Structural, Mechanical, Electronic, and Optical Properties of Hydrogen-Storage Magnesium-Based Mg₂XH₉ (X = Cs, Rb)

Abstract

Metal hydrides are emerging hydrogen-storage materials that have attracted much attention for their stability and practicality. The novel magnesium-based metal hydride Mg₂CsH₉ was investigated using the CALYPSO software (version 7.0). First-principles predictive methods were then employed to investigate the structural, mechanical, electronic, optical, and hydrogen-storage properties of Mg₂CsH₉ and its alkali metal substitution structure Mg₂RbH₉. The negative formation energy, compliance with the Born stability criterion, and absence of imaginary modes in the phonon spectrum collectively confirm the thermodynamic, mechanical, and dynamic stability of Mg₂XH₉ (X = Cs, Rb), fulfilling the basic criteria for practical hydrogen-storage applications. Mg₂RbH₉ is particularly outstanding in terms of its hydrogen-storage capacity, with a gravimetric capacity of 6.34 wt% and a volumetric capacity as high as 92.70 g H₂/L, surpassing many conventional materials. The pronounced anisotropic characteristics of both compounds further enhance their practicality and adaptability to complex working conditions. An analysis of Poisson’s ratio revealed that the chemical bonding in both compounds is predominantly ionic. The details of the band structures and density of states indicate that Mg₂CsH₉ and Mg₂RbH₉ are semiconductors. Their optical properties confirm them as being high-refractive-index materials.

1. Introduction

Carbon combustion and inefficient fossil fuel utilization are the primary causes of a ~35% increase in CO₂ emissions [1]. Consequently, the growing global emphasis on sustainable development has made clean energy a focus of interest in the energy sector [2,3,4,5,6,7]. Hydrides, long regarded as promising energy carriers, have attracted increasing attention for their high calorific value and zero pollutant emissions [8]. Their outstanding degree of applicability and environmental compatibility compared with other proposed fuels, makes them a choice material for energy storage [9]. For stationary power systems and portable devices, hydrides offer significant advantages in terms of safety, environmental performance, and cost-effectiveness [10].

However, hydrogen faces numerous technical challenges to its industrialization as a sustainable energy source. Current extensive research efforts aim to discover novel materials with a high hydrogen capacity and a suitable operating temperature range to meet industrial requirements [11]. The superior safety of metal hydrides with regard to compressed or liquefied hydrogen has been demonstrated in recent years, leading to their inclusion in commercial supply chains. Their practical usability is enhanced by their ability to release hydrogen under ideal conditions of ambient temperature and pressure [6,12]. However, metals, hydrides, hydroxides, and their alloys or composites still exhibit certain drawbacks such as relatively weak resistance to corrosive influences from environmental factors like temperature, oxygen, and electromagnetic radiation. In contrast, oxide compounds demonstrate significantly higher stability when used up to 1000 °C [13]. Considering the various available hydrogen-storage materials, magnesium-based hydrides have unique advantages that make them some of the most promising candidates. Magnesium exhibits a high hydrogen- storage capacity (7.65 wt% gravimetric and 110 g H₂/L volumetric) and is abundant in the Earth’s crust, promising conditions for cost-effective large-scale applications [14]. Cs atoms, which are also uniquely advantageous in hydrogen-storage material design, are characterized by the largest atomic radius (265 pm). The hydrogen storage capacity of cesium-containing hydrogen storage structures can be significantly enhanced by expanding the lattice spacing and optimizing hydrogen adsorption sites [15]. Similarly, the double-perovskite structure has displayed remarkable hydrogen-storage capability. For example, the hydrogen capacities of Mg₂FeH₆ and Be₂FeH₆ are 5.43 and 7.9 wt%, respectively, highlighting their potential as hydrogen-storage materials [16]. Similarly, Be₂CrH₆ and Be₂MnH₆ exhibit 7.9 and 7.6 wt% hydrogen contents, respectively, making them strong candidates for onboard hydrogen-storage in new energy vehicles [17].

