Two-Dimensional Porous Beryllium Trinitride Monolayer as Multifunctional Energetic Material

Abstract

Polynitrogen compounds have broad applications in the field of high-energy materials, making the exploration of two-dimensional polynitride materials with both novel properties and practical utility a highly attractive research challenge. Through global structure search methods and first-principles theoretical calculations at the Perdew–Burke–Ernzerhof (PBE) level of density functional theory (DFT), the globally minimum-energy configuration of a novel planar BeN₃ monolayer (tetr-2D-BeN₃) is predicted. This material exhibits a planar quasi-isotropic structure containing pentagonal, hexagonal, and dodecagonal rings, as well as “S”-shaped N6 polymeric units, exhibiting a high energy density of 3.34 kJ·g⁻¹, excellent lattice dynamic stability and thermal stability, an indirect bandgap of 2.66 eV (HSE06), high carrier mobility, and ultraviolet light absorption capacity. In terms of mechanical properties, it shows a low in-plane Young’s stiffness of 52.3–52.9 N·m⁻¹ and a high in-plane Poisson’s ratio of 0.55–0.56, indicating superior flexibility. Furthermore, its porous structure endows it with remarkable selectivity for hydrogen (H₂) and argon (Ar) gas separation, achieving a maximum selectivity of up to 10²³ (He/Ar). Therefore, the tetr-2D-BeN₃ monolayer represents a multifunctional two-dimensional polynitrogen-based energetic material with potential applications in energetic materials, flexible semiconductor devices, ductile materials, ultraviolet photodetectors, and other fields, thereby expanding the design possibilities for polynitride materials.

1. Introduction

High-energy-density materials are crucial in fields such as propellants, explosives, and rocket fuels due to their ability to store exceptionally high energy [1]. Polynitrogen compounds are considered ideal candidates for such materials, primarily because the N≡N triple bond energy in nitrogen gas (N₂) (954 kJ·mol⁻¹) is significantly higher than that of N-N single bonds (~160 kJ·mol⁻¹) and N=N double bonds (~418 kJ·mol⁻¹) [2]. This allows for the release of enormous energy when N-N/N = N bonds break to form N≡N bonds. Various polynitrogen structures have been investigated, including the cubic gauche phase [3], layered polymeric phases [4], black phosphorus-like structures [5], adamantane-type N₁₀ [6], P4/nbm phase [7], and ring/chain/cage configurations [8,9,10]. Alkaline (earth) metal polynitrogen compounds (e.g., MN₃, MN₅, MN₁₀, MN₄; M = Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, Ba, etc.) [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] often contain abundant polymeric nitrogen networks, such as N₃/N₅/N₆ rings or N_∞ chains [11,14,16,26]. Among them, beryllium (Be)-based polynitrogen compounds exhibit unique advantages in energy density due to their smallest atomic mass and radius when forming compounds with polymeric nitrogen. For instance, the most stable γ-BeN₄ features a chair-like nitrogen chain structure and exhibits an energy density of 3.1 kJ·g⁻¹ [27]. High-pressure-synthesized β-BeN₄ (obtained from the reaction of Be₃N₂ and N₂ at 25.4 GPa) demonstrates an even higher energy density of 3.6 kJ·g⁻¹ while retaining the same chair-like nitrogen chain configuration [28]. Notably, δ-BeN₄ [27] and P2₁/c-BeN₄ [29] exhibit exceptionally high energy densities of 4.7 kJ·g⁻¹ and 6.3 kJ·g⁻¹, respectively. These values significantly surpass those of alkaline earth metal nitrides such as P1-MgN₄ (2.084 kJ·g⁻¹) [30] and P1-CaN₁₀ (2.438 kJ·g⁻¹) [31] and even exceed that of the conventional explosive TNT (4.3 kJ·g⁻¹). Furthermore, theoretical predictions suggest that α-BeN₆ and β-BeN₆ [32] possess high energy densities of 3.32 kJ·g⁻¹ and 3.59 kJ·g⁻¹, respectively. Therefore, the development of novel high-energy-density materials based on the beryllium–nitrogen (Be-N) system is a highly promising and important direction.

