Stability, Electronic Structure, and Dehydrogenation Properties of Pristine and Doped 2D MgH 2 by the First Principles Study

: Based on ﬁrst principles calculations, we theoretically predict the new two-dimensional (2D) MgH 2 . The thermodynamic stability, partial density of states, electron localization function, and Bader charge of pure and the transition metal (Ti, V, and Mn) doped 2D MgH 2 are investigated. The results show that all the systems are dynamically stable, and the dehydrogenation properties indicate that the decomposition temperature can be reduced by introducing the transition metal, and the Mn doped system exhibits good performance for better hydrogen storage and dehydrogenation kinetics. Mg 8 H 18 , which are calculated using the PBE functional. We can see the stronger hybridization between H and Mg atoms near the Fermi level, which indicates the strong interaction between H and Mg atoms. Mg 8 H 18 X, the electronic structure is different from that of the pure Mg 9 H 18 , is shown in Figure 4. We can see that the d orbitals of Ti/V/Mn are mainly located near the Fermi level in doped-2D MgH 2 , and there are few H-s orbitals and states of Mg atoms at the Fermi level, which indicates that the interactions between Ti/V/Mn and H/Mg atoms are relatively weaker. Meanwhile, since the H-s orbitals are reduced at the Fermi level, the hybridization between H and Mg atoms is weaker compared to pure Mg 9 H 18 atoms. These suggest that the ionic bonds exist between Mg and H atoms, and the Mg atoms act as the charge donor, according well with the discussions of PDOS and ELF of bulk MgH 2 . The Bader charges were also calculated (see Table 3), and it can be seen that Mg atoms contributed two electrons, and H atoms acquired electrons to form anions. Meanwhile, the H atoms obtained fewer electrons due to the Mg vacancy and doping with Ti/V/Mn elements, thereby weakening the interactions between H and the metal atoms.


Introduction
Hydrogen energy is considered to be the most promising alternative because it is lightweight, environmentally friendly, highly efficient, renewable, and abundant on earth. However, the storage limits the application of hydrogen. Metal hydrides are considered as the most promising materials for hydrogen storage and have been widely investigated in the past decades [1]. Among them, magnesium-based alloys and magnesium hydrides can achieve the hydrogen storage capacity of 7.6 wt % [2][3][4][5][6][7][8]. However, the high thermodynamic stability (the heat of formation is around −75.99 kJ/mol·H 2 ), high desorption temperatures (above 573 K), and slow dehydrogenation kinetics seriously limit the practical applications [3,9,10]. Therefore, it is always a central task to design new materials or adopt efficient strategies for achieving lower desorption temperatures and good dehydrogenation performances.
Previous studies show that the bonding nature of MgH 2 is a mixture of strong ionic and weak covalent bonding [11], and weakening the interactions may be an effective strategy to improve dehydrogenation performance. It has been reported that doping with transition metal elements or their oxides mixtures with MgH 2 can effectively reduce its stability and improve the hydrogen desorption thermodynamics [3,[12][13][14][15][16][17]. Oelerich [15] [3] et al. have studied the hydrogen storage performance of (MgH 2 + M) systems (M = Al, Ti, Fe, Ni, Cu, and Nb) experimentally and theoretically, and they found that MgH 2 mixed with those metals can reduce the stability and improve the hydrogen desorption kinetics. Nonetheless, the MgH 2 systems still have a high desorption temperature around 500 K. It is noted that the bulk MgH 2 has been extensively investigated, however, the single-layer magnesium hydrides have been largely ignored. Motivated by the above mentioned details, we focus on exploring new structures with good dehydrogenation performance in this work.