To screen for novel materials with high hydrogen density, we increased the number of hydrogen atoms within the magnesium-based perovskite framework. Subsequently, leveraging the large atomic radius of cesium (Cs), we introduced Cs atoms to expand the structural space. Finally, we employed the particle swarm optimization crystal structure analysis software (CALYPSO7.0) [18] to search for Mg₂CsH₉-type structures. Density functional theory (DFT) calculations confirmed that both the Mg₂CsH₉ structure obtained through structural search and the Mg₂RbH₉ structure derived via alkali metal substitution exhibited stability and demonstrated excellent hydrogen storage performance. In addition, optical properties such as transmittance, reflectivity, and absorption are closely related to the electronic structure, hydrogenation state, and kinetic behavior of hydrogen-storage materials. The present study therefore also analyzed the optical properties. In both compounds, the incorporation of specific metal atoms (Cs/Rb) into the Mg-H framework may weaken the strong ionic Mg-H bonds, potentially reducing the desorption energy barrier and lowering the required hydrogen release temperature. This mechanism suggests a potential pathway for addressing current energy storage challenges.

2. Computational Details

The variable cellular crystal structure of Mg₂CsH₉ was simulated using the CALYPSO code, a widely used tool whose reliability for stable crystal structure prediction has been verified in various systems [19,20]. During the prediction process, the number of individuals in each generation was set to 30, and the initial structure was constructed randomly within the symmetry constraints. A total of 50 generations were set to ensure that the structural evolution met the convergence criteria. The structural, electronic, elastic, dynamic, and optical properties of Mg₂XH₉ (X = Cs, Rb) were then predicted using the Vienna Ab initio Simulation Package (VASP5.4.4) [21] based on density functional theory (DFT) [22]. Exchange and correlation effects in electron–electron interactions were described using the generalized gradient approximation (GGA) combined with the Perdew–Burke–Ernzerhof functional (PBE) [23]. A plane-wave cutoff energy of 600 eV was applied, and a 6 × 6 × 6 Monkhorst-Pack k-point grid was used to ensure sufficient convergence of the total energy, with a precision of 1 × 10⁻⁵ eV [24,25]. All structures were subjected to lattice optimization and fully relaxed throughout the computational process. The phonon dispersion curves were computed using the Phonopy(version 2.12) package, employing a 2 × 2 × 2 supercell to evaluate the dynamic stability of the materials.

3. Results and Discussion

3.1. Structural Stability and Hydrogen Storage Performance

Mg₂XH₉ adopts a cubic structure with space group Pn$\overline{3}$ (No. 201). The spatial structure of Mg₂XH₉ (X = Cs, Rb) is shown in Figure 1a. Views along the [111] directions are displayed in Figure 1b, where 18 hydrogen atoms form hydrogen cages surrounding the X atom. Specific atomic fractional coordinates are provided in Appendix A. The formation energies of Mg₂XH₉ (X = Cs, Rb) were calculated using the following formula [26]:

$${\mathsf{\Delta }H}_f=\left[E\left({\mathrm{M}\mathrm{g}}_2\mathrm{X}{\mathrm{H}}_9\right)-2E\left(\mathrm{M}\mathrm{g}\right)-E\left(\mathrm{X}\right)-9E\left(\mathrm{H}\right)\right]/12$$

(1)

where E(Mg₂XH₉) represents the total energy of Mg₂XH₉, and E(Mg), E(X), and E(H) represent, respectively, the average energies of each Mg, X, and H atom in their elemental crystal forms. The formation energies of the two compounds (see

Table 1. The possible decomposition pathways and relative formation energies E_f (eV/atom) of these Mg₂XH₉ structures.

Structures	Possible Decomposition Path	Ef
Mg2CsH9	Mg2CsH9 = 2MgH2 + CsH + 2H2	−0.118
Mg2RbH9	Mg2RbH9 = 2MgH2 + RbH + 2H2	−0.165

) were negative, confirming their thermodynamic stability.

