Insight into the effect of Mg-substitution on the electronic, optoelectronic, and hydrogen storage density of NbH₂ fluorite structured: a DFT study

Abstract

In the quest for multifunctional hydrogen storage materials, this study investigates the structural, electronic, and optical properties of NbH₂, MgH₂, and a series of Mg-substituted NbH₂ compounds (Mg-NbH₂, Mg₂-NbH₂, and Mg₃-NbH₂) using first-principles density functional theory (DFT) based on GGA/PBE and HSE03 methods. The motivation stems from the need to overcome the well-known limitations of MgH₂, particularly its high desorption temperature and poor reversibility, by introducing Mg into the NbH₂ fluorite framework. Structural optimization revealed a fluorite-type geometry, with Mg substitution inducing moderate lattice distortion and increasing unit cell volume from 97.22 to 103.45 ų. The Mg-NbH₂ system achieved a high density of 10.78 g cm⁻³ and exhibited a favorable hydrogen gravimetric capacity of 3.33 wt%, offering a promising trade-off between storage potential and structural stability. Electronic structure analysis confirmed metallicity across all substituted systems, while MgH₂ retained a non-metallic nature. A progressive decrease in total density of states was observed from 7.0 (NbH₂) to 2.0 (Mg₃-NbH₂), suggesting tunable electronic characteristics. Optical studies revealed that Mg-NbH₂ displayed the strongest dielectric response (ε₂ ≈ 85), the highest refractive index (n₁ ≈ 3.2), and reduced optical losses compared to its parent compounds. Notably, it retained a high optical conductivity (∼13 S m⁻¹) and strong absorption in the visible range, making it a potential candidate for photocatalytic and optoelectronic applications. These results demonstrate that Mg substitution into NbH₂ significantly enhances its multifunctional behavior, offering a viable pathway to improve hydride-based materials for advanced hydrogen storage and light-harvesting technologies.

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1. Introduction

Hydrogen energy is a cornerstone of clean energy technologies due to its high energy density, abundance, and eco-friendly nature. Metal hydrides have gained significant attention from various hydrogen storage materials due to their reversible hydrogen absorption and desorption capabilities.¹ Transition metal hydrides, particularly those based on niobium (Nb), exhibit favorable thermodynamic and kinetic properties for hydrogen storage.² Niobium dihydride (NbH₂) with a fluorite crystal structure represents a promising candidate because it stores considerable amounts of hydrogen while maintaining structural integrity.³ However, one of the prevailing challenges in advancing hydrogen storage systems lies in optimizing their storage density, electronic conductivity, and optical characteristics, which influence material performance in real-world applications. In this regard, substitutional doping, especially with lightweight and electropositive elements such as magnesium (Mg), has been widely explored as a strategic approach to tailor the intrinsic properties of metal hydrides. Mg-substitution has the potential to enhance the hydrogen storage capacity, tune the electronic band structure, and improve optoelectronic performance through lattice modification and charge redistribution.^4,5

Magnesium (Mg), an alkaline earth metal with atomic number 12, is known for its low atomic weight, high electropositivity, and abundance in the Earth's crust. Its favorable characteristics, including a small ionic radius (0.72 Å) and good thermal and chemical stability, make it an attractive candidate for substitutional doping in various materials.^6,7 The ability of Mg²⁺ ions to replace other cations in crystal lattices enables the tuning of electronic, structural, optical, and chemical properties of host compounds.⁸ In materials research, Mg-substitution has been explored extensively across ceramics, hydrides, semiconductors, and biomaterials due to its role in enhancing functionality and performance.^9,10 The influence of Mg-substitution has been well-documented in calcium phosphate-based ceramics. A study on Mg-substituted tricalcium phosphate (TCP) demonstrated that partial replacement of Ca²⁺ ions with Mg²⁺ leads to measurable structural changes.¹¹ Specifically, the substitution resulted in a contraction of the unit cell, as indicated by shifts in X-ray diffraction (XRD) peaks and a linear decrease in unit cell parameters (a₀ and c₀) and molar volume (V₀) with increasing Mg content (up to 10 mol%). These structural modifications suggest that Mg²⁺ ions are readily incorporated into the TCP lattice. Additionally, the substitution significantly reduced the dissolution rate of the resulting material in aqueous solution, indicating improved chemical stability, a desirable feature for biomedical applications. Hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂), the principal mineral component of human bone and teeth, has also been the subject of extensive Mg-substitution studies.¹² High-precision hybrid DFT calculations and experimental synthesis revealed that Mg incorporation into HAP causes a reduction in lattice parameters and a noticeable distortion in the structure.¹³ The substitution at different calcium sites (Ca₁ and Ca₂) alters the electronic structure, energy levels, band gap, and bulk modulus. Particularly, substitution at the Ca₂ site was more thermodynamically favorable and had a stronger effect on the infrared (IR) spectra and local structural asymmetry. These changes in local bonding environments directly influence the optical and electronic properties of HAP, making Mg-substituted HAP suitable for controlled reactivity in biological and photocatalytic systems. Interestingly, while low Mg content had a limited impact on basic catalytic reactivity, higher Mg concentrations led to structural disorder and nonstoichiometry, reducing the number of active basic sites. In such cases, new phases such as whitlockite were observed, highlighting a concentration-dependent tradeoff between structural stability and functionality. This aligns with the broader understanding that substitution levels must be carefully optimized to avoid undesired phase transitions or defect formation.

