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Research Article  |  Open Access  |  27 May 2024

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

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Microstructures 2024;4:2024032.
10.20517/microstructures.2023.80 |  © The Author(s) 2024.
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The recent synthesis of a two-dimensional (2D) MBene sheet, referred to as the boridene sheet (Mo4B6Tz), has ignited considerable interest in exploring 2D transition metal borides. Boridene has an ordered arrangement of metal vacancies, which are pivotal to its stability. Employing first-principles calculations, we explored the stable phases, electronic properties and catalytic abilities of boridene with different vacancy concentrations (Vm). Our results demonstrate that Vm significantly influences the cohesive energies of boridene sheets. Phonon spectrum and ab initio molecular dynamics simulations reveal the high stability of the vacancy-free boridene Mo6B6T6 (T = O, -OH), underscoring their potential for experimental realization. Substituting Mo atoms with Nb, Ta, or W enhances the structural stability of boridene sheets, leading to the identification of four stable variants: Nb6B6F6, Ta6B6F6, Ta6B6O6, and W6B6O6. These boridene sheets exhibit metallic behavior, with five structures displaying near-zero Gibbs free energy for hydrogen atom adsorption, indicating their potential as catalysts for the hydrogen evolution reaction. The uncovering of vacancy-free boridenes and their 2D derivatives greatly broadens the scope of the MBene family.


2D materials, boridene, first-principles calculations, hydrogen evolution reaction


The emergence of graphene has spurred the exploration and production of numerous other two-dimensional (2D) materials[1-4]. These include transition metal carbides, nitrides, and carbides/nitrides, commonly known as MXenes, which present intriguing prospects for expanding the realm of 2D materials[5-8]. MXenes are a class of materials formed by selectively removing atomic layers from their parent “MAX” phase, where “M” represents a transition metal, “A” indicates an element predominantly from columns IIIA and IVA, and “X” denotes either carbon or nitrogen[9,10], with over 100 MXenes having been either theoretically predicted or experimentally synthesized. This growing repertoire of MXenes demonstrates their immense potential for diverse applications, such as transistors, batteries, and magnetism-based technologies[11-20]. In particular, they have found extensive use in catalytic applications such as hydrogen/oxygen evolution reactions, oxygen reduction reactions, nitrogen reduction reactions, CO2 reduction reactions, and more[21-23].

The boom of MXenes has further inspired efforts to extend their composition beyond the carbon/nitrogen elements. This has resulted in the emergence of transition metal borides, also known as MBenes, in recent years[24-26]. MBenes are derived from ternary or quaternary MAB phases, with “B” representing the boron element, and they exhibit a diverse range of complex structures and stoichiometries[27]. Currently, several types of MBenes, such as Cr2B2 and Mo2B2, have been synthesized[28,29], and over 50 MBene candidates have been predicted[22]. They have displayed fascinating properties, including exceptional electrical conductivity, high mechanical strength and stability, and remarkable thermal conductivity[30-33]. Consequently, MBenes hold great promise in various fields such as batteries, biomedicine[34], and catalysts for energy conversion[35].

In a recent experimental study, a new MBene sheet called the boridene sheet was successfully synthesized, with the formula Mo4/3B2Tz (Tz denotes O, F, or OH surface terminations)[36]. The boridene sheet consists of three atomic layers arranged as Mo-B-Mo. Unlike previously reported MXene and MBene sheets, the boridene sheet exhibits ordered Mo vacancies above and below the B layer, which result from the selective etching of Y atoms in the bulk phases of (Mo2/3Y1/3)2AlB2. Since vacancies substantially influence the stability and physical and chemical properties of materials, it is natural to ask: How would the vacancy concentration (Vm) affect the stability of the boridene sheet? Is it possible to discover stable boridene sheets with lower energy and unique properties?