To further evaluate the thermodynamic stability of these ternary compounds, we searched the Open Quantum Materials Database (OQMD) for relevant stable compounds and constructed decomposition reaction pathways for the Mg₂XH₉ structures. The relative formation energy (E_f) was calculated to assess stability: If E_f < 0, the structure is thermodynamically stable and likely synthesizable via the proposed pathway. If E_f > 0, the structure has lower thermodynamic stability and risks decomposition. As shown in Table 1, all E_f values were negative, confirming that these two structures are thermodynamically stable and potentially synthesizable from related compounds.

Mg₂XH₉ adopts a cubic crystal structure with three independent elastic constants (C₁₁, C₁₂, and C₄₄) and its mechanical stability was assessed using the Born criteria [27]:

$$C_{11}-C_{12}>0,C_{11}+2C_{12}>0,C_{44}>0$$

(2)

As shown in

Table 2. Optimized lattice constants, volume, formation energies, elastic constants, gravimetric hydrogen capacity, volumetric hydrogen capacity, and desorption temperature of the compounds Mg₂XH₉ (X = Cs, Rb).

Parameters	Mg2CsH9	Mg2RbH9
$a\left(\mathrm{\AA }\right)$	8.867	8.663
$\mathrm{V}\left({\mathrm{\AA }}^3\right)$	697.1	650.1
${\mathsf{\Delta }H}_{\mathrm{f}}\left(\mathrm{e}\mathrm{V}/\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\right)$	−0.387	−0.382
$C_{11}\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	19.6	20.9
$C_{12}\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	10.1	11.1
$C_{44}\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	14.1	14.6
$C_{\mathrm{w}\mathrm{t}}\mathrm{\%}$	4.76	6.34
${\rho }_{\mathrm{v}\mathrm{o}\mathrm{l}}\left(\mathrm{g}{\mathrm{H}}_2/\mathrm{L}\right)$	86.46	92.70
$T_{\mathrm{d}\mathrm{e}\mathrm{s}}\left(\mathrm{K}\right)$	286	282

, both metal hydrides satisfy the stability criteria expressed in Equation (2), confirming their mechanical stability. In cubic crystals, uniaxial compression along the x-axis is represented by C₁₁, whereas resistance to deformation under pure shear stress is represented by C₄₄. The C₁₁ values of both hydrides were higher than their corresponding C₄₄ values, indicating that their resistance to uniaxial compression was greater than that to shear deformation.

Phonon dispersion spectra are key indicators of the dynamical stability of materials. As shown in Figure 2, the phonon frequencies of both compounds were non-negative throughout the Brillouin zone. Imaginary frequencies below zero were not observed within the Brillouin zone, thereby confirming the dynamical stability of Mg₂CsH₉ and Mg₂RbH₉.

To evaluate the hydrogen-storage performance of Mg₂XH₉, the gravimetric hydrogen-storage capacity was assessed based on the following formula [28]:

$$C_{\mathrm{w}\mathrm{t}}\mathrm{\%}=\left({\displaystyle \frac{{nm}_{\mathrm{H}}}{m_{\mathrm{H}\mathrm{o}\mathrm{s}\mathrm{t}}+{nm}_{\mathrm{H}}}}\times 100\right)\mathrm{\%}$$

(3)

where n denotes the atomic ratio between hydrogen atoms and the host material (Mg₂X), and $m_{\mathrm{H}}$ and $m_{\mathrm{H}\mathrm{o}\mathrm{s}\mathrm{t}}$ are the molar masses of hydrogen and the host material (Mg₂X), respectively. The hydrogen-storage capacity of Mg₂RbH₉ was 6.34 wt%, demonstrating significant potential compared with common hydrogen-storage materials such as NaAlH₄ (5.6 wt%) [29] and LaNi₅H₆ (1.4 wt%) [30], thus Mg₂RbH₉ demonstrates significant potential as a hydrogen-storage material.