Two-dimensional (2D) materials have been extensively studied, exhibiting various and novel physical and chemical properties with wide applications [33,34,35,36]. In contrast, 2D polynitrogen materials is still in its early stages, that only some 2D polynitrogen materials have been reported, such as, 2D KN₃ [37], h-MN₂ (M = Be, Mg) [38], h-MN₃ (M = Be, Ge) [39], and 2D MN₄ (M = Be, Mg, Ir, Rh, Ni, Cu, Au, Pd, Pt) [40]. Similar to bulk polynitrogen compounds, these 2D materials also contain diverse polymeric nitrogen structures, such as N₃ trimers (2D KN₃) [37], N₄ tetramers (h-MgN₂) [38], N₆ hexagons (h-BeN₃) [39], and infinite N_∞ chains (2D MgN₄) [20]. For the 2D Be-N system, many 2D N-rich beryllium polynitrogen compounds have been intensively explored, e.g., BeN₄, BeN₃, BeN₂, Be₂N₃, Be₃N₄, BeN, and Be₃N₂, revealing rich properties and broad application prospects [22,38,41,42]. For example, h-BeN₂ monolayer [38], featuring isolated “Y”-shaped N₄ tetramers, is predicted to possess a direct bandgap, excellent carrier mobility, ultrahigh on-current in transistors, and water photocatalysis capability. Furthermore, α-2D-BeN₂ consists of penta-, hexa-, and hepta-atomic rings, along with an N₄ tetramer, currently the most stable 2D BeN₂ structure, theoretically exhibits a direct bandgap of 1.82 eV, and demonstrates outstanding performance in oxygen reduction/evolution reaction catalysis and potassium-ion storage [43]. A benzene-like N₆ hexagonal honeycomb monolayer material, h-BeN₃, shows high stability, excellent carrier mobility, and n-type semiconductor properties, making it promising for nanoelectronic device applications [39]. In addition, recent studies have achieved multiscale correlation from atomic mechanisms to mesoscopic morphology in group III nitride nanosystems by coupling DFT with phase-field modeling, establishing a theoretical foundation for predicting broader semiconductor nanostructures and advancing the development of novel nitrogen-containing compounds [44]. Experimentally, the successful synthesis of a 2D BeN₄ monolayer with parallel armchair-like infinite [N]_n chains possesses anisotropic characteristics and potential applications in ion battery storage, CO₂ capture, and hydrogen storage [22]. Nevertheless, searching for more practical 2D polynitrogen materials with novel, advanced properties is in the ascendant.

In this work, using the artificial bee colony (ABC) algorithm for 2D global structure search, a novel tetragonal porous BeN₃ monolayer (tetr-2D-BeN₃), consisting of Be atoms and “S”-shaped N₆ tetramer segments, is systematically investigated. Compared with h-BeN₃ [39], it has lower energy while maintaining excellent lattice dynamics and thermal stability, along with a high energy density of 3.34 kJ·g⁻¹. This new structure exhibits an indirect bandgap (2.66 eV) with high carrier mobilities, strong ultraviolet light absorption, and a large-pore structure that enables superior gas separation performance. It is expected to serve as a highly stable multifunctional material with broad application prospects in various fields.

2. Materials and Methods

2.1. Materials

The artificial bee colony (ABC) algorithm within the CALYPSO code [45] is employed to conduct a global structural search for two-dimensional (2D) compounds with a Be:N = 1:3 (BeN₃) stoichiometric ratio. This study focuses on the lowest-energy structure from these 1800 candidates, a 2D planar BeN₃ structure with P4m 2D space group (wallpaper group).

