Stability, Electronic Structure, and Dehydrogenation Properties of Pristine and Doped 2D MgH₂ by the First Principles Study

Abstract

Based on first principles calculations, we theoretically predict the new two-dimensional (2D) MgH₂. 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 MgH₂ 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.

1. 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·H₂), 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 MgH₂ 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 MgH₂ can effectively reduce its stability and improve the hydrogen desorption thermodynamics [3,12,13,14,15,16,17]. Oelerich [15] et al. have reported that MgH₂ milled with Fe₃O₄, V₂O₅, Mn₂O₃, or Cr₂O₃, etc. can accelerate the hydrogen desorption kinetics. Shang [3] et al. have studied the hydrogen storage performance of (MgH₂ + M) systems (M = Al, Ti, Fe, Ni, Cu, and Nb) experimentally and theoretically, and they found that MgH₂ mixed with those metals can reduce the stability and improve the hydrogen desorption kinetics. Nonetheless, the MgH₂ systems still have a high desorption temperature around 500 K. It is noted that the bulk MgH₂ 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) 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.

2. 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].

3. Results and Discussion

Figure 1 shows the fully relaxed structure of the top and side view of pure 2D MgH₂ of the hexagonal structure with space group P-3m1 ($D_{3d}^3$). 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 MgH₂, named Mg₉H₁₈. The corresponding lattice parameters, Wyckoff [28] and atomic positions, are shown in

Table 1. The relaxed structural parameters and atomic positions of Mg₉H₁₈.

Lattice Parameters	Atom	Wyckoff	Atomic Positions (Fractional)
		Positions	x	y	z
164(P-3m1)	Mg1	1b	0	0	0.5
a = b = 9.033 Å	Mg2	6h	0	0.33333	0.5
c = 15 Å	Mg3	2d	0.33333	0.66667	0.5
d = 1.86 Å	H1	6i	0.11111	0.22222	0.43783
α = β = 90°	H2	6i	0.22222	0.44444	0.56217
γ = 120°	H3	6i	0.11111	0.55556	0.43783

. 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 (Mg₈H₁₈) 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 as ΔE = E_tot(Mg₈H₁₈X_n) − E_tot(Mg₉H₁₈) − n E_tot(X) + E_tot(Mg), 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. The energy (ΔE), the lattice parameter (a), and bond length of Mg₉H₁₈, Mg₈H₁₈ and Mg₈H₁₈X (X = Ti, V, and Mn).

Hydride	ΔE (eV)			Parameter	Bond Length (Å)
	Mg1	Mg2	Mg3	a (Å)	Sub-H1	Mg2-H1	Mg2-H2	Mg2-H3	Mg3-H2	Mg3-H3
Mg9H18	0	0	0	9.033	1.972	1.972	1.972	1.972	1.972	1.972
Mg8H18	2.968	2.968	2.968	9.062	-	1.894	2.043	1.976	1.947	1.992
Mg8H18Ti	1.113	1.114	1.114	9.027	1.915	1.997	1.964	1.982	1.946	1.990
Mg8H18V	1.818	1.818	1.819	8.951	1.822	1.999	1.945	1.992	1.939	1.983
Mg8H18Mn	1.279	1.279	1.279	8.815	1.691	2.028	1.911	2.008	1.937	1.965

. It is noticed that the Mg₈H₁₈ and Ti/V/Mn doped systems have positive energy, indicating that the stability of all the systems are lower than that of pure Mg₉H₁₈. In addition, for the three high symmetry sites of Mg1 (1b), Mg2 (6h), and Mg3 (2d), the ΔE 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 Mg₉H₁₈ and Mg₈H₁₈X (X = Ti, V, and Mn) are listed in Table 2, and for the detailed lattice parameters, see

Table A1. The relaxed structure parameters of pure, vacancies, and doped Mg₉H₁₈ using Perdew-Burke-Ernzerhof (PBE) and local density approximation (LDA) functionals.

Hydride	PBE				LDA
	a (Å)	α (°)	β (°)	γ (°)	a (Å)	α (°)	β (°)	γ (°)
Mg9H18	9.033	90.0	90.0	120.0	8.894	90.0	90.0	120.0
Mg8H18	9.062	90.0	90.0	120.0	8.888	90.0	90.0	120.0
Mg8H18Ti	9.027	90.0	90.0	120.0	8.883	90.0	90.0	120.0
Mg8H18V	8.951	90.0	90.0	120.0	8.803	90.0	90.0	120.0
Mg8H18Mn	8.815	90.0	90.0	120.0	8.662	90.0	90.0	120.0

(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 MgH₂ 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 (ΔH) [7,34,35,36] is one of the most fundamentally thermodynamic properties. The heat of formation can be obtained directly from the equation ΔH = [E_tot(Mg_9-nH₁₈X_n+m) − (n + m) E_tot(X) − (9-n) E_tot(Mg) − 9 E_tot(H₂)]/9, 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 Mg₉H₁₈, respectively. The value of E_tot(H₂) of −6.762 eV in a 10 × 10 × 10 ų cubic cell is very close to −6.773 eV reported in Ref. [37].

