18H₂, K–Bi₂Se₃, (g) 1H₂, (h) 9H₂ and (i) 19H₂.

Table 2 Calculated average adsorption energies (E_ads), binding energies (E_b), gravimetric storage capacity (wt%), and temperature desorption (T_D)

Atoms	No. of H2 molecules	E ads (eV)	E b (eV)	wt%	T D	β (Å)
Li	1H2	−0.23	−1.42	0.39	294.2	2.50
	2H2	−0.53		0.79	677.9	2.78
	3H2	−0.42		1.18	537.2	2.64
	4H2	−0.35		1.57	447.6	4.26
	5H2	−0.31		1.96	396.5	2.31
	6H2	−0.27		2.34	345.3	2.26
	7H2	−0.26		2.72	332.5	2.24
	8H2	−0.25		3.09	319.7	2.21
	9H2	−0.23		3.47	294.2	2.20
	10H2	−0.22		3.84	281.4	2.21
	11H2	−0.22		4.21	281.4	2.30
	12H2	−0.21		4.57	268.6	4.12
	13H2	−0.21		4.97	268.6	2.24
	14H2	−0.20		5.30	255.8	4.06
	15H2	−0.20		5.65	255.8	4.18
	16H2	−0.20		6.01	255.8	4.26
	17H2	−0.19		6.36	243.0	4.44
	18H2	−0.19		6.66	243.0	2.18
Na	1H2	−0.20	−1.72	0.38	255.8	2.58
	2H2	−0.48		0.76	613.9	2.55
	3H3	−0.39		1.14	498.8	2.56
	4H2	−0.33		1.52	422.1	2.66
	5H2	−0.29		1.90	370.9	2.71
	6H2	−0.27		2.27	345.3	2.59
	7H2	−0.25		2.64	319.7	2.61
	8H2	−0.24		3.00	307.0	4.54
	9H2	−0.23		3.37	294.2	4.64
	10H2	−0.22		3.73	281.4	4.69
	11H2	−0.21		4.08	268.6	2.94
	12H2	−0.21		4.44	268.6	4.53
	13H2	−0.20		4.79	255.8	4.80
	14H2	−0.20		5.14	255.8	2.65
	15H2	−0.20		5.49	255.8	2.71
	16H2	−0.19		5.83	243.0	2.70
	17H2	−0.19		6.18	243.0	2.64
	18H2	−0.19		6.50	243.0	2.65
K	1H2	−0.67	−1.99	0.37	856.9	3.09
	2H2	−0.46		0.74	588.3	3.00
	3H2	−0.37		1.11	473.2	3.07
	4H2	−0.32		1.48	409.3	3.08
	5H2	−0.29		1.84	370.9	3.07
	6H2	−0.26		2.20	332.5	3.11
	7H2	−0.25		2.56	319.7	3.07
	8H2	−0.23		2.91	294.2	3.07
	9H2	−0.23		3.27	294.2	3.59
	10H2	−0.22		3.62	281.4	3.15
	11H2	−0.21		3.97	268.6	3.14
	12H2	−0.21		4.31	268.6	3.15
	13H2	−0.20		4.65	255.8	6.99
	14H2	−0.20		4.99	255.8	3.16
	15H2	−0.20		5.33	255.8	3.18
	16H2	−0.19		5.67	243.0	6.84
	17H2	−0.19		6.00	243.0	3.13
	18H2	−0.18		6.33	230.2	3.12
	19H2	−0.18		6.71	232.2	3.14

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As shown in Table 2, the (E_ads) values are negative for LiNa/K-decorated Bi₂Se₃ + nH₂ complexes, indicating that hydrogen adsorption is an exothermic reaction, resulting in thermally stable complexes. As successive H₂ adsorptions occur, a decrease in (E_ads) values is observed (Table 2). For Li- and Na-decorated Bi₂Se₃, gradual decreases in (E_ads) values (after the second H₂ molecule) and for K (after the first H₂ molecule) are mainly attributed to repulsive behavior between H₂ molecules, which are influenced by positively charged metal dopants.^65,66 Despite a decrease in the (E_ads) values with increasing numbers of H₂ molecules, they remain well within the DOE-US limit. Therefore, decorating Bi₂Se₃ with alkali metals significantly improves its H₂ storage efficiency. These adsorption energy values show that Li/Na/K–Bi₂Se₃ complexes are stable and could be good choices for reversible hydrogen storage because they are within the range of reversible physical adsorption, which is between −0.1 and −0.6 eV.^18,66 Additionally, to assess H₂ uptake, Li/Na/K–Bi₂Se₃ complexes were charged with specific metal atoms. In the Li–Bi₂Se₃ within the complex, lithium metal was effectively filled onto the surface of Bi₂Se₃.