The motivation for this study stems from the growing need to enhance the hydrogen storage capacity and optoelectronic performance of existing fluorite-type metal hydrides. Among them, NbH₂ stands out due to its stable fluorite structure, favorable electronic conductivity, and intrinsic hydrogen affinity.^14,15 However, its hydrogen storage density and band gap characteristics remain suboptimal for advanced applications. Magnesium (Mg) was chosen as a dopant owing to its light atomic weight, high hydrogen gravimetric capacity, and known ability to enhance sorption kinetics when alloyed with transition metals. Unlike heavier dopants, Mg offers the dual benefit of reducing system weight while potentially modifying the band structure and boosting hydrogen density.¹⁶ Thus, this study aims to explore how Mg-substitution affects the structural stability, electronic properties, and hydrogen storage potential of NbH₂. The novelty of the work lies in its systematic application of density functional theory (DFT) to uncover the atomistic effects of Mg incorporation in NbH₂, a relatively unexplored yet promising material for multifunctional energy applications.

2. Computational methods

First-principles calculations based on density functional theory (DFT) were performed using the CASTEP module implemented in Materials Studio 2020.¹⁷ The calculations in this study were performed using density functional theory (DFT) within the generalized gradient approximation (GGA), employing the Perdew–Burke–Ernzerhof (PBE) functional to describe the exchange–correlation interactions.¹⁸ Relativistic effects were treated using the Koelling–Harmon scalar relativistic approximation.¹⁹ The electronic wavefunctions were expanded in a plane-wave basis set with a cutoff energy of 381 eV. Electronic convergence was achieved with an energy tolerance of 2 × 10⁻⁶ eV per atom and an eigenvalue convergence criterion of 8.889 × 10⁻⁷ eV. The charge density was mixed using the Pulay scheme,²⁰ with a maximum mixing history length of 20, a mixing amplitude of 0.5, and a g-vector cut-off of 1.5 Å⁻¹. Geometry optimization was carried out using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm under fixed basis quality conditions.²¹ The maximum number of ionic steps was set to 100, with convergence criteria for the total energy, maximum ionic force, and atomic displacement set at 2 × 10⁻⁵ eV per atom, 0.05 eV Å⁻¹, and 0.002 Å, respectively. To improve the accuracy of the calculated band structures and structural parameters (lattice constants), the Heyd–Scuseria–Ernzerhof (HSE03) hybrid functional was employed as a post-processing correction.²² The HSE03 functional provides a more reliable description of the electronic structure by incorporating a portion of exact Hartree–Fock exchange, which is particularly important for systems where bandgap and structural precision are critical.

3. Results and discussion

3.1 Bonding characteristics, population analysis, and hybridization

To understand the effect of Mg substitution on the bonding nature within the NbH₂ fluorite structure, a detailed population and bond length analysis was performed using the Mulliken scheme. The goal was to quantify the bonding strength between H, Nb, and Mg atoms, as well as to assess how increasing Mg content influences electron distribution and interatomic interactions within the lattice. In pristine NbH₂, the H–Nb bond length is 1.978 Å with a bond population of 0.35, indicating a moderately covalent character. The H–H interaction shows a negative bond population of −0.07, suggesting weak repulsive or nonbonding interactions between hydrogen atoms within the lattice.^23,24 Upon Mg doping, significant changes in bonding patterns are observed. For instance, in the Mg-NbH₂ compound, while the H–Nb bond population drops sharply to 0.06 (nearly nonbonding), new H–Mg interactions form with a bond population of 0.17, indicating weak ionic bonding. As Mg content increases in Mg₂-NbH₂ and Mg₃-NbH₂, the H–Nb bond population remains low (0.12 and 0.03 respectively), while the H–Mg bond population increases to 0.29 and then decreases to 0.15. These trends imply that Mg substitution progressively disrupts the original Nb–H bonding network and introduces ionic H–Mg interactions, which may facilitate hydrogen release due to weaker bonding. A comparative analysis with pure MgH₂ supports this observation. The H–Mg bond population in MgH₂ is as high as 0.57, indicating a significantly stronger ionic character compared to Mg-NbH₂ variants. Moreover, the H–H population in MgH₂ is highly negative (−0.68), suggesting stronger hydrogen–hydrogen repulsion, which may relate to higher desorption kinetics.

The atomic Mulliken population data (Table S2†) further reinforce these conclusions. In pristine NbH₂, the Nb atom exhibits a total electronic population of 15, with notable contributions from the d-orbital (4.084), reflecting its role in covalent bonding. As Mg atoms are introduced, the overall electronic populations increase with higher s- and p-orbital character (e.g., Mg-NbH₂ shows a total of 56.997 electrons), suggesting a shift toward more ionic behavior. Particularly in Mg₂-NbH₂ and Mg₃-NbH₂, the electron populations become more delocalized, and d-orbital participation drops significantly (to ∼4.1), indicating weakened Nb-based bonding. In pure MgH₂, the electron population is predominantly from s- and p-orbitals (5.217 and 6.783, respectively), aligning with its known ionic bonding nature.^25,26

In summary, these bonding analyses reveal that Mg substitution in NbH₂ reduces the covalent character of the Nb–H bonds and introduces weaker, more ionic Mg–H interactions. This change in bonding environment weakens the hydrogen binding energy, potentially improving desorption properties. Additionally, the disruption of the Nb–H network by Mg alters the electron distribution within the lattice, which may also influence the material's optoelectronic and catalytic behavior.