2.2. Calculation Details

First-principles simulations based on density functional theory (DFT) [46,47] are performed using the VASP (vesion 6) software package [48]. The electron–ion interactions are described by the projector augmented wave (PAW) method [49], with a plane-wave basis set energy cutoff of 520 eV. The exchange–correlation effects are treated using the Perdew–Burke–Ernzerhof (PBE) correlation–exchange (XC) functional. For geometric optimization and electronic property calculations, the Γ-centered k-point mesh in the Brillouin zone is set to 6 × 6 × 1. The energy convergence threshold is set to 10⁻⁵ eV, and the atomic force convergence threshold is 0.01 eV/Å. All intrinsic pristine structures are optimized using the ISIF = 3 tag in VASP, where stress convergence is automatically controlled by the force convergence criterion. The more accurate electronic structure is obtained using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional [50]. The lattice dynamical stability of the material is verified through phonon spectra calculations using the finite displacement method [51]. Ab initio molecular dynamics (AIMD) simulations are conducted in the NVT ensemble with a time step of 1 fs for a total duration of 5 ps to evaluate the structural stability at elevated temperatures. The structural search within the CALYPSO code [45] settings included parallel calculations for unit cells with varying numbers of atoms, specifically examining 2:6, 3:9, and 4:12 configurations. All calculations use a population size of 20 and 30 generations of evolution, generating a total of 1800 candidate structures.

The formation energy of tetr-2D-BeN₃ is calculated using the following equation:

$$E_f=\left(E_{\mathrm{B}\mathrm{e}{\mathrm{N}}_{\mathrm{3}}}-E_{\mathrm{B}\mathrm{e}}-3E_{\mathrm{N}}\right)/4$$

Here, $E_{\mathrm{B}\mathrm{e}}$ and $E_{\mathrm{N}}$ represents the energy of per metal atoms in the Be bulk metal phase and the energy of per atoms in the N₂ gas.

The vacancy formation energies (E_F-vac) are calculated using the following equation:

$$E_{\text{F-vac}}=E_{{\mathrm{V}}_{\mathrm{B}\mathrm{e}}/{\mathrm{V}}_{\mathrm{N}}@\mathrm{B}\mathrm{e}{\mathrm{N}}_3}+E_{\mathrm{B}\text{e-}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}/\text{N-}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}}-E_{\mathrm{B}\mathrm{e}{\mathrm{N}}_3}$$

Here, $E_{\mathrm{B}\text{e-}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}}$ and $E_{\text{N-}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}}$ represents the energy of a single Be and N atom.

The in-plane Young’s stiffness $Y\left(\mathsf{\theta }\right)$ and Poisson’s ratio $v\left(\mathsf{\theta }\right)$ are calculated as functions of θ based on the equations as listed below [52]:

$$Y\left(\mathsf{\theta }\right)={\displaystyle \frac{C_{11}{C}_{22}-{C_{12}}^2}{C_{11}{\sin }^4\mathsf{\theta }+C_{22}{\cos }^4\mathsf{\theta }+(\frac{C_{11}{C}_{22}-{C_{12}}^2}{C_{66}}-2C_{12}){\cos }^2\mathsf{\theta }{\sin }^2\mathsf{\theta }}}$$

$$v\left(\mathsf{\theta }\right)={\displaystyle \frac{(C_{11}+C_{12}-\frac{C_{11}{C}_{22}-{C_{12}}^2}{C_{66}}){\cos }^2\mathsf{\theta }{\sin }^2\mathsf{\theta }-C_{12}{\sin }^4\mathsf{\theta }-C_{12}{\cos }^4\mathsf{\theta }}{C_{11}{\sin }^4\mathsf{\theta }+C_{22}{\cos }^4\mathsf{\theta }+(\frac{C_{11}{C}_{22}-{C_{12}}^2}{C_{66}}-2C_{12}){\cos }^2\mathsf{\theta }{\sin }^2\mathsf{\theta }}}$$

According to the DP theory [53], the carrier mobility of a 2D structure is calculated as

$${\mu }_{2D}={\displaystyle \frac{e{\mathrm{\hslash }}^3{C}_{2D}}{k_{B}T{m}^{\mathrm{*}}{m}_d{\left(E_1\right)}^2}}$$

where $e$, $\mathrm{\hslash }$, and $k_B$ are the electron charge, reduced Planck constant, and Boltzmann constant, respectively. $C_{2D}$ are the elastic moduli, T is the temperature (300 K), $m^{\mathrm{*}}$ is the effective mass along the transport direction, which can be obtained by fitting the band structure at the CBM and VBM, and $m_d=\sqrt{m_x^{\mathrm{*}}{m}_y^{\mathrm{*}}}$ is the average effective mass. $E_l$ is the deformation potential constant, which is the key to the magnitude of mobility, defined by $E_l=\partial E_{edge}/\partial \epsilon$, where $E_{edge}$ is the energy of the band edge and $\epsilon =∆l/l_0$. The strain range is from −0.6% to +0.6% with an interval of 0.2%.