The addition of hydrogen resulted in a significantly increased H₂ gravimetric density of 6.66 wt% for Li. Na–Bi₂Se₃ and K–Bi₂Se₃ complexes resulted in gravimetric hydrogen uptakes of 6.52 wt% and 6.71 wt%, respectively. This indicates that the Li/Na/K–Bi₂Se₃ complexes can achieve hydrogen weight percentages higher than the DOE-US limit, making them highly effective H₂ retention materials. To facilitate this, the average adsorption/desorption energies and gravimetric H₂ densities are summarized and compared in Table 3. This clearly illustrates that decoration with light metals improves H₂ storage capacity relative to most previously examined transition metal-embedded complexes. Furthermore, the impact of interactions between bound H₂ and Li/Na/K–Bi₂Se₃ complexes on their electronic properties was investigated. These findings are discussed below.

Table 3 Desorption energy of hydrogen from alkali metal-decorated Bi₂Se₃ with hydrogen atoms

nH2	Li Edes (eV)	Na Edes (eV)	K Edes (eV)
1	0.23	0.20	0.67
2	0.17	0.19	0.18
3	0.21	0.20	0.19
4	0.15	0.20	0.18
5	0.12	0.14	0.17
6	0.12	0.18	0.14
7	0.17	0.14	0.15
8	0.17	0.13	0.11
9	0.13	0.15	0.19
10	0.13	0.16	0.18
11	0.16	0.15	0.16
12	0.17	0.18	0.16
13	0.13	0.15	0.17
14	0.17	0.17	0.17
15	0.15	0.15	0.11
16	0.17	0.13	0.15
17	0.14	0.14	0.14
18	0.13	0.13	0.11
19	—	—	0.14

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The desorption energy (E_des), which is the energy required to release a hydrogen molecule from the Bi₂Se₃ monolayer, is expressed as follows:^67,68

E_des = E_H2 + E_{(n−1)H2+Metal+Bi2Se3} − E_{nH2+Metal+Bi2Se3}, (6)

where E_H2 denotes the energy of a standalone hydrogen molecule; E_{(n−1)H2+Metal+Bi2Se3} is the overall energy of the system with (n − 1) adsorbed hydrogen molecules, where n denotes the maximum number of hydrogen molecules that can be adsorbed on the monolayer; and E_{nH2+Metal+Bi2Se3} is the total energy of the Bi₂Se₃ with n adsorbed molecules.

Table 3 presents desorption energies E_des of hydrogen molecules (nH₂) from Li-, Na-, and K-decorated Bi₂Se₃. Desorption energy represents the energy required to release adsorbed hydrogen molecules, which is a critical parameter in hydrogen storage applications because it determines how easily stored hydrogen can be released when needed. In the case of Li, the desorption energy is relatively high with the adsorption of a single hydrogen molecule (0.23 eV), but it decreases as additional hydrogen molecules are adsorbed, such as 0.12 eV for 5 H₂. Overall, the desorption energy values remain fairly consistent, ranging from 0.12 to 0.23 eV. For Na, the desorption energy varies slightly but stays in the range of 0.13–0.20 eV, exhibiting less fluctuation compared to Li. For K, the desorption energy is initially high at 0.67 eV for 1 H₂, but it drops significantly to a range of 0.11–0.19 eV once 2 H₂ molecules are adsorbed. K exhibits a much higher desorption energy for the first hydrogen molecule (0.67 eV) compared to Li and Na, indicating a stronger initial interaction between K and H₂, which makes desorption more challenging. In contrast, lithium consistently shows lower desorption energies, suggesting that hydrogen adsorbed on Li can be released more easily than on Na or K. It is observed that E_des(K) > E_des(Na) > E_des(Li) irrespective of the adsorbing atom. The values presented for Li and Na align with the optimal range for effective hydrogen storage, while K may present challenges owing to its initially high desorption energy.

