First-Principles Investigation of Energetics and Electronic Structures of Ni and Sc Co-Doped MgH 2

First-principles calculations were used to study the energetics and electronic structures of Ni and Sc co-doped MgH2 system. The preferential positions for dopants were determined by the minimal total electronic energy. The results of formation enthalpy indicate that Ni and Sc co-doped MgH2 system is more stable than Ni single-doped system. The hydrogen desorption enthalpies of these two hydrides are investigated. Ni and Sc co-doping can improve the dehydrogenation properties of MgH2. The lowest hydrogen desorption enthalpy of 0.30 eV appears in co-doped system, which is significantly lower than that of Ni doping. The electronic structure analysis illustrates that the hybridization of dopants with Mg and H atom together weakens the Mg-H interaction. And the Mg-H bonds are more susceptible to dissociate by Ni and Sc co-doping because of the reduced magnitude of Mg-H hybridization peaks. These behaviors effectively improve the dehydrogenation properties of Ni and Sc co-doped cases.


Introduction
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Computational Model and Method
MgH 2 has a rutile type tetragonal structure (P42/mnm, group No.136) with experimentally measured lattice parameters of a = 4.501 Å and c = 3.010 Å [23]. In the unit cell of MgH 2 , two Mg atoms occupy the 2a (0, 0, 0) site and four H atoms occupy the 4f (0.303, 0.303, 0) site. Previously, we calculated the lattice parameters of MgH 2 are a = 4.477 Å and c = 2.989 Å, these results are in full agreement with experimental and other theoretical values [12] [20]. For Ni and Sc co-doped on MgH 2 system, we simulate a 3 × 3 × 1 supercell model (see Figure 1) that contained a total of 54 atoms with four non-equivalent positions for Mg and six non-equivalent positions for H. The MgH 2 3 × 3 × 1 supercell is computed using the bulk parameters. Relaxations of the atomic coordinates were carried out, the optimal atomic positions of Mg and H atoms are good agreement with other theoretical data [20].
All energy and electronic structure calculations were performed under the framework of the density functional theory (DFT) via the Vienna ab initio Simulation Package (VASP) [24]. The electron-ion core interactions were described by the projector augmented wave (PAW) method [25]. The Perdew-Wang 91 (PW91) functional as generalized gradient approximation (GGA) was adopted for the exchange-correlation term [26]. For the plane-wave basis set a cutoff energy of 350 eV was used. A Gaussian smearing method for geometry optimization and a tetrahedron method with Blöchl corrections for electronic structures with an energy broadening of 0.05 eV were used throughout. Dependence of total energy on k-mesh was checked, a 3 × 3 × 7 Monkhorst-Pack k-point mesh for geometry optimization and a 5 × 5 × 9 Monkhorst-Pack k-point mesh for electronic structures were used to save the computing cost. The total energy convergence was chosen to be 10 −7 eV and the absolute magnitude of force on each atom was below 0.01 eV/Å.

Dopant Site Preference and Substitution Energy
In order to find the optimum geometry and doped sites of dopants (Ni and Sc) in MgH 2 , the total electronic energies of dopants in every non-equivalent position need to be calculated. In the Ni-doped system, each of the four non-equivalent positions of Mg is substituted by Ni in order. The calculated total electronic energies are shown in Figure 2(a). Due to the minimal total electronic energy, Ni prefers to substitute for the Mg3 position, and the new compound is denoted as (Mg, Ni)H 2 . Then, Mg is substituted by Sc in other three non-equivalent positions (Mg1, Mg2 and Mg4) of (Mg, Ni)H 2 compound. The calculated total electronic energies are shown in Figure 2(b). It can be seen that Sc prefers to substitute for the Mg4 position due to its lowest total electronic energy, and the new compound is denoted as (Mg, Ni, Sc)H 2 . Hence, in co-doped system, the Mg3 and Mg4 would be simultaneously substituted by Ni and Sc, respectively.
To identify the favorability of Ni and Y co-doping in MgH 2 comparing to Ni single-doping, the substitution energies (E sub ) of (Mg, Ni)H 2 and (Mg, Ni, Sc)H 2 are estimated via the definition [21] [27]: where E t (M) refer to the total energies of supercell of hydrides. E b represents the total energies per atom in the bulk structure. The x and y are the number of dopants in the supercell. The obtained substitution energies of (Mg, Ni)H 2 and (Mg, Ni, Sc)H 2 are 0.16 and 0.12 eV/atom, respectively. From energy point of view, the smaller substitution energy corresponds to the more favorable substitution doping. Therefore, the co-doping Ni and Sc into MgH 2 is most energetically favorable than the single-doping Ni into MgH 2 .

