Hydrogen adsorption behavior on AXenes Na2N and K2N: a first-principles study

It is a consensus that the hydrogen economy has come to a standstill due to the lack of feasible hydrogen storage solutions, especially, the suitable hydrogen storage materials. In this work, the potential of a new kind of two-dimensional (2D) AXenes, Na2N and K2N, as hydrogen storage materials are evaluated by the first-principles calculations. In particular, we find that Na2N in T phase indicates a hydrogen storage capacity as high as 6.25 wt% with a desirable hydrogen adsorption energy of –0.167 eV per H2 molecule and a desorption temperature of 216 K, identifying T-phase Na2N to be a very promising reversible hydrogen storage material. In accordance to our results, H2–Na2N interaction causes H2 charge polarization, which is responsible for the moderate binding strength. In addition, Gibbs adsorption free energy reveals that the system will be more stable as more H2 molecules are loaded on the surface.


Introduction
It is well known that hydrogen is a renewable and environmentally friendly energy source, and as a clean energy source hydrogen is regarded as an alternative to fossil fuels [1]. It should be highlighted that the only product of hydrogen combustion is water, which can effectively avoid environmental pollution. In current stage, safe and efficient storage of hydrogen is however a significant challenge, conventional storage methods via liquefaction and pressurization are suffering from low efficiency and low capacity. It is therefore a crucial issue to find or design promising materials for hydrogen storage [2][3][4].
In 2004, graphene was realized, ever since then the study of two-dimensional (2D) material has generated a lot of interest. In the light of the large surface-to-volume ratio and special electronic structures, 2D materials are used to immobilize hydrogen molecules with superiority [5][6][7][8]. In general, doping and decoration are commonly used to improve the hydrogen storage properties of 2D materials, in terms of modulating the surface properties of the material and adjusting the hydrogen adsorption energy [9]. It should be pointed out that carbon-based nanomaterials, which are extensively studied as hydrogen storage systems, indicate weak binding to hydrogen molecule and thus are not suitable for hydrogen storage [10,11]. In addition, an effective way to increase the hydrogen binding energy is doping with transition metals (TMs), light alkali metals, alkaline earth metals and nonmetals [12]. In a recent work, e.g., Holec et al reported theoretically and experimentally the enhancement of H 2 adsorption capacity on metal-doped graphene [13]. In particular, their experimental measurements demonstrated that although the specific area of the metal-decorated carbon material is smaller than that of the carbon material, the existence of Ru and Pt nanoparticles leads to an improvement in H 2 absorption performance at room temperature. In addition, Zhou et al investigated the H 2 adsorption on Ni functionalized defective h-BN substrates on the basis of density functional theory (DFT) simulations [14], and their results revealed that the Ni-doped h-BN sheets exhibit an ideal adsorption energy in the range of from 0.40 to 0.51 eV, meeting the H 2 storage requirements. In a recent experiment, Nair et al investigated the hydrogen storage capacity on Pd-decorated graphitic carbon nitride (g-C 3 N 4 ), and they found that the hydrogen storage capacity at 25°C and 4 MPa reaches 2.6 wt% [15]. It should be pointed out that, however, the doped or decorated Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. materials with considerable hydrogen storage properties are often complex and difficult to prepare [16,17], and the stability under different conditions cannot be assured [18].
It is therefore urgent to design materials with high gravimetric and volumetric density under favorable thermodynamic conditions. In an alternative way, phase transition was considered to improve the performance; for example, MoS 2 is one of the most studied. In particular, the potential of monolayer 1T and 1T′ MoS 2 as hydrogen storage materials was compared by Chen et al and 1T′ MoS 2 was demonstrated to have good hydrogen storage capability with a capacity of 3.9 wt% [19]. In comparison to the 2H counterpart, the hydrogen storage capability was significantly improved through phase transition.
In this work, the potential in hydrogen storage of a class of new 2D materials, namely, AXenes [20], is studied by means of the first-principles calculation based on DFT. In particular, 2D Na 2 N and K 2 N in different phase ( i.e., T, I and H phases) are featured as metal-shrouded monolayers, that is, the exposed light s-orbital metal atoms (Na and K) are the active centers for hydrogen adsorption. It is of interest that the nonstoichiometric Na 2 N and K 2 N behave as hole-doped materials, which probably is responsible for the moderate hydrogen binding strength. In light of the 2D nature, large amount active sites and unique electronic structures render AXenes Na 2 N and K 2 N appealing candidates of hydrogen storage materials. In accordance to our results, average hydrogen adsorption energy on T-Na 2 N is -0.167 eV/H 2 , and the hydrogen storage capacity is as high as 6.25 wt%. It therefore can be concluded that T-Na 2 N could be a very promising material for reversible hydrogen storage without stability problems of doped or decorated materials.