3.5 Hydrogen storage capacity and desorption temperature for AM-decorated Bi₂Se₃

Hydrogen molecules are progressively bonded to the Li/Na/K–Bi₂Se₃ compound (Fig. 4). Table 2 analyzes the average energy of hydrogen adsorption evaluated using GGA-PBE. Nevertheless, the outcomes of both methods exhibit strong agreement. The spatial proximity of H₂ molecules leads to mutual repulsion, yielding a decrease in energy associated with the adsorption of H₂ molecules during the adsorption process. As hydrogen molecules are adsorbed individually, each encounters a slightly distinct environment. Consequently, the adsorption energy of hydrogen on the material's surface may fluctuate slightly. Nonetheless, as the number of hydrogen molecules increases, the difference in adsorption energy between the upper surfaces gradually decreases. Simultaneously, the average separation between H₂ and Bi₂Se₃ tends to enlarge as adsorption weakens. Initially, polarization induces electrostatic interaction, thereby enhancing adsorption energy. However, as ionized hydrogen molecules gather near lithium atoms, they repel each other owing to electrostatic forces, leading to a reduction in adsorption capacity, particularly as the number of H₂ molecules increases. In essence, polarization reinforces hydrogen molecule adsorption, as electrostatic interactions leading to repulsion between hydrogen molecules reduce subsequent adsorption effectiveness. These opposing phenomena significantly influence hydrogen adsorption.

The maximum hydrogen storage capacity depends on the polarized state and charge repulsion with ongoing molecular hydrogen adsorption onto the surface of Li/Na/K–Bi₂Se₃, with adsorption energies of −0.19 eV, −0.19 eV, and −0.18 eV, respectively. The 15th H₂ molecule's bond length is 0.75 Å, which is approximately that of free hydrogen. Eqn (4) is used to determine the gravimetric density of hydrogen. The substrate contains three active sites. The average adsorption energy decreased with increasing hydrogen quantity, with each molecule maintaining a stable adsorption state. Li/Na/K–Bi₂Se₃ surpasses the DOE's 2025 hydrogen storage goal, fully utilizing the active sites and offering exceptional gravimetric hydrogen density compared to other materials (see Table 4).

Table 4 Analyzing the total number of adsorbed H₂ (n), the average adsorption energy (E_ads in eV), and the weight percentage by mass for X–Bi₂Se₃–nH₂ (X = Li, Na, K) systems relative to earlier reports of metal-decorated two-dimensional nanosheets

Modified structure	Binding energies with metal	H2 molecule adsorption energy (eV)	Amount of adsorbed H2 molecules	Adsorbed H2 gravimetric density (wt%)
Li@Bi 2 Se 3 (this work)	−1.42	−0.24	18	6.66
Na@Bi 2 Se 3 (this work)	−1.44	−0.22	18	6.52
K@Bi 2 Se 3 (this work)	−1.99	−0.25	19	6.71
Li@C9N4^65	−2.51	−0.20	6	11.9
K@C9N4^65	−2.01	−0.17	7	8.1
Na@C9N4^65	−2.31	−0.19	6	8.7
Li@POG^69	2.42	−0.22	3	9.9
Na@POG^69	2.45	−0.16	5	7.7
K@POG^69	2.80	−0.15	5	6.8
Li@SnC^70	2.46	−0.20	3	5.5
Na@SnC^70	2.06	−0.19	5	5.5
K@SnC^70	2.12	−0.18	6	5.5
Li@Borophene^71	2.47	−0.36	10	9.0
Na@Borophene^71	2.50	−0.34	15	6.8

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Kaur et al. explored the capability of alkali metals (two-dimensional carbon–nitride (C₉N₄)) functionalized with Li/Na/K monolayers for hydrogen preservation through a primary approach using DFT analyses. The connection between Li/Na/K dopants, such as C₉N₄, is strong owing to the charge transfer from metals to the carbon–nitride monolayer. It was observed that every Li atom in Li@C₉N₄ can persistently bind as many as 6 H₂ particles without causing structural breakdown, leading to an average adsorption energy of 0.20 eV and remarkably significant hydrogen capacity of 11.9 wt%. Similarly, the storage capacities and average adsorption energies for H₂ for Na- and K-decorated C₉N₄ complexes are 8.7 wt% and 8.1 wt% with adsorption energy at −0.19 eV and −0.17 eV, respectively, complying with U.S. DOE criteria⁶⁵.