Volumetric storage capacity, which quantifies the amount of hydrogen stored within a specific volume, is a key parameter for evaluating the hydrogen storage capability of materials [31]. Its mathematical expression is given as follows:

$${\rho }_{\mathrm{v}\mathrm{o}\mathrm{l}}={\displaystyle \frac{N_{\mathrm{H}}·m_{\mathrm{H}}}{V\left(L\right)·N_{\mathrm{A}}}}$$

(4)

where $N_{\mathrm{H}}$ denotes the number of absorbed hydrogen atoms, $m_{\mathrm{H}}$ represents the molecular weight of hydrogen, V(L) indicates the absorbent volume (i.e., the cubic unit cell volume in Table 2), and $N_{\mathrm{A}}$ is Avogadro’s number. As shown in Table 2, Mg₂RbH₉ exhibited a higher hydrogen-storage capacity due to its smaller volume, which is determined by the cation size (Rb⁺). Larger cation sizes lead to increased unit cell volumes, and consequently, a lower volumetric storage capacity.

During desorption, thermodynamic and kinetic factors act synergistically to influence the desorption rate and temperature. The desorption temperature, a key parameter for characterizing hydrogen-storage, is the temperature at which hydrogen becomes released from solid hydrides [32]. Its value is primarily calculated as:

$$T_{\mathrm{d}\mathrm{e}\mathrm{s}}={\displaystyle \frac{\left|∆H_f\right|}{∆S}}$$

(5)

where ∆H_f (see Table 2) and ∆S represent, respectively, the formation enthalpy of solid hydride and the entropy change of hydrogen (approximately −130.7 J/mol) [33]. The ideal temperature range is typically between 233 and 333 K [34]. The calculation results presented in Table 2, show that the desorption temperatures of both Mg₂CsH₉ and Mg₂RbH₉ fall within this ideal range. The $T_{\mathrm{d}\mathrm{e}\mathrm{s}}$ values of 285.69 K or 282 K in Table 2 suggest that these structures may release hydrogen at room temperature. Therefore, the materials should be stored in environments slightly below $T_{\mathrm{d}\mathrm{e}\mathrm{s}}$ or under pressure regulation to suppress hydrogen release. This property makes them suitable for mobile devices requiring rapid low-temperature hydrogen release, avoiding risks associated with high-temperature operations.

3.2. Mechanical Properties

The calculation of elastic constants facilitates the assessment of material stiffness, brittleness, ductility, mechanical stability, and elastic anisotropy. In VASP-based calculations, elastic constants are determined using the stress-strain method to comprehensively analyze the mechanical properties of the metal hydrides. Typically, elastic moduli include the bulk modulus, Young’s modulus, shear modulus, and Poisson’s ratio, which are calculated using the following formulas [35,36]:

$$B={\displaystyle \frac{C_{11}+2C_{12}}{3}}$$

(6)

$$E={\displaystyle \frac{9BG}{3B+G}}$$

(7)

$$G_{\mathrm{V}}={\displaystyle \frac{C_{11}-C_{12}+3C_{44}}{5}}$$

(8)

$$G_{\mathrm{R}}={\displaystyle \frac{5C_{44}\left(C_{11}-C_{12}\right)}{4C_{44}+3\left(C_{11}-C_{12}\right)}}$$

(9)

$$G={\displaystyle \frac{G_V+G_R}{2}}$$

(10)

$$v={\displaystyle \frac{3B-2G}{6B+2G}}$$

(11)

When investigating mechanical properties, the bulk modulus (B), Young’s modulus (E), and shear modulus (G) characterize a material’s resistance to volumetric compression, elastic deformation, and shear strain, respectively. As shown in

Table 3. Calculated bulk modulus, Young’s modulus, shear modulus, elastic anisotropy, B/G ratio, Poisson’s ratio, Vickers hardness, melting temperature, machinability index, average sound velocity, and Debye temperature for the Mg₂XH₉ (X = Cs, Rb) structures.