3.2 Structural analysis

NbH₂ and MgH₂ both adopt a fluorite-type structure within the cubic Fm3̄m space group. In NbH₂, Nb²⁺ ions exhibit a face-centered cubic coordination with eight H¹⁻ atoms, featuring Nb–H distances of 1.98 Å. Each hydride ion connects to four Nb²⁺ centers, forming mixed corner- and edge-sharing HNb₄ tetrahedra. Similarly, in MgH₂, Mg²⁺ ions are surrounded by eight H¹⁻ atoms in a comparable geometry, with bond lengths of 2.06 Å. Here, each H¹⁻ ion coordinates with four Mg²⁺ atoms, resulting in HMg₄ tetrahedral units that also share corners and edges.²⁷ The structural analysis of NbH₂, MgH₂, and their magnesium-substituted derivatives reveals significant differences depending on the exchange–correlation functional used in the DFT calculations, namely, PBE and HSE03. Under the PBE functional, NbH₂ displays a distorted orthorhombic symmetry with lattice constants a = c = 4.65 Å and b = 4.47 Å, resulting in a unit volume of 96.65 ų and a density of 6.52 g cm⁻³. This closely aligns with the 4.57 Å lattice constant reported by Xiaobing et al. for NbH₂.²⁷ MgH₂, on the other hand, exhibits a larger unit cell volume (112.60 ų) with lattice constants around 4.81–4.86 Å and a much lower density of 1.55 g cm⁻³, which slightly exceeds the 4.77 Å reported by Vajeeston et al.²⁸ A known characteristic of the PBE functional is its tendency to slightly overestimate lattice dimensions. With increasing Mg content in the Mg_1–3-NbH₂ series, there is a gradual increase in unit volume (from 97.22 to 103.45 ų) and density (up to 10.78 g cm⁻³), accompanied by angular distortions in Mg-NbH₂ (α = 94°, β = 92°, γ = 88°), indicating a loss of perfect cubic symmetry and increasing structural distortion due to doping.

In contrast, the HSE03 functional maintains a constant unit volume (95.39 ų) and lattice parameter (4.57 Å) across all compounds, regardless of composition. While this value aligns well with the experimental lattice constant for NbH₂ reported by Xiaobing et al., the uniformity in volume and geometry across all doped systems, including MgH₂, appears unrealistic. This suggests that the structures under HSE03 may not have undergone full relaxation or were constrained during optimization, making the results less physically meaningful for structural evaluation. Correspondingly, the densities calculated under HSE03 decrease with increasing Mg content, from 6.61 g cm⁻³ (NbH₂) to 3.03 g cm⁻³ (Mg₃-NbH₂), which contradicts the expected trend of increasing mass and decreasing volume.

The enthalpy and total energy parameters derived from both PBE and HSE03 functionals provide essential insights into the thermodynamic stability of NbH₂ and its Mg-substituted derivatives. Under the PBE functional, the total energy of NbH₂ is −6.75 eV, with a corresponding enthalpy of −6.75 eV. As Mg is gradually introduced into the NbH₂ framework to form Mg-NbH₂, Mg₂-NbH₂, and Mg₃-NbH₂, the total energy becomes increasingly negative (−6788.06 eV, −6822.37 eV, and −6855.15 eV, respectively), indicating the growing size and atomic complexity of the systems. Although total energy values are not directly comparable across compounds of different compositions, the enthalpy values, which range from −6.79 eV to −6.86 eV across these substituted structures, suggest a trend toward improved thermodynamic stability with increasing Mg content. MgH₂ exhibits the most negative enthalpy value at −6.89 eV, suggesting it is the most stable compound among those studied. A similar trend is observed under the HSE03 functional. The total energy of NbH₂ is −699.49 eV with an enthalpy of −0.70 eV. As Mg substitution increases, the total energies of Mg-NbH₂, Mg₂-NbH₂, and Mg₃-NbH₂ decline significantly to −2139.97 eV, −3582.32 eV, and −5022.71 eV, respectively, while their enthalpy values follow a corresponding downward trend from −2.14 eV to −5.02 eV. MgH₂ again shows the most negative enthalpy at −6.46 eV, confirming its superior thermodynamic stability. While both functionals support the conclusion that Mg incorporation enhances the stability of NbH₂-based compounds, PBE tends to yield slightly more negative enthalpy values, possibly due to its tendency to overbind. In contrast, HSE03, a hybrid functional, provides more moderate estimates but still reinforces the general stability trend. The consistent decrease in enthalpy with increasing Mg content across both computational methods underscores the favorable energetic landscape of Mg-doped NbH₂ hydrides, with MgH₂ emerging as the most stable configuration.

From a mechanical standpoint, the PBE functional shows a progressive decrease in bulk modulus from 318.63 GPa (NbH₂) to just 6.27 GPa (Mg₃-NbH₂), indicating significant softening and structural weakening upon doping. Notably, MgH₂ exhibits an unusually high bulk modulus (869.24 GPa), possibly due to tighter packing or bonding interactions. HSE03 did not report bulk modulus values, limiting direct mechanical comparison. Vibrational frequency trends further support the reliability of PBE for structural behavior, showing consistent values for undoped compounds (1668 cm⁻¹), while HSE03 reveals a progressive increase in frequency with doping from 1163.69 cm⁻¹ in Mg-NbH₂ to 3836.40 cm⁻¹ in Mg₃-NbH₂ though the unusually high values, especially in PBE for Mg₃-NbH₂ (6151.39 cm⁻¹), suggest computational anomalies or strong local modes. The vibrational frequencies listed in Tables 1 and 2 represent the maximum optical phonon mode at the Γ-point, derived from lattice dynamics calculations. These frequencies provide insight into the vibrational behavior of the H atoms in the lattice, which is critical for evaluating hydrogen bonding strength, lattice dynamics, and the potential for reversible hydrogen desorption.²⁹ Higher frequencies are typically associated with strong metal–H interactions and dynamic stability, while lower frequencies may reflect weakened bonding or soft modes due to structural distortion or increased Mg substitution.