Stability and Dehydrogenation Properties
In general, the structural stability of crystal is closely related to the formation enthalpy (ΔH form ), negative formation enthalpy indicates that the crystal can exist stably. Furthermore, the more negative formation enthalpy suggests the higher stability of crystal [28]. The formation enthalpy (ΔH form ) is calculated in order to recognize the stability of the co-doped system compared to single-doped system, using the follow definition [28] [29]: where E t represents the total energies of supercell of hydrides. E b is the total energies per atom in the bulk structure. The x and y are the number of dopants in the supercell. E(H 2 ) denotes the total energy of free H 2 molecule is computed as −6.77 eV, which was evaluated via a 8 × 8 × 8 Å supercell in full agreement with experimental [5] and other theoretical data [12] [18]. The calculated formation enthalpies of (Mg, Ni)H 2 and (Mg, Ni, Sc)H 2 are −0.06 and −0.10 eV/atom, respectively. It can be seen that the formation enthalpies of these two compounds are both negative, which means that these compounds can exist stably. Besides, Ni and Sc co-doped system has lower enthalpy value, which means co-doped system exhibits higher stability compared to Ni single-doping. In order to further assess the dehydrogenation abilities of (Mg, Ni)H 2 and (Mg, Ni, Sc)H 2 , their hydrogen desorption enthalpies (ΔH des ) are also calculated by using Equation (3) where For the Ni single-doped MgH 2 system, the hydrogen desorption enthalpies are shown in Figure 3(a). The corresponding ΔH des values are 1.86, 1.67, 1.72, 0.52, 1.02 and 0.57 eV/H 2 for H1 -H6 respectively. Compare with the hydrogen desorption enthalpy of ΔH des = 0.77 eV/H 2 results for MgH 2 in 570 K [16], part desorption enthalpies of Ni-doped MgH 2 are decreased. Therefore, the H (H4, H6) around dopant Ni would be released easily, due to the smaller hydrogen desorption enthalpy. For the Ni and Sc co-doped MgH 2 system, the hydrogen desorption enthalpies of Ni and Sc co-doped are shown in Figure 3(b). The corresponding ΔH des values are 0.75, 1.35, 0.67, 0.34, 1.09 and 0.30 eV/H 2 for H1 -H6, respectively. It can be observed that most of the hydrogen desorption enthalpies for this hydride are significantly decreased in comparison with Ni doping, except for the ΔH des value of H5 around Mg. Thus most hydrogen dissociation is much easier than single-doped case, which indicates the Ni and Sc co-doped system has more promising dehydrogenation properties. Although the partial substitution of Mg by Ni and Sc has significant effects on MgH 2 , the detailed understanding of the effect of co-doping of Ni and Sc on the hydrogen desorption process and kinetics of MgH 2 requires a further investigated, which will be the subject of our future work.  Table 1 presents the bond distances between metallic elements of undoped and doped MgH 2 systems. The bond length of Mg-Mg range from 3.500 Å to 4.476 Å with an average of 3.663 Å in pure MgH 2 system, which is in good agreement with other theoretical results [20] [31]. In Ni single-doped MgH 2 system, Mg2 and Mg4 are the nearest neighboring metallic atoms of the dopant Ni. The average of Mg-Ni bond length is 3.692 Å, shorter than that of Mg-Mg bond in pure MgH 2 , which implies the bond strength of Mg-Ni is enhanced. The bond length of Mg-Mg is also decreased, thus the strength of Mg-Mg bond is enhanced in comparison with that of the pure MgH 2 . For Ni and Sc co-doped system, the bond length of Mg-Mg is further decreased, enhancing the strength of Mg-Mg bond. The distances between the Mg and Ni atoms are longer than that of the single-doped system, indicates that its bond strength are weakened. Furthermore, the length of Mg2-Sc bond and the Ni-Sc bond are shorter than the Ni-doped system, thus the bond strength of Mg2-Sc and Ni-Sc are enhanced. These can be inferred that the dopant Sc has alloying trend with Mg and Ni atoms, which would be weakened the strength of Mg-H and Ni-H bonds.