In this study, we systematically investigated the stable phases and properties of boridene sheets with varying Vm. Our study begins by analyzing the vacancy-dependent stabilities of the experimentally realized Mo4B6 boridene sheet. We found that the vacancy-free configuration, namely the Mo6B6 structure, exhibits lower cohesive energy (Eco) than Mo4B6. We then expanded our study to explore the stabilities of Mo6B6 and its derivatives by replacing Mo with Ta, Nb, or W atoms. We totally considered twenty-four possible M6B6T6 phases and examined their phonon spectrum and ab initio molecular dynamics (AIMD) results. We have identified six M6B6T6 (M = Mo, Nb, Ta, and W, T = O, F, and OH) sheets with high stabilities: Mo6B6O6, Mo6B6(OH)6, Nb6B6F6, Ta6B6F6, Ta6B6O6 and W6B6O6. Electronic property analysis indicates these materials exhibit metallic properties and display good conductivity. Notably, boridene sheets, including Mo6B6O6, Mo6B6(OH)6, and Ta6B6O6, demonstrate high catalytic activity for the hydrogen evolution reaction (HER), with near-zero Gibbs free energies of hydrogen binding. Additionally, the catalytic performance of Nb6B6F6 and W6B6O6 monolayers can be activated when they are negatively charged. The high stability and excellent catalytic properties of the M6B6T6 sheets make them the competitive candidates in the MBene family for potential energy application.


Our first-principles calculations were based on density functional theory (DFT) and implemented in the Vienna ab initio simulation package (VASP)[37]. The interactions between the ionic cores and the valence electrons were described by the projector-augmented-wave (PAW)[38] method. Electrons in the brackets of Mo[4d55s1], Nb[4d45s1], Ta[5d36s2], W[5d46s2], H[1s1], O[2s22p4] and F[2s22p5] are treated as valence electrons. The Perdew-Burke-Ernzerhof functional (PBE)[39] within the generalized gradient approximation (GGA) was used throughout our computations. The energy cut off of the plane waves was set to 400 eV. The structures were completely relaxed, and the numerical convergence was achieved with a tolerance of 0.005 eV/Å in force and 10-6 eV in energy. The Monkhorst pack k-point grid of 7 × 7 × 1 and 14 × 14 × 1 was used for geometric optimization and self-consistent calculation, respectively. To avoid artificial interactions between the neighboring layers, we set the vacuum slab larger than 20 Å in the z-direction. The phonon spectrum was calculated based on the density functional perturbation theory using the PHONOPY package[40]. In phonon calculations, tighter convergence criteria (0.002 eV/Å for force and 10-8 eV for energy) with a finer k-point grid (2π × 0.02 Å-1) were employed. The AIMD simulations were performed using the canonical ensemble with temperature controlled by a Nosé-Hoover bash scheme[41]. The time scale is set to 5 ps with a time step of 1.0 fs.

The strain ε is defined as ε = (a - a0)/a0, where a is the lattice parameter in the strained state and a0 represents that for the strain-free state. The total HER pathway can be written as H+ + e- → 1/2H2[42]. The Gibbs free energy (ΔGH*) of hydrogen atom adsorption is the critical descriptor for hydrogen evolution,[43,44] defined as ΔGH* = ΔEH + ΔEZPE - TΔSH, where ΔEH, EZPE, and ΔSH are the hydrogen chemisorption energy, the reaction zero-point energy, and the entropy change between the adsorbed state and the gas phase, respectively. As EZPE - TΔSH = 0.24 eV is a well-established approximation[42], we simplify the ΔGH* as ΔGH* = ΔEH + 0.24.


Vacancy concentrations of boridene sheets

Vacancies are inherent point defects in the experimentally realized crystal structures. Vm substantially affects the heat transport of atoms, thus influencing the electronic, thermal, and magnetic engineering properties of materials. Experimentally, vacancy defects in 2D materials can be deliberately produced during post-synthesis by several approaches, such as ion/electron irradiation[45], plasma treatments[46] and high-temperature annealing in the presence of different gases[47].