Bi et al. investigated the storage efficiency for H₂ in penta-octa-graphene (POG) decorated with low-density alkali metals (Li, Na, and K) using density functional theory. They concluded that 3, 5, and 5 hydrogen molecules involved in polarization and hybridization mechanisms can be consistently adsorbed around each metal atom. POG modified with Li, Na, and K metals shows average H₂ adsorption energy values of −0.15 eV, −0.16 eV, and −0.22 eV, respectively. Binding energies for Li-, Na-, and K-based POG are 2.42, 2.45, and 2.80 eV, respectively, which exceed the cohesive energy. Hydrogen gravimetric densities for Li-, Na-, and K-functionalized POG can attain H₂ storage levels associated with 9.9 wt%, 7. 7 wt% and 6.8 wt% in that order, respectively.⁶⁹

L. et al. conducted DFT research regarding hydrogen storage in alkali metallic element-decorated tin carbide monolayers (2DSnC), including Li, Na, and K elements. The optimal adsorption location for these alkali metal atoms on 2DSnC is positioned over a tin atom. The data indicate that alkali metal atoms are chemically linked with 2DSnC, with voltage transferring from decorating atoms to 2DSnC. In every case examined, hydrogen molecules were physisorbed onto 2D SnC complexes involving AM, suggesting that these systems may be ideal for storing hydrogen. Specifically, the K-2DSnC single layer demonstrates the most efficient hydrogen storage, with a lone K atom capable of adsorbing as many as 6 hydrogen molecules. Next is Na-decorated 2DSnC, which can uptake 5 hydrogen molecules, followed by Li-decorated 2DSnC, which can adsorb 3 hydrogen molecules. Hydrogen molecule adsorption energies for alkali metal atom-functionalized 2D SnC are −0.20, −0.19, and −0.18 eV. It is likely that when coverage AM concentrations reach 40%, 44%, and 70%, respectively, AM-2D SnC's gravimetric capacities for hydrogen storage could exceed the 5.5 wt% objectives set by US-DOE for automotive technologies.⁷⁰

Haldar et al. present an in-depth examination of H₂ holding capabilities among alkali metal-functionalized and error-rich 2D boron sheets via DFT. The binding energy values for one H₂ molecule on Li- and Na-modified borophene were measured at −0.36 and −0.34 eV per H₂ molecule, respectively. To better understand the H₂ adsorption process and pinpoint electron transfer sources, fluctuations in charge densities and the projected density of states were determined through calculations. The results showed a notable buildup and reduction, leading to intense polarization effects in hydrogen molecules. Ultimately, Na and borophene functionalized with Li achieved weight percent densities of 9.0% and 6.8%, respectively.⁷¹

3.6 Hydrogen desorption temperature (T_D)

We computed the van’t Hoff desorption temperature to determine the feasible desorption temperature using eqn (3) in computational detail,^59,66 with pressure values ranging from 1 to 10 atm. The maximum and minimum desorption temperatures are referenced as T_Dmax and T_Dmin, respectively. These values are designed by considering the uppermost and lowermost adsorption energies. To establish a suitable desorption temperature, we take the estimated normal van’t Hoff temperature for desorption (T_Dave) by averaging T_Dmax and T_Dmin. Supplementary Information 1 presents the maximum, minimum, and average desorption temperatures across the specified pressure range. The T_Dmin for hydrogen desorption in Li/Na/K–Bi₂Se₃ calculation yields 255.4 K at 1 atm pressure, while the corresponding T_Dmax values at pressure are 676.8 K, 613 K, and 855.6 K, respectively. This indicates that the minimum temperature for Li/Na/K–Bi₂Se₃ to initiate desorption is 255.4 K under standard conditions, which can be enhanced to 676.8 K, 613 K, and 855.6 K. As pressure increases, the desorption temperature also increases. Fig. 6 shows that Li-/Na-/K-decorated Bi₂Se₃ can withstand temperatures of up to 906.9 K, 821.3 K, and 1112.2 K at 10 atm. The T_Dave falls within an operational range of 344.8–419.1 K for Bi₂Se₃–Li, 319.2–388 K for Bi₂Se₃–Na, 408.6–496.7 K for Bi₂Se₃–K below a pressure range of 1–5 atm. Analysis of van’t Hoff temperature results reinforces the assertion of the reversible hydrogen storage within the operable thermodynamic range of Li/Na/K–Bi₂Se₃.⁶⁸