Parameters	Mg2CsH9	Mg2RbH9
$B\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	13.3	14.4
$E\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	22.3	23.3
$G\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	9.1	9.5
$A$	2.97	2.96
$B/G$	1.46	1.52
$\mathsf{\nu }$	0.22	0.23
$H_{\mathrm{v}}\left(\mathrm{G}\mathrm{P}\mathrm{a}\right)$	1.68	1.56
$T_{\mathrm{m}}\left(\mathrm{K}\right)$	613	618
${\mu }^M$	0.95	0.98
$V_{\mathrm{m}}(\mathrm{k}\mathrm{m}/\mathrm{s})$	2.49	2.82
${\theta }_{\mathrm{D}}\left(\mathrm{K}\right)$	303	352

, Mg₂RbH₉ exhibits a high resistance to compression. The ductility and brittleness of materials can be assessed using the Pugh ratio (B/G). When B/G > 1.75, the material is considered ductile, whereas B/G < 1.75 indicates brittleness. The calculated B/G values for Mg₂CsH₉ (1.46) and Mg₂RbH₉ (1.52) were both below this critical value, confirming their brittle nature. This observation is consistent with the commonly reported low B/G ratios in metal hydrides [34]. Notably, the brittle characteristics of these compounds have significant engineering relevance in the context of the safe handling and transportation of hydrogen storage systems. Further analysis based on Poisson’s ratio indicates that the ν values of Mg₂CsH₉ (0.221) and Mg₂RbH₉ (0.23) are both close to 0.25, suggesting that their chemical structures are predominantly governed by ionic bonding. This result agrees well with the theoretical predictions derived from the charge-density distribution calculations.

The elastic anisotropy factor can be expressed using the three independent elastic constants C₁₁, C₁₂, and C₄₄, as defined by the following equation.

$$A={\displaystyle \frac{2C_{44}}{C_{11}-C_{12}}}$$

(12)

As shown in Table 3, the anisotropy factor of the metal hydrides Mg₂XH₉ deviate from 1, indicating elastic anisotropy.

Vickers hardness, melting point, and machinability index (${\mu }^M$) are key indicators used for assessing mechanical properties, as they not only reflect structural strength but also play decisive roles in practical applicability. To evaluate the mechanical properties, Vickers hardness (based on the Chen model), melting temperature, and machinability index, are estimated using the following formulas [37,38,39]:

$$H_{\mathrm{v}}={2\left(k^{2}G\right)}^{0.585}-3$$

(13)

$$T_{\mathrm{m}}=\left[553+5.911\times C_{12}\right]\pm 300$$

(14)

$${\mu }^{\mathrm{M}}={\displaystyle \frac{B}{C_{44}}}$$

(15)

The parameter k is defined as the ratio of shear modulus to bulk modulus (i.e., k = G/B). Based on the data in Table 3, the comparable melting points and hardness values of Mg₂CsH₉ and Mg₂RbH₉ confirm their virtually equivalent crystal structural strength and thermal stability. The machinability index ${\mu }^{\mathrm{M}}$, which correlates with machinability, exhibits a direct proportionality to mechanical processability enhancement [40,41,42,43,44]. As shown in Table 3, it can be reasonably inferred that Mg₂RbH₉ shows superior processability compared with Mg₂CsH₉.

To further understand the structural stability of the materials, the Debye temperature ${\theta }_D$ was also calculated using the following formula [45]:

$${\theta }_{\mathrm{D}}={\displaystyle \frac{h}{k}}{\left({\displaystyle \frac{3n}{4\pi V}}\right)}^{{\displaystyle \frac{1}{3}}}{v}_{\mathrm{m}}$$

(16)

where h denotes the Planck constant, k is the Boltzmann constant, n is the number of atoms per unit cell, V is the crystal volume, and $v_m$ is the average sound velocity. The Debye temperature generally reflects the highest excited state of the atomic vibrational energy levels in a crystal, and its value is closely associated with the chemical bond strength, lattice dynamic characteristics, and thermal transport properties. A high Debye temperature implies strong interatomic bonding and intense internal interactions within the system [46]. The results in Table 3 suggest that Mg₂RbH₉ exhibits tighter internal atomic bonding, demonstrating superior structural cohesion performance.