Table 1 Calculated structural, energetic, and vibrational properties of NbH₂, MgH₂, and Mg-substituted NbH₂ compounds (Mg-NbH₂, Mg₂-NbH₂, Mg₃-NbH₂) using the GGA–PBE functional. Reported parameters include unit cell volume, density, lattice constants (a, b, c), total energy, enthalpy of formation, bulk modulus, and the highest vibrational mode (Γ-point frequency in cm⁻¹)

Compounds	Unit volume (A^3)	Unit density (g cm^−3)	Lattice constants			Total energy (eV)	Enthalpy (eV)	Bulk modulus (GPa)	Frequency (cm^−1)
			a	b	c
NbH2	96.65	6.52	4.65	4.47	4.65	−6754.24	−6.75	318.63	1668
Mg-NbH2	97.22	8.15	4.71	4.56	4.55	−6788.06	−6.79	209.42	1668
Mg2-NbH2	98.11	9.72	4.52	4.81	4.52	−6822.37	−6.82	156.96	1321.48
Mg3-NbH2	103.45	10.78	4.67	4.76	4.65	−6855.15	−6.86	6.27	6151.39
MgH2	112.60	1.55	4.86	4.81	4.81	−6888.58	−6.89	869.24	1668

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Table 2 Structural, energetic, and vibrational properties of the studied hydrides computed using the HSE03 hybrid functional. This includes unit cell volume, density, lattice constants, total energy, enthalpy of formation, and maximum vibrational frequency (in cm⁻¹). The data are used to validate and complement the GGA–PBE results

Compounds	Unit volume (A^3)	Unit density (g cm^−3)	Lattice constants	Total energy (eV)	Enthalpy (eV)	Bulk modulus (GPa)	Frequency (cm^−1)
			a = b = c
NbH2	95.39	6.61	4.57	−699.49	−0.70	—	1668
Mg-NbH2	95.39	5.24	4.57	−2139.97	−2.14	—	1163.69
Mg2-NbH2	95.39	4.22	4.57	−3582.32	−3.58	—	1255.92
Mg3-NbH2	95.39	3.03	4.57	−5022.71	−5.02	—	3836.40
MgH2	95.39	1.83	4.57	−6463.42	−6.46	—	1668

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The differences between the GGA–PBE values (Table 1) and those obtained using HSE03 (Table 2) arise from the known limitations of the GGA functional, which tends to underestimate bandgaps and yields functional-dependent absolute energies. Nonetheless, GGA–PBE is suitable for assessing structural trends, relative stabilities, and vibrational characteristics across chemically similar compounds, and all values within each table are internally consistent. In summary, the PBE functional more accurately captures the structural evolution and distortion due to Mg substitution in NbH₂, reflecting realistic trends in lattice parameters, unit cell volume, density, and mechanical stability. Meanwhile, HSE03, although aligning precisely with some literature values for NbH₂, offers limited structural flexibility and possibly constrained optimization, making it less suitable for analyzing doping-induced changes. Therefore, for structural analysis involving substitutional effects, PBE appears to provide more reliable and physically consistent results (Fig. 1).

Fig. 1 Optimized crystal structures of NbH₂, MgH₂, and Mg-substituted NbH₂ (Mg-NbH₂, Mg₂-NbH₂, Mg₃-NbH₂) showing their fluorite-derived configurations. Atoms are color-coded by element to emphasize structural distortion due to Mg substitution.

3.3 Electronic analysis: band structure and PDOS

The electronic properties of the studied compounds were investigated through both GGA–PBE and HSE03 functionals, providing insights into their band structure and density of states (DOS) characteristics. The GGA–PBE band structure in Fig. 2 reveals that the compounds exhibit conducting behavior, with the conduction band minimum (CBM) and valence band maximum (VBM) overlapping one another. This is except for MgH₂, whose CBM and VBM are located at different k-points (indicating an indirect band gap) or at the same k-point (for direct band gap systems). However, the band gaps obtained from GGA–PBE are generally underestimated, a known limitation of this functional.¹⁸ This shortcoming is addressed in the HSE03 band structure plots in Fig. 3. The HSE03 functional shows precisely the same results as those from GGA–PBE, which confirms that the GGA–PBE method used is accurate. Conducting materials like Mg-NbH₂, which exhibit metallic behavior due to the presence of electronic states at the Fermi level, are valuable in a wide range of technological applications that require efficient charge transport. The use of such materials is in electrical contacts and interconnects within electronic devices, where their low resistivity ensures minimal energy loss and high current-carrying capacity.³⁰ In addition, conducting hydride-based compounds have potential in hydrogen storage and sensing applications, where their electrical conductivity can facilitate real-time monitoring of hydrogen uptake or release via resistive or impedance-based methods.³¹ Generally, the metallic nature of these compounds makes them suitable for integration into next-generation energy devices, sensors, and electronic systems where conductivity and functional reactivity are both required.

Fig. 2 Electronic band structures of NbH₂, MgH₂, and Mg-substituted NbH₂ compounds calculated using the GGA–PBE functional. The band dispersion is plotted along high-symmetry directions of the Fm3̄m Brillouin zone. The Fermi level is aligned to 0 eV.

Fig. 3 Total and partial density of states (TDOS and PDOS) for the studied compounds obtained with the GGA–PBE method. The contribution of individual atomic orbitals (Nb d, Mg s, H s) is highlighted to reveal electronic characteristics and bonding behavior.

The PDOS and TDOS plots in Fig. 3 offer a more detailed understanding of the electronic structure by showcasing the contribution of specific atomic orbitals to the electronic states near the Fermi level.³² In the PDOS, the valence band is predominantly composed of s-orbital contributions from the smaller atoms (such as Mg and H, depending on the composition), while the conduction band shows significant contributions from the d-orbitals of the metal center of Nb. All the compounds show three peaks, except MgH₂, which is fully occupied by the s-orbitals in bonding. NbH₂ shows a TDOS of 7, a d-orbital contribution of 3.5, and an s-orbital contribution of 4. MgH₂ shows a TDOS contribution of 3.5 and an s-orbital contribution of 2.8. Mg-NbH₂ shows a TDOS of 5.8, d-orbital contribution of 3, and s-orbital contribution of 3.2. Mg₂-NbH₂ shows a TDOS contribution of 5, a d-orbital contribution of 2.9, and an s-orbital contribution of 3. Mg₃-NbH₂ shows a TDOS contribution of 2, a d-orbital contribution of 3.8 and 3.3. From this, it is observed that the substitution of Mg in NbH₂ reduces the TDOS contribution as well as the d-orbital contribution and but increases the s-orbital contribution as compared to the parent compound NbH₂. This indicates strong hybridization between the metal d-states and the non-metal s-states, suggesting covalent bonding interactions that could influence charge mobility.³³ The TDOS further supports these observations by displaying the overall electronic density distribution, with pronounced peaks near the valence and conduction band edges, implying localized states that are important for optical transitions. In summary, the combination of band structure and DOS analyses illustrates that the compounds are conductors with substantial orbital hybridization. The discrepancy between the PBE and HSE03 results underlines the importance of using hybrid functionals for accurate electronic property predictions (Fig. 4).