The pristine boridene Mo4B6 sheet [Figure 1A and B] crystallizes in a hexagonal lattice (space group: P321) with three atomic layers stacked as Mo-B-Mo. The centered boron layer possesses a honeycomb pattern sandwiched by two metal layers with misaligned vacancy sites. The metal atoms in pristine Mo4B6 are undercoordinated, making them chemically active. Previous studies[48] have shown that the bare structures are vulnerable to surface terminations such as O, OH, and F, and the functional groups tend to prefer adsorption on the bridge sites of M atoms. Therefore, the chemical formula of functionalized boridene can be expressed as M4B6T6 (T = O, OH, F) with the unit cell containing four metal atoms, six boron atoms, and six functional groups.

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 1. (A and B) Top view and side view of the Mo4B6 sheet. The vacancy sites are indicated by dashed circles. (C) Computed Cohesive energies of boridene sheets with different vacancy concentrations (Vm).

Different from previously reported 2D materials such as graphene, transition metal dichalcogenides, and MXenes, whose pristine structures are vacancy-free, the synthesized boridene contains two Mo vacancies in a unit cell [Figure 1B]. To explore the effect of vacancy defects on the stabilities of the boridene sheet, different concentrations of Mo and B vacancies were considered in 1 × 2, 1 × 3 and 2 × 2 supercells.

We defined the Vm of pristine Mo4B6 as the ratio of vacancies to the total number of atoms. Therefore, the metal Vm of the pristine structure is 2/12 (16.67%). Initially, we increased the metal vacancies by removing one or two Mo atoms from a unit cell. This resulted in Mo3B6 and Mo2B6 with the Vm values of 3/12 (25%) and 4/12 (33%), respectively. Noticeably, the two cases exhibit various structural configurations with multiple defects. In Supplementary Figures 1 and 2, we have depicted the potential positions of vacancies in each phase and computed their respective formation energies. Further investigations were carried out exclusively on the structure with the lowest energy.

Next, we aim to reduce the Vm in the structure. This can be achieved by either introducing additional atoms into the primitive cell (such as Mo5B6 and Mo6B6) or by removing atoms from the larger supercells (such as Mo10B12, Mo16B18, and Mo22B24 in a 1 × 2, 1 × 3 and 2 × 2 supercell, respectively [Supplementary Figures 3 and 4]. The Vm ranges from 0% to 33.3%, and then all lattices were fully relaxed to their lowest energy configurations. The geometric parameters, including lattice constants, Mo-B distances, average B-B bond lengths, energy values, and Eco for each defective structure, were summarized in Table 1.

Table 1

Lattice constants a and b (in Å), average bond length for Mo-B and B-B (in Å), the vacancy concentrations (Vm) and cohesive energy (in eV per atom) for different structures

FormulaabMo-BB-BVm (%)Cohesive energy

The stability of the defective structures was assessed by calculating their Eco, defined as:

$$ \begin{equation} \begin{aligned} E_{\mathrm{co}}=\left[E\left(\mathrm{Mo}_{\mathrm{x}} \mathrm{B}_{\mathrm{y}}\right)-\mathrm{x} E(\mathrm{Mo})-\mathrm{y} E(\mathrm{~B})\right] /(\mathrm{x}+\mathrm{y}) \end{aligned} \end{equation} $$

where E(MoxBy) is the total energies of the 2D sheets, and E(Mo) and E(B) are the energy of isolated Mo and B atoms, respectively. Taking the pristine Mo4B6 sheet as the reference (Vm = 16.67%), we found that the change of Vm decreases Eco [Figure 1C, Table 1], indicating the enhancement of material stability. For example, the Eco of vacancy-free boridene Mo6B6 is -6.87 eV/atom, lower than many other transition metal borides such as FeB2 (-4.87 eV/atom)[49], FeB3 (-5.93 eV/atom)[50], and FeB6 (-5.79 eV/atom)[51] monolayers.