According to the frequency-dependent permittivity of $\epsilon \left(\mathsf{\omega }\right)={\epsilon }_1\left(\mathsf{\omega }\right)+i{\epsilon }_2\left(\mathsf{\omega }\right)$, the absorption coefficient is obtained based on the following equation [54,55]:

$$\alpha \left(\mathsf{\omega }\right)={\displaystyle \frac{\sqrt{2}\mathsf{\omega }}{c}}{\left[\sqrt{{\epsilon }_1^2\left(\mathsf{\omega }\right)+{\epsilon }_2^2\left(\mathsf{\omega }\right)}-{\epsilon }_1\left(\mathsf{\omega }\right)\right]}^{1/2}$$

The selectivity $S_{gas1/gas2}$ is an important indicator of the efficiency of gas separation and can be assessed with the Arrhenius equation [56]:

$$S_{gas1/gas2}={\displaystyle \frac{r_{gas1}}{r_{gas2}}}={\displaystyle \frac{A_{gas1}}{A_{gas2}}}{\displaystyle \frac{e^{-E_{gas1}/RT}}{e^{{-E}_{gas2}/RT}}}$$

where r is the diffusion rate, A is the diffusion prefactor (assuming that the A of gas molecules are the same as 10¹¹) [57], E is the diffusion energy barrier, R is the gas constant, and T is the temperature.

3. Results and Discussion

3.1. Structural Search and Energetic Properties of BeN₃

First-principles calculations reveal that the global energy-minimum configuration of BeN₃ is found in the largest unit cell system (containing 4 Be atoms and 12 N atoms) (Figure 1a,b), while previously reported monolayer structure (h-Be₂N₆) [39] with the same stoichiometry are identified in the corresponding smallest unit cells. This result suggests that increasing the unit cell size facilitates the discovery of global energy-minimum structures for two-dimensional (2D) Be-N compounds, providing a new strategy for global structural searches of similar 2D materials.

As shown in Figure 1a, the global energy-minimum 2D-Be₄N₁₂ (here named tetr-2D-BeN₃) exhibit significant thermodynamic advantages over the reported h-Be₂N₆ [39], with a total energy reduction of 110 meV/atom. The tetr-2D-BeN₃ monolayer possesses a tetragonal orthogonal lattice with lattice constants a = b = 7.74 Å and a space group (wallpaper group in 2D) symmetry of P4m. As shown in Figure 1b, the unit cell contains four equivalent Be atoms and three types of nitrogen atoms (N1, N2, N3), where N1 adopts a Be-N-N tri-coordination mode, N2 exhibits N-N di-coordination, and N3 shows Be-Be-N tri-coordination. The tetr-2D-BeN₃ planar structure consists of five-membered, eight-membered, and twelve-membered rings, featuring an “S”-shaped N₆ cluster. The Be-N bond lengths range from 1.61 to 1.65 Å, while the N-N bond lengths (1.32–1.41 Å) lie between the typical single N–N bond (1.45 Å) [58] and double N=N bond (1.25 Å) values [59], suggesting its potential as an energetic material. Under ambient pressure, the exothermic decomposition of BeN₃ yields the most stable Be-N compound Be₃N₂ ($Ia\overline{3}$) [28] and N₂, as shown in the following equation:

$$6\mathrm{B}\mathrm{e}{\mathrm{N}}_3\to {2\mathrm{B}\mathrm{e}}_3{\mathrm{N}}_2+7{\mathrm{N}}_2+10.6 \mathrm{e}\mathrm{V}$$