In this paper, the new two-dimensional (2D) MgH 2 structure is theoretically predicted and studied by first principles calculations. The stabilities of pure and Ti/V/Mn doped MgH 2 are discussed by the Figure 1 shows the fully relaxed structure of the top and side view of pure 2D MgH 2 of the hexagonal structure with space group P-3m1 (D 3 3d ). The primitive cell has the lattice constant of a = b = 3.01 Å, the Mg-H bond length of l = 1.97 Å, and the buckled height of d = 1.86 Å. The next calculations were performed for the 3 × 3 × 1 supercell of 2D MgH 2 , named Mg 9 H 18 . The corresponding lattice parameters, Wyckoff [28] and atomic positions, are shown in Table 1. As is seen, there are nine Mg atoms located at 1b (Mg1), 6h (Mg2), and 2d (Mg3) sites, while the eighteen H atoms are located in three identical Wyckoff positions, i.e., 6i, as shown in Figure 1. In this paper, the new two-dimensional (2D) MgH2 structure is theoretically predicted and studied by first principles calculations. The stabilities of pure and Ti/V/Mn doped MgH2 are discussed by the phonon spectra and heat of formation. The calculated heat of formation for pure and Ti/V/Mn doped 2D MgH2 are −37.57, −25.67, −18.14, and −23.90 kJ/mol·H2, respectively, which are significantly lower than that of −75.99 kJ/mol·H2 of bulk MgH2. The electronic structure and hydrogen desorption kinetics results show that the predicted two-dimensional magnesium hydride are promising candidates for hydrogen storage.

Computational Details
The structural optimization and electronic property calculations were performed using the projector augmented plane-wave method (PAW) based on the density functional theory (DFT) in the Vienna ab initio simulation package (VASP) [18,19]. The exchange-correlation potential was approximated by generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form [20,21]. To avoid the interlayer effects of the c-axis, the vacuum region around 15 Å was set in all the systems. The energy cutoff of 600 eV and the 9 × 9 × 1 Γ-centered Monkhorst-Pack k-points [22] were employed for all calculations. The atomic positions were fully relaxed and the force tolerance between each atom was less than 0.01 eV/Å for the structural optimization. The convergence criteria of 10 −6 eV per atom was applied to be self-consistent. Meanwhile, for calculation of electronic structures, we also applied the local density approximation (LDA) [23] and HSE06 [24] was functional. The kinetic stability was discussed using the phonon spectra calculations in PHONOPY code coupled with VASP using the density functional perturbation theory (DFPT) method [25][26][27].  Table 1. As is seen, there are nine Mg atoms located at 1b (Mg1), 6h (Mg2), and 2d (Mg3) sites, while the eighteen H atoms are located in three identical Wyckoff positions, i.e., 6i, as shown in Figure 1.   In this work, three different Mg sites are considered as possible positions for substitution doping. Meanwhile, defects are inevitable in synthesis or processing and can usually affect their properties [29][30][31][32][33]. The most common types of defect are vacancy defects, so we also considered the vacancies of Mg (Mg 8 H 18 ) for comparison to the doped systems. The formation energies were calculated to determine the favorable positions of doping elements of Ti/V/Mn, which is defined

Results and Discussion
where E tot is the total energy of the system, the parameter n = 0/1 represents Mg vacancy, and X (X = Ti, V, and Mn) doped. The energies are listed in Table 2. It is noticed that the Mg 8 H 18 and Ti/V/Mn doped systems have positive energy, indicating that the stability of all the systems are lower than that of pure Mg 9 H 18 . In addition, for the three high symmetry sites of Mg1 (1b), Mg2 (6h), and Mg3 (2d), the ∆E are nearly identical, therefore, we assume that all the doped-sites are located at the Mg1 site in the following work. The relaxed parameters and bond lengths of Mg 9 H 18 and Mg 8 H 18 X (X = Ti, V, and Mn) are listed in Table 2, and for the detailed lattice parameters, see Table A1 (Appendix A). As is seen, the bond length of Mg-H is changed, which indicates that the doped X atoms break the symmetry of