Computational methodology
In the present work, the projector augmented wave (PAW) [21] method as implemented in the Vienna ab initio simulation package (VASP) [22,23] was employed for all our calculations. In order to describe the exchangecorrelation functional, the generalized gradient approximation (GGA) [24] with Perdew-Burke-Ernzerhof (PBE) formalism was employed [25]. It is necessary to include the van der Waals (vdW) interactions for the adsorption of H 2 molecule on AXenes, which were considered by using the DFT-D2 semiempirical correction [26,27]. In order to prevent the interactions between two periodic layers, a vacuum space of about 20 Å was added in direction perpendicular to the material plane. In the integration of the Brillouin zone, a 11×11×1 Monkhorst-Pack k-point mesh was adopted, and the energy cutoff was set to 500 eV for the plane wave basis [28]. In case of geometry optimization, the calculation will stop when the residual force on each atom was less than −0.01 eV Å and the energy tolerance was 10 −6 eV.

Results and discussion
3.1. Structure and electronic properties of Na 2 N and K 2 N In figure 1, atomic structures of the new 2D AXenes Na 2 N and K 2 N in different phases (T, H and I) are presented, with the unit cells denoted. In particular, the T-phase structure is isomorphic to the experimentally synthesized 2D electrode Ca 2 N, while the H phase is isomorphic to 2H MoS 2 . In respect to the structure of I phase, each N atom is bonded to eight Na atoms from both sides, with a different tetragonal symmetry from the H and T phases. In each unit cell of the AXenes considered in this work, it can be seen that two alkali metal atoms and one N atom constitute a three-atomic-layer Na/K-N-Na/K sandwich structure. In other words, the new Na 2 N and K 2 N of AXenes can be regarded as metal-shrouded 2D materials. In comparison to carbon-based materials, the exposed metal atoms guarantee the moderate hydrogen adsorption energy, which is the key for reversible hydrogen storage. In table 1, the lattice constants and relevant structural parameters of Na 2 N and K 2 N in three phases are summarized, and it can be found that our results are consistent with previous study [20].
In figure 2, band structures of the 2D AXenes of consideration are shown. It can be seen that Na 2 N and K 2 N in different phases are all characterized to be metallic or half-metallic, indicative of desired electric conductivity. In particular, for example, T-Na 2 N shows a 100% spin polarization at the Fermi level. It should be pointed out in passing that the metallic properties of these materials suggest great potential in applications in electrochemical catalysis, such as nitrogen reduction reaction (NRR), hydrogen/oxygen evolution reaction (HER/OER), and so forth.

3.2.
Atomic and molecular hydrogen adsorption on Na 2 N and K 2 N In order to give a complete picture for hydrogen adsorption on Na 2 N and K 2 N, atomic H adsorption are evaluated before studying the molecular H 2 adsorption. In our study, we consider the hydrogen adsorption and subsequent desorption as an electrochemical HER process, that is, where * denotes the active site. In case of atomic H adsorption, the Gibbs free energy change (ΔG H* ) can be obtained by the following expression where ΔE H* represents the adsorption energy of hydrogen, ΔE ZPE and ΔS H* are the differences in zero-point energy and entropy between the adsorbed hydrogen (H * ) and hydrogen in gas phase (H 2 ) at 298.15 K, respectively. In figure 3, results are shown for Na 2 N and K 2 N in different phases. In most cases, ΔG H* values are large and positive, approaching 2.0 eV; it is an indication of rather weak adsorption. In these cases, atomic H is adsorbed on top of metal atoms from one or two sides of the material. It can be seen that, however, one H atom adsorption on I-Na 2 N and two H atoms adsorption on I-K 2 N reveal strong binding strength, with ΔG H* being -1.08 and -0.87 eV, respectively, which suggests difficult hydrogen desorption from the surfaces. In these two situations, the strong adsorption can be attributed to the fact that H species are bound close to the N atoms after full structure relaxation. It therefore can be concluded that Na 2 N and K 2 N used for hydrogen storage in an electrochemical manner is not suitable, because of the either too weak or too strong binding strength.