3.7 Electronic properties of the Li/Na/K with multiple hydrogens

First, the electronic properties of the PDOS diagrams depicted in Fig. 5(a) demonstrate the 1s orbital of the initially adsorbed hydrogen peaks at −7.62 eV. Although the PDOS diagrams for Bi₂ and Se₃ exhibit minimal variation, there is a notable change in that of lithium. At this energy level, a resonance peak occurs between lithium's 2s and 2p orbitals and hydrogen's 1s orbital, suggesting the relatively weak hybridization of orbital interaction. The lithium 2s atomic orbital experiences hybridization owing to the interplay between lithium and hydrogen, while hybridization of the lithium 2p orbital occurs because, at this juncture, lithium serves as a conduit for the passage of electric charges. As presented in Fig. 5(c), after the adsorption of eighteen molecules of hydrogen, both hydrogen molecules absorb electrons, while the charge on the lithium atom increases rather than decreases. Upon adsorption of eighteen hydrogen molecules, the energy level of the hydrogen 1s orbital broadens and separates beneath the Fermi level. Peaks of s-orbitals disperse into two smaller peaks, suggesting the potential for the adsorption of several hydrogen molecules. Simultaneously, the focal peak of hydrogen 1 orbital shifts toward the left, indicating a transition. The stability of the all-hydrogen molecule's adsorption is inferior to that of the other. In the PDOS of the adsorbed hydrogen material, orbital overlaps between the hydrogen 1s orbital and lithium 2s and 2p orbitals are observed in energies of −7.9, −5.9, and −6.9 eV, indicating electrostatic interaction. This overlap validates the robust bonding between lithium atoms and hydrogen molecules. This leads to the formation of bonding orbitals of lithium and hydrogen. Charge distribution within hydrogen molecules is split into two segments: an individual hydrogen atom carries an excess of negative charge, while an alternate hydrogen atom shows an excess of positive charge. This evident charge polarization signifies the polarization of the hydrogen molecule.

Fig. 5 Projected density of states (PDOS) for (a) Bi₂Se₃–Li–1H₂, (b) Bi₂Se₃–Li–9H₂, (c) Bi₂Se₃–Li–18H₂, (d) Bi₂Se₃–Na–1H₂, (e) Bi₂Se₃–Na–9H₂, (f) Bi₂Se₃–Na–18H₂, (g) Bi₂Se₃–K–1H₂, (h) Bi₂Se₃–K–9H₂, and (i) Bi₂Se₃–K–19H₂.

As depicted in Fig. 5(d), the PDOS diagrams show the initial 1s orbital peak of adsorbed hydrogen at −7 eV. Although the PDOS diagrams for Bi₂ and Se₃ remain stable, sodium exhibits a notable change. At this energy level indicated by a resonance peak, weak orbital hybridization occurs between the 2s and 2p orbitals of Na and the 1s orbital of hydrogen. The Na 2s orbital hybridizes owing to its interaction with hydrogen, while its 2p orbital acts as a charge conduit. In Na–Bi₂Se₃, the charge is channeled back to the Na atom, increasing its electron count and confirming the charge transfer.

Hydrogen 1 orbital energy level extends and fragments under the Fermi level, suggesting potential for multiple hydrogen molecule adsorption. Additionally, the maximum of the hydrogen 1s orbital shifts leftward. The stability of adsorbing all hydrogen molecules is lower than that of individual molecules. In the PDOS of the adsorbed H₂ material, orbital overlaps are observed between the hydrogen 1s orbital and the Na 2s and 2p orbitals at −7.1, −6, and −5.9 eV, suggesting electrostatic interaction. This overlap indicates strong hybridization between Na atoms and H₂ molecules, resulting in sodium–hydrogen bond orbitals, where the adsorption process involves local electric field polarization by positive charges and orbital hybridization. This results in the division of charge within the hydrogen molecule, with one atom becoming negatively charged and the other positively charged, indicating polarization.