This process releases a chemical energy of 10.6 eV, corresponding to an energy density of approximately 3.34 kJ·g⁻¹, which is slightly lower than that of BeN₄ (3.60 kJ·g⁻¹) [28], δ-BeN₄ (4.70 kJ·g⁻¹) [27], β-BeN₆ (3.59 kJ·g⁻¹) [32], and HEDM TNT (4.30 kJ·g⁻¹) but higher than CNO (2.2 kJ·g⁻¹) [60], LiN₅ (2.72 kJ·g⁻¹) [61], GdN₆ (1.62 kJ·g⁻¹) [62], YN₁₀ (3.05 kJ·g⁻¹) [63], γ-BeN₄ (3.10 kJ·g⁻¹) [27].

3.2. Bonding Characteristics and Stability of BeN₃

To further elucidate the bonding characteristics in tetr-2D-BeN₃, deformation charge density, electron localization function (ELF), and Bader charge analysis are calculated (Figure 1c). The deformation charge density reveals electron accumulation at Be-N bridging sites and partial electron distribution between adjacent nitrogen atoms within the N₆ chain segment, indicating significant covalent hybridization between Be-N atoms and within the N₆ chains. Additionally, significant electron density is observed on the N2 surface along the direction opposite to the N1-N2-N3 angle bisector. Analysis of the ELF (where high values (>0.5) correspond to lone pairs, core electrons, or covalent bonds, low values (<0.5) represent ionic bonds, and ELF~0.5 signifies metallic bonding) shows a highly localized electron cloud (ELF ≈ 1) on the N2 surface, indicating the presence of unhybridized p-orbitals along the direction normal to the plane. The high ELF values at Be-N and N-N sites further suggest the formation of strong covalent bonds. Bader charge analysis quantifies electron transfer, revealing that Be atoms transferred 1.66 e⁻, while nitrogen atoms exhibited significant charge variation. Specifically, the tri-coordinated N1 (Be-N-N), di-coordinated N2 (N-N), and tri-coordinated N3 (Be-Be-N) acquired charges of +0.47 e⁻, +0.05 e⁻, and +1.14 e⁻, respectively. Crucially, the notably low charge acquisition and the high ELF localization on the di-coordinated N2 atom, indicative of poorly hybridized/underbonded states due to its low coordination and minimal charge transfer, are highly pertinent to the observed high energy density of tetr-2D-BeN₃. The electron-rich N2 center, featuring unpaired electrons or highly localized electrons within its p_z orbital with a lone pair electron perpendicular to the plane, represents a significant metastable site storing considerable strain energy. Upon decomposition or reaction initiation, these energetically frustrated sites, particularly the under-bonded and electron-deficient N2, provide a substantial thermodynamic driving force, facilitating the rapid release of stored chemical energy and thereby underpinning the material’s high energy density.

Furthermore, the stability of the novel tetr-2D-BeN₃ monolayer is evaluated from three perspectives: structural stability, thermodynamic feasibility, and dynamical stability. The formation energy (E_f, referenced to Be metal and N₂ molecules) is calculated as +0.02 eV/atom, suggesting that the formation of tetr-2D-BeN₃ from Be metal and N₂ molecules requires slight external energy input. Phonon spectrum analysis (Figure 2a) confirms the dynamical stability of tetr-2D-BeN₃, as no imaginary frequencies are observed across the entire Brillouin zone. Finally, AIMD simulations verify the thermal stability of this new structure. Figure 2b displays geometric snapshots after 5 ps of simulation at temperatures of 300, 500, 1000, 1200, and 1400 K, showing that the tetr-2D-BeN₃ monolayer maintains structural integrity below 1400 K, exhibits partial bond breaking at 1500 K. At 2000 K, tetr-2D-BeN₃ completely decomposes into amorphous Be-N clusters and N₂ molecules. This theoretical prediction of decomposition temperatures (2000 K) is higher than the experimentally measured decomposition temperatures of graphene and MoS₂ monolayers (1100–1300 K) [64,65], and serves as a reference for comparative thermal stability analysis. Furthermore, the environmental stability of tetr-2D-BeN₃ through AIMD simulations at 300 K under both H₂O and O₂ atmospheres is investigated. As shown in Figure 3, the tetr-2D-BeN₃ monolayer demonstrated excellent structural stability during 5 ps AIMD simulations in H₂O environment, with energy fluctuations remaining within a stable range. However, in an O₂ environment, significant oxidation is observed, characterized by the formation of localized Be-O compounds and the cleavage of Be-N bonds. These results, combined with vacuum stability tests, demonstrate that while tetr-2D-BeN₃ maintains thermal stability up to 1400 K in vacuum, it shows pronounced oxygen sensitivity at ambient conditions, necessitating oxygen-free environments during both preparation and application.