In order to illustrate the hydrogen storage capacity of Na 2 N and K 2 N, H 2 molecules are introduced on the surface step by step (hydrogenation). In order to evaluate the binding strength, the average hydrogen adsorption energy on the surface of AXenes is defined as with m H 2 and M AXenes being the molar masses of H 2 and AXenes (Na 2 N and K 2 N), respectively. In our calculations, up to four H 2 molecules per unit cell of AXenes are taken into account; for example, one, two, three and four H 2 molecules adsorbed on the unit cell of T-Na 2 N are referred to as T-Na 2 N+1H 2 , T-Na 2 N+2H 2 , T-Na 2 N+3H 2 and T-Na 2 N+4H 2 , respectively. In respect to T-Na 2 N+1H 2 , it corresponds to a H 2 layer on one side of T-Na 2 N; when introducing the second H 2 layer onto the other side gives rise to T-Na 2 N+2H 2 , and T-Na 2 N+4H 2 implies that there are two H 2 layers on each side of the T-Na 2 N. In figure 4, as representatives, the optimized structures of T-Na 2 N loaded with 1, 2, 3 and 4 hydrogen molecules per unit cell are shown. It can be noted that the first H 2 layers on both sides of T-Na 2 N are located above N atoms with the H-H bond perpendicular to the material plane (end-on), while the second two H 2 layers are on top of the Na atoms with the H-H bond parallel to the material plane (side-on). In table 2, average adsorption energy, consecutive adsorption energy, hydrogen storage capacity, M-H 2 distance and H-H bond length for different systems are summarized.
It can be found that, generally, both the average and consecutive adsorption energies decrease with the increase of H 2 molecules on the surface, which is an indication of limited number of H 2 molecule to be adsorbed. In case of T-Na 2 N+1H 2 , as an example, the adsorption energy of one H 2 is calculated to be -0.169 eV, a desirable value for hydrogen adsorption. In regard to T-Na 2 N+2H 2 , the average and consecutive adsorption energies are -0.167 and -0.164 eV, respectively, which are still the acceptable values in hydrogen storage. In the case for a free H 2 molecule, its bond length is calculated to be 0.751 Å, which is consistent with previous calculation [29]. In T-Na 2 N+1H 2 and T-Na 2 N+2H 2 , while the H-H bond lengths are 0.791 and 0.787 Å, respectively. It is an indication that H 2 molecules adsorbed on T-Na 2 N are activated. In the situation of T-Na 2 N+3H 2 , the average adsorption energy reduces to -0.132 eV, and the consecutive adsorption energy turns out to be -0.060 eV, which is too small to firmly adsorb the third layer of H 2 . In principle, too weak binding strength is not conducive to hydrogen adsorption while too strong binding strength is detrimental to the hydrogen desorption from the surface. In the energy point of view, therefore T-Na 2 N is identified to a promising candidate for hydrogen storage with a storage capacity as high as 6.25% (T-Na 2 N+2H 2 ). In addition, the hydrogen storage capacity of H-Na 2 N maximizes also at 6.25% (H-Na 2 N+2H 2 ) but with slightly reduced hydrogen binding strength.
In figure 4, hydrogen adsorption structures are also shown for T-K 2 N. It is different from H 2 adsorption on T-Na 2 N, the first two layers of H 2 are adsorbed above the K atoms with the H-H bond parallel to the surface, while the second two layers of H 2 will be located on top of the opposite K atoms with the H-H bond perpendicular to the surface. In case of T-K 2 N+1H 2 , the adsorption energy is -0.237 eV, corresponding to a storage capacity of 2.13%. In respect to T-K 2 N+2H 2 , the average adsorption energy turns out to be -0.142 eV and the consecutive adsorption energy is only -0.046 eV (-0.017 eV for H-K 2 N and -0.084 eV for I-K 2 N with the same H 2 loading). In consideration of the unstable adsorption, therefore, hydrogen adsorption behavior on K 2 N will not be discussed. r H 2 and r Na N 2 are the charge densities of H 2 adsorbed T-Na 2 N, H 2 molecule and T-Na 2 N, respectively. In figure 5, charge redistribution upon H 2 molecule adsorption is shown for T-Na 2 N+2H 2 . It can be found that the first two H 2 layers show apparent charge polarization and some charge are transferred to the N p z orbitals, which is responsible for the moderate binding strength (-0.167 eV per H 2 molecule). In respect to the T-Na 2 N+4H 2 , while deposition of the second two H 2 layers does not cause charge redistribution, corresponding to the weak binding strength.