The estimated heats of formation are listed in

Table 3. The heat of formation (ΔH), the decomposition temperature (T), Bader charge of Mg and H atoms, and the dehydrogenation energies (E_d) of Mg₉H₁₈, Mg₈H_18, and Mg₈H₁₈X (X = Ti, V, and Mn).

Hydride	ΔH	T	Bader Charge (e)			Ed
	(kJ/mol·H2)	(K)	Mg	X	H	(eV)
Mg9H18	−37.57	268~396	+2.000	-	−0.997	1.589
Mg8H18	31.71	-	+2.000	-	−0.886	−1.931
Mg8H18Ti	−25.67	183~270	+2.000	+1.825	−0.988	1.305
Mg8H18V	−18.14	130~191	+2.000	+1.523	−0.971	1.044
Mg8H18Mn	−23.90	171~252	+2.000	+0.975	−0.940	0.853

. As is seen, the heat of formation of Mg₉H₁₈, Mg₈H₁₈, Mg₈H₁₈Ti, Mg₈H₁₈V, and Mg₈H₁₈Mn are −37.57, 31.71, −25.67, −18.14, and −23.90 kJ/mol·H₂, respectively. The results show that the stability decreased for the doped 2D MgH₂, followed by Mg₈H₁₈Ti, Mg₈H₁₈Mn, and Mg₈H₁₈V, and Mg₈H₁₈ is the most unstable. In comparison, we also obtained the heat of formation of the bulk MgH₂ of ΔH = −54.56 kJ/mol·H₂, which is close to the theoretical values −54.4 in Ref. [36] and −53.85 kJ/mol·H₂ in Ref. [38]. At the same time, we estimated the decomposition temperature according to the following relationship: $\ln \frac{P}{P_0}=\frac{\Delta H}{RT}-\frac{\Delta S}{R}$, where P, P₀, R, T, and ΔS represent the pressure, the standard pressure, the gas constant, the decomposition temperature, and the entropy change, respectively. At the standard pressure, the ΔH is defined as ΔH = TΔS [39,40]. For most of the dehydrogenation reactions of simple metal hydrides, the ΔS is in the range of 95 J/mol·K < ΔS(H₂) < 140 J/mol·K [41]. Consequently, the decomposition temperatures 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 experimental values 5.16 eV [42] or 5.6 eV [43] of bulk MgH₂. 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 Mg₉H₁₈. 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 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/ų. 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 MgH₂ 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-nH₁₇X_n+m) − E_tot(Mg_9-nH₁₈X_n+m) + 1/2 E_tot(H₂), 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 Mg₉H₁₈, respectively. The dehydrogenation energies are listed in Table 3. The results show that the dehydrogenation energy of the Mg₈H₁₈ was significantly reduced compared to the pure and doped Mg₉H₁₈, while there are high ΔE of 2.968 eV and positive ΔH of 31.71 kJ/mol·H₂, indicating that it is almost impossible to steadily occur. For doped systems, their dehydrogenation energies are significantly smaller than 1.589 eV of pure Mg₉H₁₈, especially Mg₈H₁₈Mn with the dehydrogenation energy of 0.853 eV. Therefore, doping with Ti/V/Mn elements can improve the dehydrogenation thermodynamic properties of 2D MgH₂.

4. Conclusions

In summary, we theoretically predicted two-dimensional MgH₂ and studied the electronic and dehydrogenation properties of pure and Ti/VMn doped 2D MgH₂. 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 Mg₈H₁₈Ti, Mg₈H₁₈Mn, and Mg₈H₁₈V, and Mg₈H₁₈ is the most unstable. Importantly, the dehydrogenation temperatures for all the systems are significantly lower than that of bulk MgH₂ at 573~673 K. Especially, Mg₈H₁₈Ti (183~270 K), Mg₈H₁₈V (130~191 K), and Mg₈H₁₈Mn (171~252 K) have much lower decomposition temperature than that of pure 2D MgH₂ (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 MgH₂.