Stabilities of boridene sheets and its derivatives

To further identify the dynamical stability of boridene sheets with different defect concentrations, the phonon spectrum for each structure was calculated. Previous research has demonstrated that the bare Mo4B6 sheet is highly unstable. However, introducing functional groups (-OH, -O, -F) on its surfaces has proven to significantly enhance its stability[48]. By employing a similar approach, we conducted phonon spectrum calculations for Mo5B6, Mo6B6, Mo10B12, Mo16B18, and Mo22B24 sheets with various functional groups. We found that the vacancy-free Mo6B6 layers [Supplementary Figure 5] functionalized with -O and -OH groups, namely Mo6B6O6 and Mo6B6(OH)6 sheets, become stable with no soft modes in the calculated phonon spectra, as shown in Figure 2A and B. Importantly, the highest frequencies of Mo6B6O6 are up to 28.1 THz (937 cm-1), higher than that found in silicene (580 cm-1)[52], MoS2 (473 cm-1)[53] and Cu2Si (420 cm-1)[54] monolayers. The high-energy phonons indicate the robust Mo-B and B-O interactions in the boridene sheets.

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 2. (A-F) Phonon spectrum of different M6B6T6 (M = Mo, Nb, Ta, W, T = O, F, OH) sheets.

We further evaluated their thermal stabilities by conducting AIMD simulations at 300 K over the time scale of at least 5 ps. Analysis of the snapshots captured at the end of AIMD simulation reveals the excellent preservation of both hexagonal frameworks, with no observable fractures in chemical bonds [Figure 3A and B]. This finding further confirms the thermodynamic stability of both Mo6B6O6 and Mo6B6(OH)6 sheets.

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 3. AIMD simulated results for different M6B6T6 (M = Mo, Nb, Ta, W, T = O, F, OH) sheets at 300 K for 5 ps.

The above analysis not only demonstrates the high stability of the vacancy-free Mo6B6T6 sheets but also indicates that these materials exhibit even lower formation energy than the experimentally synthesized boridene sheets. This suggests that the vacancy-free boridene sheets hold great promise for future experimental validation.

The high stability of the Mo6B6 framework has prompted us to further explore whether other transition metals can stabilize this structure. To investigate this, we replaced Mo with neighboring transition metals, such as Nb, W, and Ta, from the periodic table. We performed dynamical and thermal stability tests on the functionalized M6B6T6 sheets (M = Nb, W, or Ta and T = O, OH, or F). As a result, we additionally identified four M6B6T6 sheets, namely Nb6B6F6, Ta6B6F6, Ta6B6O6, and W6B6O6, to be very stable (see Figure 2C and F, Figure 3C-F). Although a W6B6(OH)6 sheet displays dynamical stability, its thermodynamic instability prompts us to exclude it from further discussion. However, we have included its structural and electronic properties in the Supplementary Material [Supplementary Figures 6 and 7, Supplementary Table 1].

Bonding and charge analysis

We have identified six stable M6B6T6 sheets, in which the element M can be Mo, Nb, W, or Ta, and the terminal T can be -O, -OH, or -F. The lattice parameters and Eco for these structures are summarized in Table 2. Noticeably, the Eco values range from -5.79 to -7.50 eV, lower than many previously reported boron-based layers[49,50,55,56].

Table 2

Lattice constants (in Å) and cohesive energies (in eV) of different M6B6T6 sheets

SystemabCohesive energy

To gain a deeper understanding of the high stability exhibited by the functionalized M6B6T6 sheets, we have calculated the electron localization function (ELF) for all these sheets, as shown in Figure 4. For the bare M6B6 layers, the electron localization is predominantly located between the boron atoms, indicating the presence of covalent bonds between B-B atoms. The absence of electron localization between the metal and boron atoms suggests the existence of ionic bonds in these regions. In the case of the functionalized M6B6T6 layers, a larger ELF is observable between the B-B atoms in most structures, implying the strengthening of the B-B bonds. Interestingly, a considerable electron localization is observed around the functional groups, demonstrating that the surfaces of M6B6T6 layers are chemically inert compared to the pristine M6B6 sheets. Among the six M6B6T6 sheets, we found a higher electron population concentrated around the B atoms and functional groups in the Ta6B6O6 and W6B6O6 sheets [Figure 4I and J]. This suggests stronger bonding interactions in the two sheets. This is consistent with the calculated Eco, as the Ta6B6O6 and W6B6O6 sheets exhibit the lowest values among all the sheets [Table 2].