Fig. 5(g) PDOS presents the initial adsorbed hydrogen's 1s orbital peaks at −6.9 eV. Although Bi₂ and Se₃ show little change, there is a significant shift in K-PDOS. A resonance peak appears between the 2s and 2p orbitals of potassium and the 1s orbital of hydrogen, indicating weak orbital hybridization. Potassium's 2s orbital hybridizes owing to hydrogen interaction, while its 2p orbital acts as a charge conduit. K–Bi₂Se₃ redirects some charge back to potassium, increasing its electron count and confirming charge transfer. The 1s orbital of hydrogen extends and drops below the Fermi level, suggesting the potential for the adsorption of multiple hydrogen molecules. In the PDOS of adsorbed H₂ material at −7, −6.6, and −5.9 eV, orbital overlaps occur between hydrogen's 1s orbital and K 2s and 2p orbitals, suggesting electrostatic interaction. This overlap confirms robust hybridization between potassium atoms and hydrogen molecules, forming potassium–hydrogen bond orbitals. The bonding process between the substance and hydrogen primarily entails the polarization of positive charges and orbital fusion. The charge distribution within the hydrogen molecule divides into dual segments: one hydrogen atom carries an excess negative charge, and additional hydrogen holds an excess positive charge, illustrating the molecule's polarization.

3.8 Electron localization function

ELF determines the kinetic energy density, which is used to assess electron localization and delocalization. It spans from 0.5 to 1.0, indicating localized electron positions for bonding and nonbonding scenarios. Electron localization typically occurs within nucleus shells, covalent bonds, or lone pairs. Values between 0.0 and 0.5 indicate weak intermolecular van der Waals forces and suggest that electron delocalization manifests across electron shells.

As illustrated in Fig. 6(a), (d), and (g), the prominent green color signifies a decrease in surface charge, with ELF values ranging from 0.5 to 0.0, indicating ionic bonding. Conversely, Fig. 6(b), (e), and (h) depict ELF values between 1.0 and 0.5, suggesting the presence of covalent bonding. Fig. 6(c), (f) ad (i) illustrate ELF values between 0.5 and 0.0, indicating ionic bonding.

Fig. 6 ELF (a) 1H₂, (b) 9H₂, and (c) 18H₂ represent Li-decorated Bi₂Se₃; (d) 1H₂, (e) 9H₂, and (f) 18H₂ correspond to Na-decorated Bi₂Se₃; and (g) 1H₂, (h) 9H₂, and (i) 19H₂ represent K-decorated Bi₂Se₃.

3.9 Hirshfeld charge analysis

Hirshfeld charges are a method for measuring the distribution of atomic charges within a molecule. They are determined from the Hirshfeld surface, which partitions the molecular space into areas around each atom. These charges provide information about the electron density around each atom, indicating whether it is relatively positive or negative. Unlike formal charges, which are fixed, Hirshfeld charges are variable and respond to changes in the molecular environment or structure. They are frequently utilized in computational chemistry to assess molecular characteristics, intermolecular interactions, and chemical reactivity.

The investigation seeks to verify the occurrence of charge transfer between unaltered Bi₂Se₃ with a shared charge of −0.043 and Bi₂Se₃ modified with transition metals such as Li, Na, and K. This analysis aims to determine whether these transition metals can transfer charges to the Se sites of the Bi₂Se₃ layer, with charge values of 0.315e, 0.479e, and 0.559e, respectively. According to Hirschfield charge analysis, Bi₂Se₃ modified with Li and multiple hydrogen atoms shows a high charge transfer on the first hydrogen atom at 0.315e, as shown in Table 5. As the number of hydrogen atoms increases, the charge transfer decreases, with the 18th hydrogen atom having a charge transfer of 0.008e. This indicates that the hydrogen molecules were polarized under the electric field created by the ionized lithium atom. For Na-modified Bi₂Se₃ with hydrogen adsorption, the charge transfer on the first hydrogen atom is high at 0.480e. However, as the number of hydrogen atoms increases, the charge transfer decreases, with the 18th hydrogen atom showing a charge transfer of 0.174e. Similarly, for K-modified Bi₂Se₃, as detailed in Table 5, the charge transfer on 1st hydrogen atom is 0.551e. As the number of hydrogen atoms increases, the charge transfer gradually decreases, with the 19th hydrogen atom showing a charge transfer of 0.241e. Polarization was also confirmed through differential charge analysis, which revealed clear charge accumulation between the hydrogen and Li/Na/K atoms, as well as charge depletion between the hydrogen atoms.