In figure 6, the projected density of states (PDOS) plots are shown for T-Na 2 N before and after H 2 molecule adsorption. It can be found that T-Na 2 N is spin-polarized, with a 100% polarization at the Fermi level; the states near the Fermi level are predominantly contributed by N 2p orbitals and slightly by Na 2p/3s states. In line with the band structure, T-Na 2 N is featured as half-metallic materials. In case for H 2 adsorption, H 1s states mainly appear -7.50 eV below the Fermi level, with weak interactions with N 2s/2p states. In respect to the first two layers of H 2 , H 1s states are polarized, consistent with the charge density difference; while the electronic structure of the second layer of H 2 is undisturbed due to the quite weak interaction with the substrate. In a previous study for hydrogen adsorption on Li-decorated 2D C 4 N monolayer, H 1s states appear in a similar energy range from -10 to -8 eV and hybridize with Li s states [30].
It has already been known that structure stability is closely related to the temperature and pressure, therefore, ab initio atomistic thermodynamics approach in combination to the DFT results is employed to qualitatively evaluate the effects of temperature and pressure on the stability of hydrogen storage systems. In respect to hydrogen adsorption on T-Na 2 N, H 2 adsorption free energy can be defined as   is the chemical potential of isolated H 2 molecule in the gas phase [31,32]. In regard to the Gibbs free energy of solid phase, it reads where E tot is the total energy that can be obtained from the DFT results, E , conf E vib and PV are the configurational, vibrational free energies and pressure volume work [33,34], separately. In particular, the chemical potential of H 2 in gas phase as a function of pressure p and temperature T can be written as  ( ) ( ) ZPV 2 is 0.296 eV, in accordance with previous results [31]. In addition, entropic contributions to the standard chemical potential are available in the JANAF thermochemical table.
In figure 7, the corresponding thermodynamic stability diagrams for T-Na 2 N+1H 2 (hydrogen storage capacity: 3.23 wt%) and T-Na 2 N+2H 2 ((hydrogen storage capacity: 6.25 wt%) are shown. It should be pointed out that the lower the Gibbs free energy, the more stable the structures. In comparison to low hydrogen coverage (figure 7(a)), figure 7(b) indicates that increasing hydrogen adsorption on T-Na 2 N can lower the adsorption free energy overall, and thus the system tends to be more stable. It is interesting to find that T-Na 2 N prefers to adsorb more hydrogen molecules (on the opposite surface) under different temperatures. In case of at roomtemperature (298.15 K), interestingly, the T-Na 2 N+2H 2 with a hydrogen storage capacity of 6.25 wt% illustrates desirable stability with the adsorption free energy being negative over almost the entire range of pressure. In addition, naturally, for each adsorbed system the stability deteriorates with increased temperature and decreased pressure.
In addition, ab initio molecular dynamics (AIMD) simulations were performed for T-Na 2 N+2H 2 , and a snapshot at 300 K is shown in figure 8. It can be found that H 2 molecules go away from the material surface, which is an indication of easy release of hydrogen, similar to the case of hydrogen adsorption on Li-decorated B 38 [35].
It is essential to estimate the desorption temperature (T D ) for practical hydrogen storage application, which can be calculated using the van't Hoff equation [36][37][38]: with E a being the adsorption energy per H 2 molecule, k B the Boltzmann constant (1.380×10 -23 J K -1 ); ΔS is the change in H 2 entropy from the gas to liquid phase (75.44 J mol -1 K -1 ), R is the gas constant (8.314 J mol -1 K -1 ), and p is the equilibrium pressure (1 atm). In line with these parameters, the calculated T D for releasing H 2 molecules from the T-Na 2 N+2H 2 compound is 216 K. It therefore can be concluded that, interestingly, the ambient temperature for hydrogen desorption can greatly increase the possibility of T-Na 2 N for hydrogen storage applications.

Conclusion
In summary, we have systemically investigated the hydrogen adsorption behavior on a new class of 2D AXenes, Na 2 N and K 2 N in different phases (referred to as T, H and I), by first-principles calculations on the basis of DFT. In particular, the hydrogen storage capacity of T-Na 2 N reaches 6.25 wt% with a desirable hydrogen adsorption energy of -0.167 eV per H 2 molecule. It can be concluded that interactions between H 2 molecules and N atoms cause H 2 charge polarization, which is responsible for the moderate binding strength. It is of interest that T-Na 2 N prefers hydrogen adsorption on both sides, and the adsorbed system tends to be more stable. In accordance to the van't Hoff model, the desorption temperature is calculated to be 216 K.