Electronic Structure
The total and partial density of states (DOS) of the pure MgH 2 system are plotted in Figure 4, the Fermi energy  (E F ) level is set at zero and used as a reference. The energy gap between the valence band (VB) and conduction band (CB) is 3.82 eV. The value is in good agreement with other theoretical calculations reported previously [20] [34]. The relatively large energy gap of MgH 2 leads to a high formation enthalpy and poor hydrogen sorption kinetics of MgH 2 [35]. The DOSs plot corresponding to MgH 2 shows a large dispersion of the bands signaling the s-like character. The VB is mainly dominated by H s orbitals and the CB mainly by Mg s and Mg p orbitals. The amplitude of the partial DOS of the H s orbital is a result of the weight of H in the structure, and also of the transfer of electronics from Mg to H leading to an ionic hydride. The total and partial DOS of Ni-doped MgH 2 system are plotted in Figure 5. The amplitude of the partial DOS of the Ni d orbital was minimized by 10 in order to plot the partial DOSs of all atoms in the same panel with the same scale. The total DOS curve shows a remarkable decrease in the band gap of 0 eV, show clearly metallic characteristics. Ni doping leads to the appearance of a narrow d-band in the middle of the band gap.   This d orbital is strongly hybridized with Mg p and H s orbitals giving the strongly Mg-Ni and Ni-H bonding. Furthermore, the H s orbitals distributed in the region of −5.5 to −3.1 eV are less overlapped with Mg s p orbitals comparing to pure MgH 2 , and the amplitude of the valence band is decreased, which can help to weaken the hybridization of Mg-H bond. These weak bonding interactions between Mg and H in Ni doped system are the reasons why this system has better dehydrogenation property.
The total and partial DOS of the Ni and Sc co-doped MgH 2 system are plotted in Figure 6. Similar to the Ni single-doped system, the amplitude of the partial DOS of the Ni and Sc d orbitals were minimized by 10 in order to plot the partial DOSs of all atoms in the same panel with the same scale. The similar lowered bonding peaks of H s, Mg s and p orbitals can also be observed, indicating the Mg-H bond is further weakened after Sc doping. The Sc p and d orbitals overlap with H s, Mg p, Ni p and d orbitals in the energy region of −3.2 to 6.1 eV. And the distributions of bonding peaks of Sc d orbitals are mainly concentrated in the energy region of 1.8 to 4.2 eV and overlap well with Mg s and p orbitals. These behaviors indicate that Sc atom has strong bonding interaction with H, Mg and Ni atoms and decreases Mg-H p-s mixing. Therefore, the Mg-H hybridizations are significantly weakened in Ni and Sc co-doped system, and this system exhibits more promising dehydrogenation property.

Conclusion
In summary, the Ni and Sc co-doping effects on the energetics and electronic structures of MgH 2 were studied by the first-principles calculations based on DFT. Due to the minimal total electronic energy, Ni and M dopants prefer to substitute the Mg3 and Mg4 positions, respectively. The substitution energy and formation enthalpy are used to estimate the energetic stability of the doped MgH 2 system. Ni and Sc co-doped MgH 2 system are more stable than Ni single-doped system. The hydrogen desorption enthalpies of these three systems were also studied. According to the relatively lower hydrogen desorption enthalpies, the co-doped systems possess more promising dehydrogenation properties compared with pure Ni doping. And the lowest hydrogen desorption enthalpy of 0.30 eV appears in co-doped system. The electronic structure analysis illustrates that the hybridization of dopants with Mg and H atom together weakens the Mg-H interaction. The decrease in hybridization peaks of Mg-H and band gaps leads to an easier Mg-H dissociation and lower hydrogen desorption enthalpy when the MgH 2 is co-doped with Ni and Sc. Therefore, the co-doping with Ni and Sc effectively improves the dehydrogenation properties of destabilized MgH 2 .