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 4. The slice cuts of ELF along the (001) plane for (A-D) the bare M6B6 sheets and (E-J) functionalized M6B6T6 sheets. The isovalue was set to 0.75 eÅ-3.

The Bader charge analysis reveals a significant electron transfer from the metal elements to the O, OH, and F terminals, with a range of 0.85-1.33 e (see the details in Supplementary Figure 8-13). This finding confirms that the functional groups can compensate for the extra electrons on the surface of the pristine M6B6 sheets, thereby greatly enhancing their structural stability.

Mechanical properties

The mechanical properties of the functionalized M6B6T6 sheets were analyzed by calculating the elastic constants. According to the elastic stability criteria[57], a stable 2D hexagonal sheet should satisfy C44 > 0 and C11 > |C12|, where Cij is the elastic constants. For all M6B6T6 sheets, the calculated values of Cij [Table 3] indicate that these mechanical stability criteria are fully satisfied. Additionally, the estimated Poisson’s ratios, ν, are all positive, ranging from 0.098 to 0.3. The estimated Young’s modulus (213.55~338.32 GPa·nm) is generally higher than that of phosphorene (23~92.3 GPa·nm)[58] and monolayer Be5C2(33~130 GPa·nm)[59]. However, it is similar to the Young's modulus of MoS2 (~270 GPa)[60] and WS2 (244.18 GPa)[61].

Table 3

Calculated elastic constants (in N/m), the Poisson's ratio ν, and the Young's modulus (in GPa·nm) for all structures

SystemC11C22C12C44νYoung’s modulus

Furthermore, our study reveals that the Vm significantly affects the mechanical properties of the MoxBy sheets. By computing the elastic constants [Supplementary Table 2], we found a significant alteration in Poisson's ratio due to different Vm. Specifically, this ratio varied from v = 0.14 for Mo2B6 to v = 0.35 for Mo4B6. In the absence of vacancies, the Young's modulus exhibited the highest value. However, introducing vacancies reduced the Young's modulus. For instance, in the Mo4B6 case, the Young's modulus was reduced to 101.57 GPa•nm. Despite the decrease in Young's modulus in the defective MoxBy sheets, it still surpasses that of phosphorene.

Electronic properties

Next, we analyze how the electronic properties of M6B6T6 are influenced by surface functionalization and composition. Figure 5 presents the calculated band structures for six different M6B6T6 sheets. The band structures revealed that all sheets exhibit metallic characteristics, similar to borophene[62] and some MXenes such as V2C and Nb2C[63]. The band dispersions of M6B6T6 were strongly affected by the surface terminals and different metal elements. For instance, the band structure of Mo6B6(OH)6 [Figure 5B] shows the existence of two band crossing points along the M-Γ-K lines, while these points disappear with the surface -O termination [Figure 5A]. Dirac points can be observed in W6B6O6 [Figure 5F], but they do not exist when the metal element is replaced with Ta [Figure 5E].

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 5. (A-F) Band structures of different M6B6T6 sheets. Red circles locate the band crossing points near the Fermi level.