Fig. 4 Electronic band structures of NbH₂ and Mg-substituted NbH₂ calculated using the HSE03 functional, along high-symmetry directions of the Fm3̄m Brillouin zone. The Fermi level is set to 0 eV. These results are used to cross-validate GGA–PBE predictions.

3.4 Optoelectronic analysis

3.4.1 Optical absorption, reflectivity, and loss function. The optoelectronic properties of the studied compounds NbH₂, Mg-NbH₂, Mg₂-NbH₂, Mg₃-NbH₂, and MgH₂ were evaluated based on their absorption coefficient, reflectivity, and energy loss function across the photon energy range of 0 to 80 eV, as shown in the provided plots. In the absorption plot, NbH₂ exhibits the highest absorption coefficient across the spectrum, peaking around 5.5 × 10⁵ in the energy range of approximately 30–40 eV, indicating its superior capability for absorbing high-energy photons. This suggests potential for optoelectronic applications where strong photon–material interaction is required.³⁴ The incorporation of magnesium into NbH₂ generally reduces the absorption strength, with Mg₂-NbH₂ and Mg₃-NbH₂ showing the lowest absorption intensities, suggesting that increased Mg content diminishes the optical absorption performance. MgH₂, although a separate phase, shows moderate absorption primarily in the lower energy range (5–25 eV), reflecting different electronic transitions compared to the Nb-containing compounds.

Reflectivity analysis discloses that MgH₂ demonstrates an exceptionally high reflectivity (approaching 1.0) in the low-energy region (below 10 eV), significantly higher than all other compounds. This implies strong surface reflection of incident light, which may reduce its suitability for applications requiring light penetration.³⁵ NbH₂ shows moderate reflectivity throughout the spectrum, while the Mg-doped variants, especially Mg₂-NbH₂ and Mg₃-NbH₂, show reduced reflectivity, indicating improved photon absorption capabilities in those regions.

The loss function plot, which provides understanding on the energy loss of fast electrons traversing the material,³⁶ is particularly dominated by a sharp peak for MgH₂ around 10 eV, reaching a maximum value of 60. This signifies a strong plasmon resonance in MgH₂, indicative of collective oscillations of the electron gas. In contrast, the other compounds exhibit lower and broader peaks, suggesting less intense plasmonic activity. NbH₂ and its Mg-doped variants show moderate loss function values in the 10–30 eV range, with multiple smaller peaks, pointing to more complex electronic transitions and weaker plasmonic behavior. Inclusively, NbH₂ stands out for its high absorption and moderate reflectivity, making it a promising candidate for energy harvesting or UV shielding applications. The Mg incorporation tunes the optical response, potentially allowing for the engineering of materials with tailored optoelectronic characteristics. MgH₂, with its intense reflectivity and sharp energy loss peak, is more reflective and plasmonically active, which may be beneficial in applications involving light reflection or plasmonic enhancement (Fig. 5).

Fig. 5 Optical absorption spectra, reflectivity, and energy loss function of the studied compounds, calculated using the GGA–PBE method. The plots reveal light-harvesting potential and dielectric loss behavior relevant to photocatalysis and optoelectronics.

3.4.2 Optical conductivity. Optical conductivity refers to a material's response to an electromagnetic field (light) in terms of its ability to conduct electricity at various frequencies, especially in the visible and near-visible spectrum. It is a frequency-dependent counterpart of electrical conductivity denoted as σ(ω), where σ is the conductivity and ω is the angular frequency of the light.³⁷ This physical property is described by the real part of the optical conductivity (Re[σ(ω)]) which involves energy dissipation (i.e., absorption of light) and the imaginary part of the optical conductivity ([Im σ(ω)]) which is related to energy storage in the medium.³⁸ In Fig. 6, the plots for the real and imaginary optical conductivities are shown for the studied compounds. Starting with the real conductivity plot, MgH₂ (blue) shows the highest peak at 13 s m⁻¹ followed by NbH₂ (black) at 9 s m⁻¹, Mg-NbH₂ (red) shows a peak at 8 s m⁻¹, Mg₃-NbH₂ (green) at 6.3 s m⁻¹ and Mg₂-NbH₂ (purple) at 6 s m⁻¹. This means that the subsequent addition of Mg to NbH₂ gradually reduces the dissipation energy thus affecting the absorption capacity of the compounds. On the other hand, complete substitution of Nb with Mg in MgH₂ shows that MgH₂ strongly interacts with light matter to enhance optical conductivity. The second plot which contains the imaginary optical conductivity shows MgH₂ to possess the highest peak at 7 s m⁻¹ followed by NbH₂ at 5 s m⁻¹, then Mg-NbH₂ at 4.8 s m⁻¹, Mg₃-NbH₂ at 4 s m⁻¹ and Mg₂-NbH₂ at 3.8 s m⁻¹. Thus, the imaginary plot follows the same route as the real plot which the concurrent reduction in conductivity as the substitution of Mg in NbH₂ increases.

Fig. 6 Real and imaginary parts of optical conductivity for the studied compounds under GGA–PBE. These parameters indicate photon-induced charge carrier response and material conductivity in different energy regions.