Table 5 Charge transfer of Bi₂Se₃ on alkali metal Li/Na/K with multiple hydrogen

No. of H2 molecules	Q Li (e)	Q Na (e)	Q K (e)
1H2	0.315	0.480	0.551
2H2	0.310	0.465	0.529
3H2	0.311	0.454	0.500
4H2	0.279	0.723	0.476
5H2	0.199	0.407	0.452
6H2	0.281	0.375	0.444
7H2	0.208	0.374	0.41
8H2	0.210	0.357	0.404
9H2	0.208	0.315	0.385
10H2	0.185	0.292	0.344
11H2	0.181	0.267	0.311
12H2	0.169	0.197	0.275
13H2	0.167	0.218	0.261
14H2	0.146	0.178	0.052
15H2	0.029	0.047	0.023
16H2	0.131	0.184	0.024
17H2	0.008	0.211	0.270
18H2	0.008	0.174	0.237
19H2	—	—	0.241

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3.10 Molecular dynamics simulations

The molecular dynamics (MD) simulations depicted in the figure examine the hydrogen desorption behavior of alkali metal-decorated Bi₂Se₃ (Li, Na, and K) at different desorption temperatures, and all the simulations were conducted under a constant pressure of 10 atm.⁷² The energy evolution of Bi₂Se₃ systems decorated with Li, Na, and K under hydrogen loading is shown in Fig. 7(a1)–(c1) over a 12-picosecond simulation period. The temperature stability for each system is depicted in Fig. 7(a2)–(c2), where Li-decorated Bi₂Se₃ stabilizes at a desorption temperature of 906 K, Na-decorated Bi₂Se₃ stabilizes at 821 K, and K-decorated Bi₂Se₃ exhibits a higher desorption temperature of 1112 K.

Fig. 7 MD simulation visuals for the 18H₂, 18H₂, and 19H₂ + Li/Na/K–Bi₂Se₃ systems at 906 K, 821 K, and 1112 K. The outcomes demonstrate the changes in total energy (a1)–(c1) and temperature (a2)–(c2) over time (ps).

The Li-decorated system (a1) in the energy profiles shows more pronounced fluctuations, indicating dynamic interactions between the hydrogen and the substrate. However, the Na-decorated (b1) and K-decorated (c1) systems exhibit more stable energy behavior, particularly the K-decorated Bi₂Se₃, which displays minimal fluctuations but a slightly upward trend. This suggests that K forms stronger binding interactions with hydrogen, leading to higher desorption energy and more difficult hydrogen release than Li and Na.

The simulations indicate that K-decorated Bi₂Se₃ has the highest desorption temperature (1112 K), demonstrating the strongest interaction with hydrogen, which aligns with K's lower ionization energy than Li and Na. In contrast, Na and Li demonstrate lower desorption temperatures, making them more suitable for applications in which moderate hydrogen release conditions are needed.

AIMD calculations are conducted to investigate the reliability of different configurations. NVT (constant atomic number N, volume V, and temperature T) thermostat remains utilized to sustain a temperature of 400 K during the dynamic simulation, utilizing the Andersen thermostat method. In this investigation, the total simulation time was 10 picoseconds, with a time step of 0.25 picoseconds. Fig. 7 illustrates the stability of the Li/Na/K–Bi₂Se₃ system at 400 K following the AIMD simulation. As shown in Fig. 8, the maximum bond length for lithium adsorption is 3.15 Å at 9 ps, with overall peaks varying between 2.1 and 3.0 Å. For sodium, the maximum bond length is 3.2 Å at 6.2 ps, with the overall peaks between 2.6 and 3.0 Å. In the case of potassium adsorption, the maximum bond length is 3.4 at 9.8 ps, while the overall peaks range from 2.7 to 3.3. The small change in total energy implies the absence of unstable weak bonds in these systems.

Fig. 8 Fluctuation in the bond length of Li/Na/K atoms in Li/Na/K–Bi₂Se₃ at 400 K.