the 2D MgH 2 structure. Structural stability is discussed by the phonon spectra calculations using the DFPT method, as is shown in Figure 2. Clearly, there are no imaginary frequencies in the whole Brillouin zone, indicating that all the systems are dynamically stable. Meanwhile, the heat of formation (∆H) [7,[34][35][36] is one of the most fundamentally thermodynamic properties. The heat of formation can be obtained directly where the parameters (n = 0, m = 0), (n = 1, m = −1), and (n = 1, m = 0), represent pure, Mg vacancy, and X (X = Ti, V and Mn) doped Mg 9 H 18 , respectively. The value of E tot (H 2 ) of −6.762 eV in a 10 × 10 × 10 Å 3 cubic cell is very close to −6.773 eV reported in Ref. [37]. are 268 K < T(Mg9H18) < 396 K, 183 K < T(Mg8H18Ti) < 270 K, 130 K < T(Mg8H18V) < 191 K, 171 K < T(Mg8H18Mn) < 252 K, which are significantly lower than that of 573~673 K of bulk MgH2. The discussions mentioned above show that 2D MgH2 has better dehydrogenation thermodynamic properties than that of bulk MgH2, and doping with Ti, V, and Mn elements can reduce the stability and improve the dehydrogenation thermodynamics properties of 2D MgH2.  To understand the effect of Ti/V/Mn-doped 2D MgH2 well, we analyzed the electronic structures. The band structures were obtained using PBE, LDA, and HSE06 functionals and are shown in Figure  A1. It can be seen that the pure Mg9H18 with the energy gap is 4.87 eV, which is smaller than the The estimated heats of formation are listed in Table 3 In comparison, we also obtained the heat of formation of the bulk MgH 2 of ∆H = −54.56 kJ/mol·H 2 , which is close to the theoretical values −54.4 in Ref. [36] and −53.85 kJ/mol·H 2 in Ref. [38]. At the same time, we estimated the decomposition temperature according to the following relationship: ln P P 0 = ∆H RT − ∆S R , where P, P 0 , R, T, and ∆S represent the pressure, the standard pressure, the gas constant, the decomposition temperature, and the entropy change, respectively. At the standard pressure, the ∆H is defined as ∆H = T∆S [39,40]. For most of the dehydrogenation reactions of simple metal hydrides, the ∆S is in the range of 95 J/mol·K < ∆S(H 2 ) < 140 J/mol·K [41]. Consequently, the decomposition temperatures are 268 K < T(Mg 9 H 18 ) < 396 K, 183 K < T(Mg 8 H 18 Ti) < 270 K, 130 K < T(Mg 8 H 18 V) < 191 K, 171 K < T(Mg 8 H 18 Mn) < 252 K, which are significantly lower than that of 573~673 K of bulk MgH 2 . The discussions mentioned above show that 2D MgH 2 has better dehydrogenation thermodynamic properties than that of bulk MgH 2 , and doping with Ti, V, and Mn elements can reduce the stability and improve the dehydrogenation thermodynamics properties of 2D MgH 2 . To understand the effect of Ti/V/Mn-doped 2D MgH 2 well, we analyzed the electronic structures. The band structures were obtained using PBE, LDA, and HSE06 functionals and are shown in Figure A1. It can be seen that the pure Mg 9 H 18 with the energy gap is 4.87 eV, which is smaller than the experimental values 5.16 eV [42] or 5.6 eV [43] of bulk MgH 2 . For comparison, we found that the bandgaps using HSE06 functional are larger than those using PBE and LDA functionals, and the bandgaps using LDA functional are close to those of the PBE functional for pure and vacancies of Mg 9 H 18 . For the doped systems, there are few energy bands across the Fermi level due to the d orbitals of the dopants. Figure 3 shows the total and partial density of states (PDOS) of Mg 9 H 18 and Mg 8 H 18 , which are calculated using the PBE functional. We can see the stronger hybridization between H and Mg atoms near the Fermi level, which indicates the strong interaction between H and Mg atoms. For the Mg 8 H 18 X, the electronic structure is different from that of the pure Mg 9 H 18 , as is shown in Figure 4. We can see that the d orbitals of Ti/V/Mn are mainly located near the Fermi level in doped-2D MgH 2 , and there are few H-s orbitals and states of Mg atoms at the Fermi level, which indicates that the interactions between Ti/V/Mn and H/Mg atoms are relatively weaker. Meanwhile, since the H-s orbitals are reduced at the Fermi level, the hybridization between H and Mg atoms is weaker compared to pure Mg 9 H 18 .  