3.3. Electronic Band Structure and Density of States

To investigate the electronic properties of the magnesium-based alkaline metal hydrides Mg₂XH₉ (X = Cs, Rb), we calculated their band structures using the GGA functional and the Heyd–Scuseria–Ernzherof (HSE06) hybrid functional in VASP [47,48]. The HSE06 hybrid functional is beneficial for accurately determining the band gap of Mg₂XH₉. The calculation results indicate that both materials exhibit direct band gap characteristics, as illustrated in Figure 3. Using the GGA method, the Mg₂CsH₉ band gap was calculated to be 0.87 eV, whereas that of Mg₂RbH₉ was significantly lower at 0.67 eV. The HSE06 hybrid functional accurately determined the band gap as 1.65 eV (Mg₂CsH₉) and 1.12 eV (Mg₂RbH₉). The narrowing of the band gap implied a lower electron transition barrier [49], which was identified as a critical factor for enhancing hydrogen-storage performance. This indicates the enhanced potential of Mg₂RbH₉ for application as a hydrogen-storage material. Notably, the Fermi level (marked by the red dashed lines) was biased toward the valence band maximum in both cases. Combined with the hole concentration analysis, both materials were identified as p-type semiconductors. This carrier characteristic could potentially optimize the hydrogen-storage performance through a hole-conduction mechanism.

As illustrated in Figure 3, the electronic structure of the Mg₂XH₉ (X = Cs, Rb) compounds shows the valence bands being predominantly dominated by the s-orbitals of hydrogen atoms, indicating their decisive role in the electronic structure of the valence. The conduction band region is primarily dominated by the d-orbital of the X atoms (Cs/Rb), whereas the p-orbital of the Mg atoms participates only marginally in low-energy regions. The highly electronegative X atoms dominate the formation of the conduction band, whereas hydrogen atoms maintain lattice stability through strong ionic bonding.

As illustrated in Figure 4, the electron localization function (ELF) analysis showed that Mg₂XH₉ (X = Cs, Rb) exhibits pronounced high electron density regions (ELF ≈ 1) surrounding hydrogen atoms in the (111) crystallographic plane. A pronounced electron localization gradient between the X (Cs/Rb) and H atoms indicates strong localized characteristics in H-X bonding. Bader charge analysis indicates that, on average, each H atom gains approximately 0.473 e from Mg and X atoms (X = Cs) or 0.427 e from Mg and X atoms (X = Rb), which is consistent with the high electron density distribution around H atoms observed in the ELF mapping. The highly localized electron clouds (ELF > 0.8) surrounding the H atoms, combined with significant charge transfer (>0.85 e), collectively demonstrate the ionic hybrid bonding characteristics of the Mg-X-H system. This electronic-scale evidence provides fundamental insights into the structural stability of the materials [50,51].

3.4. Optical Properties

The optical properties of Mg₂XH₉ (X = Cs, Rb) were comprehensively analyzed and described, focusing on their dielectric function, refractive index, absorption, reflectivity, and energy-loss function.

The dielectric function was calculated as [52,53]:

$$\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+{\epsilon }_2\left(\omega \right)$$

(17)

The real part of the dielectric function ${\epsilon }_1\left(\omega \right)$, which characterizes the polarizability and dispersion relations in surface electromagnetic responses (Figure 5a), displayed a higher peak value for Mg₂CsH₉ (approximately 8.6) compared with Mg₂RbH₉ (approximately 7.9) within the low-frequency region (0–10 eV), indicating a stronger polarization response to low-frequency electric fields in Mg₂CsH₉. The imaginary part ${\epsilon }_2\left(\omega \right)$, which reflects the light absorption capacity through electronic band transitions (Figure 5b), displayed peaks around 7.8 and 7.2 for Mg₂CsH₉ and Mg₂RbH₉, respectively. This confirms the superior low-frequency photon absorption efficiency in Mg₂CsH₉, which correlates with the electron transition characteristics of H-X bonds. In the high-energy region (10–20 eV), the real part of the dielectric function ${\epsilon }_1\left(\omega \right)$ for both materials approached 1 (the vacuum dielectric constant), while the imaginary part ${\epsilon }_2\left(\omega \right)$ decayed to near zero. This behavior originates from truncation effects in the calculation, which exclude high-energy interband transitions such as inner-shell electronic excitations. In real materials, plasmon resonance (>15 eV) should exist in this energy range, but the independent-particle approximation (IPA) fails to account for such many-body effects.