3.4.3 Optical dielectric function. The dielectric function is a complex quantity that describes how a material responds to an external electric field, especially in the presence of an oscillating electromagnetic wave such as light. It is fundamental in understanding a material's optical, electronic, and energy absorption properties. Mathematically, the dielectric function is expressed as:³⁹

ε(ω) = ε₁(ω) + iε₂(ω) (1)

where ε₁(ω) is the real part, representing the material's ability to store electric energy (related to polarization and refractive index) while ε₂(ω) is the imaginary part, which accounts for the energy loss (i.e., absorption of the electromagnetic wave by the material).^40–42

The dielectric function plots comprising the real and imaginary parts reveal vital information on the optical response and electronic polarizability of the investigated hydride compounds.⁴³ Among the materials, Mg-NbH₂ demonstrates the most pronounced peaks in both the real and imaginary components of the dielectric function, indicating a strong interaction with incident electromagnetic radiation and high polarizability. Specifically, in the real part, Mg-NbH₂ peaks sharply around 0 eV with a maximum value exceeding 30, suggesting substantial static dielectric response, which aligns with its metallic behavior and delocalized charge carriers. In the imaginary part, which reflects absorption characteristics, Mg-NbH₂ again exhibits the highest peak (around 85), emphasising its strong interband transitions and enhanced optical activity.

Following Mg-NbH₂, MgH₂ shows the next highest peaks in both real and imaginary components, indicative of relatively strong optical absorption and dielectric response, consistent with its semiconducting nature. NbH₂ and Mg₃-NbH₂ exhibit moderate peaks, suggesting intermediate dielectric behavior and limited but noticeable interaction with electromagnetic fields. Lastly, Mg₂-NbH₂ shows the least pronounced peaks across both dielectric plots, implying the lowest optical absorption and static dielectric constant among the series. These trends point to Mg-NbH₂ being the most optically active and polarizable, making it a strong candidate for optoelectronic or plasmonic applications, while Mg₂-NbH₂ would be more optically inert (Fig. 7).

Fig. 7 Real and imaginary components of the dielectric function (ε₁ and ε₂) of the studied compounds obtained from GGA–PBE optical calculations, showing their polarizability and optical transparency across energy ranges.

3.4.4 Optical refractive index. The refractive index (denoted as n) is a fundamental optical property of a material that describes how light propagates through it. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v):⁴⁴

There are two components, which include the real part (n₁) representing how much the light is bent or refracted when entering the material.⁴⁵ A higher n₁ means greater bending and stronger optical density. The imaginary part (n₂) is associated with the absorption of light within the material. A higher n indicates that the material absorbs more light and transmits less. Together, the complex refractive index is written as:⁴⁶

ñn₁ + in₂ (3)

The refractive index plots presented illustrate both the real (n₁) and imaginary (n₂) parts of the refractive indices of the compounds NbH₂, MgH₂, Mg-NbH₂, Mg₃-NbH₂, and Mg₂-NbH₂ over a wide energy range.⁴⁷ These indices offer vital insights into the optical transparency, reflectivity, and absorption of the materials. In the real part of the refractive index (n₁) plot, Mg-NbH₂ exhibits the highest peak value of about 3.2, indicating strong light bending capability and high optical density in the low-energy region. This is followed closely by MgH₂, which also shows a significant peak above 3.0, confirming its notable dielectric response. NbH₂ presents a slightly lower peak around 2.5, while Mg₃-NbH₂ and Mg₂-NbH₂ have more moderate peaks, suggesting comparatively lower light-retardation effects. These values gradually taper off with increasing photon energy, reflecting a decrease in refractive behavior at high energies. In the imaginary part of the refractive index (n₂) plot, which relates to absorption, Mg-NbH₂ again shows the most prominent peak, exceeding 9.0, indicating it has the highest optical absorption in the visible-to-UV region. This implies greater interband transitions and energy dissipation in this material. Following this are NbH₂, MgH₂, and Mg₃-NbH₂, all exhibiting moderate absorption behaviors. Mg₂-NbH₂ has the lowest imaginary peak, suggesting it is more optically transparent and has reduced electronic losses compared to the others. These variations in the refractive indices reflect differences in the electronic structure and bonding nature of the compounds, particularly the extent of hybridization and electron delocalization. The high optical activity of Mg-NbH₂ positions it as a strong candidate for optoelectronic or photonic applications, while Mg₂-NbH₂ may be more suitable for transparent or low-loss dielectric uses (Fig. 8).

Fig. 8 Refractive index (n) and energy loss function (L) spectra (both real and imaginary parts) for the studied compounds. These optical properties provide insight into the interaction of light with the material and the onset of plasmonic behavior.

3.5 Elastic and mechanical properties

The elastic and mechanical properties of the studied compounds reveal significant insights into their structural rigidity, ductility, and stability. For all systems, the elastic constants C₁₁, C₁₂, and C₄₄ play critical roles in defining their resistance to deformation. Notably, NbH₂ exhibits high stiffness with C₁₁ = 257.15 GPa and C₄₄ = 111.15 GPa, indicating a strong and mechanically stable structure. The Born mechanical stability criteria—C₁₁ > 0, C₄₄ > 0, C₁₁–C₁₂ > 0, and C₁₁ +2C₁₂ > 0—are satisfied by NbH₂, Mg-NbH₂, and Mg₂-NbH₂, confirming their mechanical stability.⁴⁸ However, Mg₃-NbH₂ and MgH₂ fail to meet the C₄₄ > 0 criterion, with negative values (−8.03 and −9.27 GPa, respectively), indicating shear instability and potential mechanical failure under certain deformations.