It is well-known that the PBE method can sometimes result in inaccurate electronic structures. Therefore, we employed the Heyd-Scuseria-Ernzerhof (HSE) method to obtain more accurate electronic properties. As depicted in Supplementary Figure 14, the band dispersion of each material is similar to that of the PBE results, and the Dirac points in Mo6B6(OH)6 and W6B6O6 are well-preserved, further confirming the previous analysis. Importantly, the metallic electronic properties of these structures also indicate excellent conductivity, making them suitable for applications in electronics and catalysis (which we will discuss in detail later). These properties are similar to those observed in the MXene family[64] and borophene monolayer[65]. We have additionally computed the vacancy-dependent band structures for the 2D MoxBy. As illustrated in Supplementary Figure 15, we have found that all MoxBy sheets retain their metallic characteristics. This is rational, as vacancies can generate localized electronic states, thereby promoting the dispersion of electrons and sustaining the metallic properties.

Figure 6 illustrates the partial density of states (PDOS) for the M6B6T6 sheets. The -O functionalized structures, namely Mo6B6O6, Ta6B6O6, and W6B6O6, show that the electronic states at the Fermi level are primarily dominated by the d orbitals of the metal atoms with a small contribution from the O-2p and B-2p states. In contrast, the -OH and -F functionalized structures exhibit negligible contributions from the p-orbitals. Generally, the magnitude of the density of states (DOS) at the Fermi level reflects the electron configuration of the d orbitals. For instance, among the six candidates, Mo6B6(OH)6 has the largest DOS at the Fermi level, which can be attributed to its electron configuration of 4d5. In comparison, Ta6B6O6 has the lowest DOS due to its 5d3 electron configuration in the outer shell.

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 6. (A-F) Partial density of states (PDOS) of different M6B6T6 sheets.

HER activity

By analyzing the DOS, we found that the predicted vacancy-free boridene sheets exhibit metallic properties and have significant DOS at the Fermi level. This suggests that the material has good conductivity, which could be advantageous for electrocatalytic processes. To investigate their potential as electrocatalysts, we mainly focus on their HER performance in the subsequent discussion. HER catalysts have been extensively studied in 2D materials, not only in the monolayer forms such as MBene and MXene but also in the heterostructures including N-doped graphene-based systems[35]. Hybridizing two types of 2D materials would lead to strong interlayer coupling, thus enhancing the HER performance, as exemplified in the N-doped graphene/MXenes composites[66]. Generally, the HER catalytic activity of a catalyst is closely connected to the adsorption and desorption processes of individual hydrogen atoms on its surface. To be an ideal catalyst for HER, the binding strength of the catalytic site with high HER properties should neither be too weak nor too strong. Hence, the ΔGH* for an ideal HER catalyst should be close to 0. A positive ΔGH* indicates low kinetics of hydrogen adsorption, while a negative value hampers the kinetics of hydrogen molecule release.

We calculated ΔGH* by testing different surface sites of vacancy-free boridenes. Among the six stable configurations, three are active for HER, including Mo6B6O6, Ta6B6O6, and Mo6B6(OH)6. We found that the O atoms of Mo6B6O6 and Ta6B6O6 and OH group of Mo6B6(OH)6 are active sites for HER, with the ΔGH* of -0.04, 0.18, and 0.11 eV, respectively (see Figure 7 and Supplementary Figure 16 for details). The calculated ΔGH* for Mo6B6O6 is even better than that of Pt (ΔGH* = -0.09 eV), and comparable to that of the 2D MXenes such as Ti2CO2 (ΔGH* = -0.04), Nb2CO2 (ΔGH* = 0.02)[63].

Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction

Figure 7. Gibbs free energy (ΔGH*) at the O sites of the (A) Mo6B6O6 and (B) Ta6B6O6 monolayers under different strains (ε).