The absorption coefficients of Mg₂CsH₉ and Mg₂RbH₉, shown in Figure 6a, were zero in the energy range below their respective band-gaps (0.62 eV and 0.59 eV, respectively), which confirms their semiconducting nature. With increasing photon energy, the absorption peaks were primarily distributed in the UV region (>3.1 eV), indicating a strong tendency of Mg₂CsH₉ and Mg₂RbH₉ to absorb UV light.

As shown in Figure 6b, the initial reflectivity values of Mg₂CsH₉ and Mg₂RbH₉ were approximately 0.19 and 0.18, respectively. With increasing photon energy, the maximum reflectivity of Mg₂CsH₉ reached approximately 0.36 at 3.2 eV, whereas that of Mg₂RbH₉ peaked at approximately 0.38 at 3.4 eV. In the visible light-region, the reflectivity of Mg₂CsH₉ was higher than that of Mg₂RbH₉; however, in the far-ultraviolet region, Mg₂RbH₉ was more reflective. When the photon energy exceeded 27 eV, the reflectivity of both materials approached zero, indicating enhanced transparency to high-energy photons, which is consistent with the attenuation behavior of dielectric responses.

The extinction coefficients K(ω), presented in Figure 6c, displayed peaks at approximately 1.85 for Mg₂CsH₉ and 1.83 for Mg₂RbH₉, indicating minor differences between the two hydrides. The similarity in these peak values suggests a comparable degree of interaction between the incident photon radiation and each material. With increasing photon energy, the extinction coefficient showed an overall decreasing trend, indicating a weakened attenuation effect in the high-energy region, which favors light propagation within the material.

The energy-loss function for Mg₂CsH₉, presented in Figure 6d, showed a double-peak structure at 16.8 eV (L = 2.75) and 18.9 eV (L = 2.52), while the loss peaks of Mg₂RbH₉ shifted toward the higher-energy region, appearing at 21.2 eV (L = 1.92) and 22.8 eV (L = 2.08). The overall energy-loss intensity for Mg₂CsH₉ was approximately 30% higher than that for Mg₂RbH₉, indicating more pronounced collective electron oscillations (plasmons). This may be attributed to the enhanced polarization of the electron cloud induced by the larger radius of the Cs atom. At 0 eV, both substances had a loss function value of 0. The optical and electrical characteristics of these compounds make them suitable for use in LEDs and solar cells.

Figure 6e illustrates the variation of the refractive index n(ω) of the two hydrides. The static refractive index n(0) was approximately 2.5, which meets the requirements for high-refractive-index optical materials (n > 2.0). In the range of 7.5–20 eV, the fluctuation amplitude of the refractive index of Mg₂RbH₉ (Δn = 0.4) was smaller than that of Mg₂RbH₉ (Δn = 0.8), indicating a more stable optical response. When the photon energy exceeded 25 eV, n(ω) for both materials approached 1, consistent with the dielectric response of a vacuum and confirming the physical mechanism of dielectric polarization loss in the high-energy region.

4. Conclusions

Based on first-principles methods, the thermodynamic, hydrogen-storage, mechanical, electronic, and optical properties of magnesium-based alkali metal hydrides Mg₂XH₉ (X = Cs, Rb) were predicted. According to the Born stability criteria, both hydrides are mechanically stable. The Poisson’s ratio values confirmed that bonding in both compounds is predominantly ionic. The results also indicate that these alkali metal hydrides exhibit elastic anisotropy. The band structure analyses revealed their semiconducting nature, while the density of state analysis revealed that the s-orbitals of hydrogen atoms primarily influence the valence band, whereas the conduction band is mainly contributed by the d-orbital of X atoms, with smaller contributions from Mg atoms. The hydrogen-storage performance analysis revealed that Mg₂RbH₉ has a high storage capacity of 6.34 wt%. The optical properties showed that Mg₂XH₉ (X = Cs, Rb) exhibit favorable refractive indices, thereby classifying them as high-refractive-index materials. Theoretically, Mg₂RbH₉ demonstrates excellent mechanical, electronic, and hydrogen-storage properties, suggesting its strong potential as a candidate for future solid-state hydrogen-storage applications.