Considering the tendency for point vacancies to form during the synthesis of 2D materials, four different types of point vacancies on the tetr-2D-BeN₃ surface are tested, labeled as V_Be, V_N1, V_N2, and V_N3 (Figure 4a). As shown in Figure 4b,c, after fully structural optimization, the V_Be vacancy is found to cause structural disruption in the tetr-2D-BeN₃ sheet, while the structures with V_N1, V_N2, and V_N3 vacancies only transform the original Be-N pentagonal rings into Be-N quadrilateral rings without significant changes to the overall crystal structure. Furthermore, calculations of vacancy formation energies (E_F-vac) reveal that the E_F-vac values for V_Be and V_N1/N2/N3 are 7.413 eV and 6.861 eV, respectively, indicating that V_Be is more difficult to form than V_N (Figure 4d). Additionally, E_F-vac exceeding 5 eV suggests that low-density vacancies are energetically unlikely to form on the tetr-2D-BeN₃ surface. Furthermore, considering that many nitrides require high-pressure conditions for synthesis and that tetr-2D-BeN₃ additionally possesses porous characteristics, the experimental synthesis of this material still faces significant challenges.

3.3. Mechanical, Electronic, and Optical Properties of BeN₃

For mechanical properties, the elastic constants of tetr-2D-BeN₃ are calculated as C₁₁ = C₂₂ = 76.2, C₁₂ = 42.7, and C₆₆ = 17.0 N·m⁻¹ satisfying the mechanical stability criteria for 2D structures (C₁₁ > 0, C₂₂ > 0, C₁₁C₂₂ − C₁₂C₂₁ > 0, C₆₆ > 0) [66], confirming its mechanical stability. Tetr-2D-BeN₃ exhibits quasi-isotropic mechanical behavior, the in-plane Young’s stiffness ($Y\left(\mathsf{\theta }\right)$) is in range of 52.3–52.9 N·m⁻¹ with a tiny anisotropy of Y_max/Y_min = 1.01, indicating a relatively soft in-plane characteristic, comparable to silicene (62 N·m⁻¹) [67] and phosphorene (21–91 N·m⁻¹) [68] but significantly lower than graphene (330 N·m⁻¹) [69] and h-BN (279 N·m⁻¹) [70]. The Poisson’s ratio of tetr-2D-BeN₃ is high (0.55–0.56), reflecting high ductility.

The band structure of tetr-2D-BeN₃ shown in Figure 5a, reveals an indirect bandgap of 1.68 eV (PBE), with the valence band maximum (VBM) located at the M point (1/2, 1/2, 0) and the conduction band minimum (CBM) at the Γ point (0, 0, 0). HSE06 hybrid functional calculations yielded a more accurate bandgap of 2.66 eV. As shown in Figure 5b,c, projected density of states (PDOS, PBE) and partial charge analysis show that the VBM of tetr-2D-BeN₃ is dominated by the p_z orbitals of N1 and N3, while the CBM arises from the p_z orbitals of N2 and minor contributions from Be p_z orbitals.