As a precise indicator of stability, a change in bond length fluctuation of Li/Na/K-decorated Bi₂Se₃ is observed. During the MD simulations, the bond length fluctuations for Li–Bi₂Se₃, Na–Bi₂Se₃, and K–Bi₂Se₃ throughout 10 picoseconds were plotted at an equilibrium temperature of 400 K. From this plot, it can be concluded that the overall bond length fluctuations for these are 8.3%, 7.9%, and 8.2%, respectively.⁷³

3.11 Thermodynamic stability analysis

The thermodynamic stability of a hydrogen-adsorbed composite under specific temperature and pressure conditions can be evaluated by calculating its relative energy using the following equation:^17,74

E_r = E_{(Bi2Se3+metal+nH2)} − E_{(Bi2Se3+metal)} − n[E_H2 − μ(T,P)], (7)

where E_{(Bi2Se3+metal+nH2)}, E_{(Bi2Se3+metal)}, and E_H2 are the total energy of the structure, the total energy of the metal-decorated Bi₂Se₃, and the energy of the hydrogen, respectively. Here, n is the number and the μ(T,P) can be determined using the following equation:where P₀ = 1 bar and k_B is the Boltzmann constant. The term (ΔH − TΔS) represents the change in chemical potential resulting from increasing the temperature from 0 K to the target temperature T at constant pressure P₀. In this expression, ΔH denotes the change in enthalpy, while TΔS accounts for the entropy contribution. The values of (ΔH − TΔS) were obtained from the thermochemical NIST database.⁷⁵

Efficient hydrogen storage materials must operate effectively under ambient conditions, particularly near room temperature. To assess this capability, we investigated the thermal stability of the studied systems at their maximum hydrogen storage capacities across a range of temperatures and pressures. Ambient conditions were defined as 298 K and 0.1 MPa for reference.

As shown in Fig. 9(a), the relative energy was plotted as a function of the temperature at standard pressure. A system is considered thermodynamically unstable when relative energy becomes positive, signifying the onset of spontaneous hydrogen desorption. The critical temperatures corresponding to this transition are approximately 243 K and 232.2 K for the Li/Na/K–Bi₂Se₃-decorated configurations.

Fig. 9 (a) Temperature-dependent behavior of E_r for the adsorption of nH₂ molecules on Li/Na/K–Bi₂Se₃-decorated surfaces under standard atmospheric pressure (1 bar). (b) Pressure-dependent variation in E_r for H₂ adsorption on Li/Na/K–Bi₂Se₃-decorated surfaces at a fixed temperature of 298 K.

Fig. 8(b) presents the variation of relative energy with pressure for the studied systems at room temperature (298 K). Under these conditions, the Bi₂Se₃ sheets decorated with Li, Na, and K can adsorb up to 18 and 19 hydrogen (H₂) molecules at pressures below approximately 20 MPa. Notably, hydrogen uptake for all three systems occurs at relatively moderate pressures, demonstrating favorable adsorption behavior under ambient temperature. These pressure requirements closely agree with the operational standards outlined by the U.S. Department of Energy, which indicate that hydrogen refueling stations typically operate within a pressure range of 3–13 MPa, similar to the conditions used for liquefied natural gas (LNG) storage and distribution systems.⁷⁶ These results underscore the potential of Li-, Na-, and K-functionalized Bi₂Se₃ monolayers as promising materials for practical hydrogen storage applications, particularly in onboard fuel cell technologies.

Conclusions

In summary, the first principles study of alkali metal-decorated Bi₂Se₃ for hydrogen storage applications has demonstrated the potential of Bi₂Se₃ as an efficient hydrogen storage material when enhanced with alkali metals, such as Li, Na, and K. The computational analysis revealed significant alterations in the band structure and electronic properties of Bi₂Se₃ upon decoration with these metals, possibly leading to a metallic nature and improved hydrogen adsorption capabilities. This study showed that Li/Na/K–Bi₂Se₃ substrates could be achieved within the US DOE criteria. The results indicate that alkali metal-decorated Bi₂Se₃ is a promising candidate for developing advanced hydrogen storage systems, contributing to broader efforts toward sustainable and efficient energy solutions.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

Data are available from the authors upon request.

Acknowledgements

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University, Saudi Arabia, for funding this work through the Large Research Project under grant number RGP-2/712/46.

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