Figure 3 shows the total and partial density of states (PDOS) of Mg9H18 and Mg8H18, which are calculated using the PBE functional. We can see the stronger hybridization between H and Mg atoms near the Fermi level, which indicates the strong interaction between H and Mg atoms. For the Mg8H18X, the electronic structure is different from that of the pure Mg9H18, as is shown in Figure  4. We can see that the d orbitals of Ti/V/Mn are mainly located near the Fermi level in doped-2D MgH2, and there are few H-s orbitals and states of Mg atoms at the Fermi level, which indicates that the interactions between Ti/V/Mn and H/Mg atoms are relatively weaker. Meanwhile, since the H-s orbitals are reduced at the Fermi level, the hybridization between H and Mg atoms is weaker compared to pure Mg9H18.     In order to analyze the chemical bond of all the systems, the electron localization function (ELF) was calculated and is shown in Figure 5 with the isosurfaces of 0.6 e/Å 3 . As shown in Figure 5b-f, all the systems have similar features in that the ELF values are lower between Mg and H atoms. These suggest that the ionic bonds exist between Mg and H atoms, and the Mg atoms act as the charge donor, according well with the discussions of PDOS and ELF of bulk MgH 2 . The Bader charges were also calculated (see Table 3), and it can be seen that Mg atoms contributed two electrons, and H atoms acquired electrons to form anions. Meanwhile, the H atoms obtained fewer electrons due to the Mg vacancy and doping with Ti/V/Mn elements, thereby weakening the interactions between H and the metal atoms. In order to analyze the chemical bond of all the systems, the electron localization function (ELF) was calculated and is shown in Figure 5 with the isosurfaces of 0.6 e/Å 3 . As shown in Figure 5b-f, all the systems have similar features in that the ELF values are lower between Mg and H atoms. These suggest that the ionic bonds exist between Mg and H atoms, and the Mg atoms act as the charge donor, according well with the discussions of PDOS and ELF of bulk MgH2. The Bader charges were also calculated (see Table 3), and it can be seen that Mg atoms contributed two electrons, and H atoms acquired electrons to form anions. Meanwhile, the H atoms obtained fewer electrons due to the Mg vacancy and doping with Ti/V/Mn elements, thereby weakening the interactions between H and the metal atoms. As mentioned above, doping with Ti/V/Mn elements reduces the stability of 2D MgH 2 and weakens the interactions between H and metal atoms, which facilitates the release of hydrogen. To further understand the dehydrogenation behavior, the dehydrogenation energy was estimated by the formula: E d = E tot (Mg 9-n H 17 X n+m ) − E tot (Mg 9-n H 18 X n+m ) + 1/2 E tot (H 2 ), where (n = 0, m = 0), (n = 1, m = −1), and (n = 1, m = 0) represent the pure, Mg vacancy, and X (X = Ti, V, and Mn) doped Mg 9 H 18 , respectively. The dehydrogenation energies are listed in Table

Conclusions
In summary, we theoretically predicted two-dimensional MgH 2 and studied the electronic and dehydrogenation properties of pure and Ti/VMn doped 2D MgH 2 . The phonon spectra calculations indicate that all the systems are dynamically stable. The results of heat of formation suggests that Ti/V/Mn doping can reduce the thermodynamic stability, followed by Mg 8  have much lower decomposition temperature than that of pure 2D MgH 2 (268~396 K), which is important for practical applications. The partial densities of states, electron localization function, and Bader charge calculation results show that Ti, V, and Mn elements can weaken the interaction between H and the metal atoms, which is favorable to dehydrogenation and better than that of the bulk MgH 2 .
Author Contributions: All authors contributed equally to this work.
Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 11604008) and by BUCT Fund for Disciplines Construction (Project No. XK1702).

Conflicts of Interest:
The authors declare no conflicts of interest.
Appendix A   Table A1. The relaxed structure parameters of pure, vacancies, and doped Mg 9 H 18 using Perdew-Burke-Ernzerhof (PBE) and local density approximation (LDA) functionals.