To gain deeper insight into the carrier transport properties of tetr-2D-BeN₃, deformation potential theory is employed to calculate its carrier mobility. With a tetragonal lattice structure, tetr-2D-BeN₃ exhibits identical mobility along its two principal axes (a/b directions). For electrons (E) and holes (H), the deformation potentials and effective masses of E/H along these axes are 1.012/0.986 eV and 0.974/0.806 m_e, respectively. The calculated mobilities of E/H reach 1.6/2.5 × 10³ cm²V⁻¹s⁻¹, which is lower than those of graphene (340 × 10³ cm²V⁻¹s⁻¹) [71] and monolayer black phosphorus (26 × 10³ cm²V⁻¹s⁻¹) [72], but higher than that of MoS₂ monolayer (0.072–0.2 × 10³ cm²V⁻¹s⁻¹) [73]. These findings suggest that tetr-2D-BeN₃ could be a promising candidate for microelectronic applications.

The optical properties of tetr-2D-BeN₃ (calculated at the HSE06 level) reveal anisotropic dielectric constants, satisfying ε_aa = ε_bb ≠ ε_cc. As shown in Figure 6, the tetr-2D-BeN₃ exhibits an indirect bandgap of 2.66 eV and anisotropic optical absorption spectra, with significant differences between the in-plane (a/b) and out-of-plane (c) absorption coefficients. Its absorption in the visible range is weak, with only a gradual increase along the a/b direction at 2.6 eV. However, in the ultraviolet range, absorption peaks at 3.5 eV and 8 eV, reaching 3.7 and 5.5 × 10⁵ cm⁻¹. This unique anisotropic optical response, combined with its 2.66 eV indirect bandgap, suggests that tetr-2D-BeN₃ holds potential for applications in polarization-sensitive optoelectronic devices and ultraviolet photodetection.

3.4. Gas Separation Applications of BeN₃

The tetr-2D-BeN₃ monolayer structure contains twelve-membered rings with a pore diameter of 4.98 Å, indicating its potential for gas separation. Further studies reveal that tetr-2D-BeN₃ exhibits low energy barriers for the permeation of helium (He), neon (Ne), and hydrogen (H₂), with values of 0.241 eV, 0.486 eV, and 0.564 eV, respectively. This suggests that He, Ne, and H₂ can diffuse rapidly across the membrane over a wide temperature range, as illustrated in Figure 7a,b. Moreover, tetr-2D-BeN₃ demonstrates high selectivity for Ar and H₂ compared with other noble gases and common atmospheric gases (Figure 7c). Specifically, the selectivity ratios for He/Ar, Ne/Ar, H₂/O₂, H₂/H₂O, and H₂/N₂ reach 10²³, 10¹⁹, 10⁶, 10⁸, and 10¹³, respectively. These gas separation capabilities are comparable to those of porous phosphorene and porous silicene [74,75]. Therefore, tetr-2D-BeN₃ holds significant application value and broad prospects in the field of gas separation.

4. Conclusions

In summary, based on first-principles calculations, the energetic properties, structural stability, mechanical properties, electronic properties, optical absorption characteristics, and gas separation performance of the porous tetr-2D-BeN₃ monolayer are systematically investigated. The tetr-2D-BeN₃ is a global energy-minimum 2D structure searched by the artificial bee colony (ABC) algorithm. This monolayer material exhibits high energy density of 3.34 kJ·g⁻¹, excellent lattice dynamic stability and maintains its fundamental structural framework with outstanding thermal stability up to approximately 1400 K. It demonstrates in-plane quasi-isotropic mechanical, electronic, and optical properties, including a Young’s stiffness of 52.3–52.9 N·m⁻¹, a large Poisson’s ratio of 0.55–0.56, a moderate indirect bandgap of 2.66 eV, along with high carrier mobilities of 1.6/2.5 × 10³ cm²V⁻¹s⁻¹ and strong ultraviolet light absorption capability. The porous nature of the material enables highly efficient gas separation for hydrogen and argon, achieving maximum selectivity values of 10¹³ (H₂/N₂) and 10²³ (He/Ar), respectively. Owing to these novel characteristics and exceptional performance, the tetr-2D-BeN₃ monolayer shows potential applications in energetic materials, flexible semiconductor devices, ductile materials, ultraviolet photodetectors, and other fields, thereby expanding the design possibilities for polynitride materials.