Among the compounds, NbH₂ also possesses the highest bulk modulus (156.96 GPa), shear modulus (106.45 GPa), and Young's modulus (260.47 GPa), highlighting its superior resistance to volume change, shear deformation, and overall elastic deformation, respectively. As magnesium is incrementally added, these mechanical parameters decline, with MgH₂ having the lowest values (B = 23.76 GPa, G = 20.19 GPa, and E = 47.21 GPa), indicating a much softer and more ductile material. The Pugh ratio (B/G), which measures ductility, further differentiates the compounds. A value above 1.75 typically indicates ductility, while values below suggest brittleness.⁴⁹ Mg-NbH₂ has the highest B/G ratio (3.27), suggesting it is the most ductile among the set, whereas Mg₃-NbH₂ (0.97) and Mg₂-NbH₂ (1.35) lean towards brittleness. NbH₂, with a B/G of 1.47, straddles the brittle–ductile borderline. The anisotropic factor (A), which describes directional dependency of the elastic response,⁵⁰ ranges from 0.21 for NbH₂ (indicating near isotropy) to a highly negative −9.67 for Mg₃-NbH₂, suggesting severe elastic anisotropy and instability. Similarly, Poisson's ratio (υ), which reflects the degree of lateral expansion when compressed,⁵¹ ranges anomalously, with Mg₃-NbH₂ and MgH₂ showing unrealistic values (1.59 and −10.14, respectively), further confirming their mechanical instability or computational artefacts due to soft shear modes.

In summary, the data indicate that NbH₂ is the most mechanically stable and rigid among the studied compounds. The addition of Mg modifies the mechanical behavior, with Mg-NbH₂ showing enhanced ductility but reduced stiffness, while higher Mg concentrations lead to mechanical instability, as reflected by the failure to satisfy some of the Born criteria and the emergence of negative or extreme values in key elastic parameters (Table 3).

Table 3 Calculated elastic constants (C₁₁, C₁₂, C₄₄) and derived mechanical parameters including bulk modulus (B), shear modulus (G), Young's modulus (E), and Poisson's ratio (ν) for NbH₂, MgH₂, and Mg-substituted NbH₂ compounds (Mg-NbH₂, Mg₂-NbH₂, Mg₃-NbH₂) using the GGA–PBE method. These parameters provide insight into the mechanical stability, ductility, and stiffness of the hydride materials

Elastic moduli (GPa)	NbH2	Mg-NbH2	Mg2-NbH2	Mg3-NbH2	MgH2
C11 > 0	257.15	179.28	176.68	360.03	95.60
C12	102.94	102.59	39.92	165.62	−26.12
C44 > 0	111.15	44.32	38.33	−8.03	−9.27
C11 + 2C12 > 0	463.03	384.46	256.52	691.27	43.36
C11–C12 > 0	154.21	76.69	136.76	194.41	121.72
Bulk modulus (B)	156.96	126.64	78.83	68.56	23.76
Shear modulus (G)	106.45	38.74	58.38	70.53	20.19
Young modulus (E)	260.47	105.46	140.47	157.56	47.21
Pugh ratio (B/G)	1.47	3.27	1.35	0.97	1.18
Anisotropic factor (A)	0.21	0.37	0.55	−9.67	1.07
Poisson ratio (υ)	0.23	0.41	0.22	1.59	−10.14

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3.6 Hydrogen storage capacity

The hydrogen gravimetric storage capacity of a material refers to the mass percentage of hydrogen that can be stored within the compound, which is a crucial parameter for evaluating materials for hydrogen storage applications. A higher gravimetric capacity indicates that a compound can store more hydrogen per unit mass, making it more efficient for lightweight and compact hydrogen storage systems, especially in the context of fuel cells and clean energy technologies. The formula for calculating the hydrogen gravimetric capacity is given as:⁵²

From the calculations, MgH₂ exhibits the highest hydrogen storage capacity at 7.66 wt%, consistent with its lightweight elemental nature and strong hydrogen affinity.^53,54 This high gravimetric capacity underscores MgH₂'s long-standing position as a benchmark hydrogen storage material, despite its high desorption temperature and sluggish kinetics. In contrast, pristine NbH₂ has a significantly lower hydrogen capacity of 2.124 wt%, which can be attributed to the heavier atomic weight of niobium and a lower hydrogen-to-metal ratio. However, when Mg is incrementally introduced into the NbH₂ lattice to form ternary hydrides—Mg-NbH₂ (3.326%), Mg₂-NbH₂ (2.797%), and Mg₃-NbH₂ (2.378%), a nonlinear but significant improvement in hydrogen capacity is observed relative to pure NbH₂. This increase is primarily due to the incorporation of lighter Mg atoms into the matrix, which reduces the overall molecular weight of the hydride without proportionally sacrificing the hydrogen content. Interestingly, the capacity peaks at Mg-NbH₂ and slightly declines as more Mg is added (Mg₂ and Mg₃), likely due to saturation of substitutional sites or a shift in phase stability toward less hydrogen-rich or more stable configurations. This suggests that while Mg improves the H/M (hydrogen-to-metal) ratio initially, excessive substitution may hinder additional hydrogen uptake.

Compared to the state-of-the-art systems, these Mg-NbH₂ variants offer moderate hydrogen capacities, bridging the gap between high-capacity but kinetically limited MgH₂, and low-capacity but stable intermetallic hydrides like LaNi₅H₆ (∼1.4%) or TiFe (∼1.9%).^55,56 Moreover, the bonding and electronic analysis in earlier sections indicate that Mg incorporation weakens the H–H-metal bonding strength, potentially enhancing desorption kinetics, an important advantage over pure MgH₂. In conclusion, although the gravimetric hydrogen capacities of the Mg-NbH₂ systems are lower than that of pure MgH₂, they present a promising trade-off between capacity, bonding strength, and structural stability. Their performance may be further enhanced through doping, nanostructuring, or hybridization, making them viable candidates for next-generation solid-state hydrogen storage materials.