As strain engineering is widely employed to modify the properties of 2D materials due to its simplicity and large adjustable range, we also explored the effect of strain on the HER performance for the above three sheets [Figure 7 and Supplementary Figure 16]. Experimentally, lattice strain can be readily applied for 2D materials by introducing stretchable substrates[67] or through doping methods[68]. We found that the strain engineering can modulate the HER performance of boridene sheets. Taking Mo6B6O6 as an example [Figure 7A], the tensile strain drives ΔGH* toward a more positive value, reducing the catalytic performance. On the contrary, a compressive strain can decrease the value of ΔGH*. Remarkably, applying a small strain of 1% can significantly enhance the HER performance of the O sites with the ΔGH* of 0.009 eV. Nb6B6F6 and W6B6O6 sheets are inactive for the HER due to the large ΔGH* under neutral conditions. We find that injecting a small extra charge can greatly improve their HER performance. Specifically, applying a negative charge density of 0.05-0.06 e/atom can reduce the ΔGH* for Nb6B6F6 and W6B6O6 to 0.1 and 0.09 eV, respectively, as shown in Supplementary Figure 17, making them suitable for H2 production.

As Vm can usually modulate the HER activity of 2D materials due to their ability to influence adsorption energies and affect charge transfer dynamics at the surface, we calculated the ΔGH* of the MoxBy sheets with different Vm. As shown in Supplementary Figure 18, the bare Mo4B6 sheet (Vm = 16.67%) shows the largest ΔGH* of -0.84 eV, which is unfavorable for HER. In contrast, increasing Vm to 33% (Mo2B6) can greatly improve the catalytic activity of the material, with a ΔGH* of -0.14 eV, close to the ideal ΔGH* value.


In conclusion, through first-principles calculations, we have discovered a new type of MBene sheets, namely, the vacancy-free boridene M6B6T6 (M = Mo, Nb, Ta, and W, T = O, F, and OH) monolayers. These structures show a lower Eco than the boridene Mo4B6 sheet, indicating higher stability. We have identified a total of six boridene sheets that are inherently metallic and their band dispersions are intricately linked to their termination groups. Importantly, five of the M6B6T6 sheets exhibit significant catalytic activity for HER under neutral or charged conditions. Among them, the Mo6B6O6 sheet shows the most optimal ΔGH* value of -0.04 eV. This work introduces new low-energy phases in the MBene family and highlights their potential applications in catalysis.


Authors’ contributions

Made substantial contributions to the conception and design of the study and performed data analysis and interpretation: Ma F, Jiao Y, Du A

Performed data acquisition and provided administrative, technical, and material support: Zhao Y, Zhang J, Ma F, Wu H, Meng W, Liu Y, Jiao Y, Du A

Availability of data and materials

Data will be made available upon request.

Financial support and sponsorship

This work is supported by the National Natural Science Foundation of China (Grant No. 11904077 and No. 12204144), the Natural Science Fund of Hebei Province (Grant No. A2022205027), financial support program from Hebei Province (Grant No. E2019050018, No. C20220503, and No. C20230509), Science Foundation of Hebei Normal University (Grant No. L2022B06), and the Key Program of Natural Science Foundation of Hebei Province (Grant No. A2021205024).

Conflicts of interest

All authors declared that there are no conflicts of interest.

Ethical approval and consent to participate

Not applicable.

Consent for publication

Not applicable.


© The Author(s) 2024.

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Zhao Y, Zhang J, Ma F, Wu H, Meng W, Liu Y, Jiao Y, Du A. Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction. Microstructures 2024;4:2024032.

AMA Style

Zhao Y, Zhang J, Ma F, Wu H, Meng W, Liu Y, Jiao Y, Du A. Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction. Microstructures. 2024; 4(3): 2024032.

Chicago/Turabian Style

Yuying Zhao, Jincan Zhang, Fengxian Ma, Hongbo Wu, Weizhen Meng, Ying Liu, Yalong Jiao, Aijun Du. 2024. "Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction" Microstructures. 4, no.3: 2024032.

ACS Style

Zhao, Y.; Zhang J.; Ma F.; Wu H.; Meng W.; Liu Y.; Jiao Y.; Du A. Computational exploration of two-dimensional vacancy-free boridene sheet and its derivatives: high stabilities and the promise for hydrogen evolution reaction. Microstructures. 2024, 4, 2024032.

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