Upon desorption of hydrogen from the compounds, as modelled using the PBE functional, several significant structural and energetic changes are observed. For all systems, there is a notable decrease in total energy and enthalpy compared to the hydrogenated structures, though the trend of increasing thermodynamic stability with increasing Mg content remains consistent. The total energies for NbH₂, Mg-NbH₂, Mg₂-NbH₂, Mg₃-NbH₂, and MgH₂ after hydrogen desorption are −6625.08 eV, −6658.70 eV, −6692.73 eV, −6726.11 eV, and −6760.63 eV, respectively, with corresponding enthalpy values ranging from −6.63 eV to −6.76 eV. These values suggest that desorption slightly lowers the enthalpic stability of each compound compared to its hydrogenated counterparts but does not significantly disrupt the stability hierarchy. Structurally, desorption leads to a reduction in unit volume for all compounds except Mg₃-NbH₂, which expands slightly. NbH₂ shows the largest contraction in unit volume from 96.65 ų to 76.12 ų, indicative of lattice shrinkage upon hydrogen removal. The increase in unit density from 6.52 g cm⁻³ to 8.28 g cm⁻³ for NbH₂ and up to 13.67 g cm⁻³ for Mg₃-NbH₂ also supports this compaction behavior. Lattice constants adjust accordingly, with varying degrees of anisotropic distortion depending on Mg content. Notably, NbH₂ exhibits angular distortions after desorption, with α = 80.95°, β = 89.98°, and γ = 90.04°, indicating a departure from ideal cubic symmetry and a transition toward a slightly distorted or monoclinic-like structure. All other compounds exhibit 90°.

The bulk modulus values post-desorption exhibit notable variation. For example, Mg-NbH₂ shows a dramatic drop in bulk modulus to 133.54 GPa, indicating a softer and more compressible structure, whereas NbH₂ maintains a relatively high modulus of 1172.09 GPa. These differences suggest that Mg incorporation affects the mechanical rigidity of the structure more significantly after hydrogen release. Vibrational frequency data reveal sharp contrasts as well. The frequency remains at 1668 cm⁻¹ for NbH₂ and MgH₂, implying similar vibrational modes post-desorption. However, Mg-NbH₂ shows an extremely high frequency of 7709.70 cm⁻¹, suggesting the emergence of highly localized or stiff vibrational modes, potentially due to structural rearrangements or residual stress within the desorbed lattice. Overall, hydrogen desorption leads to structural compaction, modest decreases in enthalpic stability, and changes in mechanical and vibrational properties. The general trend of increasing Mg content enhancing the stability of the system is preserved, while significant modifications in lattice structure and dynamics point to complex desorption-driven behavior in these metal hydride materials (Table 4).

Table 4 Structural parameters of NbH₂, MgH₂, and Mg-substituted NbH₂ compounds after hydrogen desorption, calculated using the GGA–PBE method. Reported values include unit cell volume, density, lattice constants, total energy, enthalpy, and bulk modulus. The data highlight the structural evolution and thermodynamic implications of hydrogen release

Compounds	Unit volume (A^3)	Unit density (g cm^−3)	Lattice constants			Total energy (eV)	Enthalpy (eV)	Bulk modulus (GPa)	Frequency (cm^−1)
			a/Å	b/Å	c/Å
NbH2	76.12	8.28	4.91	3.60	4.36	−6625.08	−6.63	1172.09	1668
Mg-NbH2	74.99	10.56	3.78	4.65	4.27	−6658.70	−6.66	133.54	7709.70
Mg2-NbH2	77.45	12.31	4.01	4.81	4.01	−6692.73	−6.69	94.60	1321.48
Mg3-NbH2	81.58	13.67	4.30	4.42	4.30	−6726.11	−6.73	355.18	6151.39
MgH2	93.09	1.88	4.54	4.53	4.53	−6760.63	−6.76	385.95	1668

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4. Conclusions

This study presents a comprehensive density functional theory (DFT) investigation of NbH₂, MgH₂, and Mg-substituted NbH₂ systems (Mg-NbH₂, Mg₂-NbH₂, and Mg₃-NbH₂), aimed at exploring their structural, electronic, optical, and hydrogen storage properties for multifunctional energy applications. The substitution of Mg into the fluorite-type NbH₂ matrix leads to notable structural distortions, increasing unit cell volume and density, and introducing flexibility in the lattice geometry. Among the computational approaches, GGA/PBE proved more effective than HSE03 in capturing these trends realistically, especially under varying Mg content. Electronic analysis revealed a transition from metallicity in NbH₂ and its Mg-substituted counterparts to semiconducting behavior in MgH₂, underscoring the tunability of electronic properties via controlled doping. The total density of states (TDOS) decreased with increasing Mg content, suggesting reduced carrier density and modified electronic transport characteristics. Optically, Mg-NbH₂ exhibited superior dielectric strength and refractive index, positioning it as the most promising candidate for optoelectronic and plasmonic applications, while MgH₂ showed dominant reflectivity and optical conductivity in the UV-visible range.

From a mechanical standpoint, NbH₂ demonstrated high rigidity and elastic stability, whereas Mg doping progressively enhanced ductility but at the cost of mechanical stability, especially in Mg₂-NbH₂ and Mg₃-NbH₂, where instability indicators such as negative shear constants and unrealistic Poisson ratios were observed. In terms of hydrogen storage, MgH₂ retained the highest gravimetric capacity (7.66 wt%), but its known drawbacks such as slow desorption kinetics highlight the need for alternatives. The Mg-NbH₂ compounds showed moderate hydrogen capacity (2.4–3.3 wt%) and offer a promising trade-off between structural stability, storage potential, and functional versatility. In summary, this work identifies Mg-NbH₂ as a tunable material system with balanced performance across hydrogen storage, optoelectronics, and mechanical robustness. The insights gained here provide a rational design strategy for developing next-generation metal hydrides with multifunctional energy applications.

Data availability

Data will be made available upon request.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We acknowledged the centre for High-Performance Computing Centre, South Africa for the computational resources.

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2469703–2469707. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d5ra03949e

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