Studies of the Electronic, Optical, and Thermodynamic Properties for Metal-Doped LiH Crystals by First Principle Calculations

3.1 Structural Properties

LiH is crystallized in the NaCl-type structure (FM-3M, space group no. 225). All the calculations are carried out using a 2 × 2 × 2 super-cell containing 31 Li atoms, 1 metal M atom, and 32 H atoms, denoted henceforth as Li₃₁MH₃₂. The metal (M=Al, Fe, and Ru) doped concentration is x = 3.125 %. The lattice constants of Li, Al, Fe, and Ru are shown in Table 1, which are comparable with the experimental data [45]. Here, because of difference of cells after doping, the lattice parameters a of the supercell we used are twice the lattice constants a₀ of pure LiH, i.e. a = 2a₀.

As a relaxed parameter, the lattice parameters for LiH with and without M dopants are optimized by fixing the relative atomic position and varying the lattice parameter a by ±10 % of the experimental data 2a₀. The total energy of LiH, as a function of volume, before and after being doped with a certain element (Al, Fe, and Ru), is calculated using the PBE functional and double-ζ basis set with Goedecker-Teter-Hutter pseudopotentials. The results are shown in Figure 1. The structural parameters, the bulk modulus B₀, and its first derivative B′₀ with respect to the pressure listed in Table 2 are given by fitting the total energies to the Murnaghan equation of state [46]:

Figure 1:

Calculated free energy versus supercell volume for pure LiH and Li_1−xM_xH. (a) LiH, (b) Li_1−xAl_xH, (c) Li_1−xFe_xH, and (d) Li_1−xRu_xH.

where E₀ is the minimum energy and V₀ is the equilibrium volume. The simulated a₀ (≈4.024 Å) and B₀ (≈33.59 GPa) of LiH are close to the experimental values (a₀ ≈ 4.083 Å [47] and B₀ ≈ 33.60 GPa [48]).

After the metal M doping, the local structures of [MH₆] octahedra are also modified with respect to the host LiH. The distances between the nearest neighbor (nn) H atoms and the central metal M are illustrated in Table 3. The increase of the cation-anion distance in the [AlH₆]⁵⁻ center related to the host [LiH₆]⁵⁻ octahedron is attributable to the larger ionic radius (≈0.93 Å [49]) of impurity Al⁺ than host Li⁺ (≈0.76 Å [47]). For Fe replacing a host Li in LiH crystal, the symmetry of the [FeH₆]⁵⁻ cluster maintains cubic with the threefold orbitally degenerated ground state ⁴T_1g of high spin (S = 3/2) under intermediate crystal fields. The slightly smaller Fe–H bond length than Li–H in host LiH may be largely ascribed to the strong covalency and hence remarkable Fe–H orbital hybridization. As for the [RuH₆]⁵⁻ cluster, the distances between central Ru⁺ and nn H⁻ exhibit similar uniform shrinkage by about 9.8 % and extra tetragonal elongation due to the Jahn–Teller effect, characterized by the axial elongation a ≈ 0.016 Å, with the error less than 1 % due to the limits of the DFT calculations. Then the original cubic two-fold orbitally degenerated ²E_g ground state is split into two orbital singlets ²A_1g and ²B_1g, with the former lying lowest. Similar tetragonally elongated d⁷ centers with low spin (S = 1/2) were also investigated with high order perturbation formulas [50] and DFT calculations [51], [52], [43]. In fact, substitution of Li⁺ by obviously covalent Fe⁺ or Ru⁺ may induce the enhancement of metal-ligand covalent interactions and hence shorter average bond lengths. The calculated spins in Table 3 for Fe- and Ru-doped LiH suitably support the high (S = 3/2) and low (S = 1/2) spins of the related systems, respectively, and can be regarded as valid in physics.

3.2 Band Structures and Density of States

The electronic structures can offer important information about the electronic and optical characteristics of materials. The density of states (DOS) is used to analyze and explain the effect of the metal dopants on the stability and kinetics of the hydrogen absorption-desorption in Li_1−xM_xH. For this purpose, the band structures and (total and projected) DOS of LiH with and without M dopants are calculated and shown in Figures 2 and 3. The Fermi level presented with a gray line is set as zero of energy. It is well known that the DFT calculations based on local-density approximations and GGA approximations underestimate the bandgaps [53], [44], while meta-GGAs and hybrid functionals are more accurate and reliable [54]. So, the PBE0 functional is adopted in the present calculations for bandgaps, which yields consistent results with the experimental data.

Figure 2:

Band structures of LiH without and with the dopants. A MIGB occurs between the VB and CB for Li_1−xM_xH system. In the band structure of the spin-polarized Li_1−xFe_xH (c) and Li_1−xRu_xH (d), blue and red lines represent the spin-up and spin-down states, respectively. (a) Pure LiH, (b) Li_1−xAl_xH, (c) Li_1−xFe_xH, and (d) Li_1−xRu_xH.

Figure 3:

Total and projected DOS for the pure LiH and Li_xM_1−xH. H1 and Li1 denote the nn H and nnn Li, respectively. H2 and Li2 stand for the corresponding atoms far away from the dopants M. (a) LiH, (b) Li_1−xAl_xH (c) Li_1−xFe_xH, and (d) Li_1−xRu_xH.

3.3 Electronic Spin Configuration

According to the crystal field theory [58], Fe⁺ and Ru⁺ ions with the same d⁷ configurations can exhibit dissimilar behaviors in octahedral crystal fields, dependent on the competition between the crystal field stabilization energy (Δ) and intra-orbital electron pairing energy (Π) (see Fig. 4). For Fe⁺ with Δ < Π, the two 3d electrons are more likely to occupy the higher e_g orbitals than to pair with the electrons in the lower t_2g orbitals, associated with the case of weak field with high spin (i.e. t_2g⁵e_g² configuration with S = 3/2). For Ru⁺ with Δ > Π, the stronger crystal field forces the six 4d electrons to pair with each other in the lower t_2g orbitals with only one unpaired 4d electron in the higher e_g orbitals, corresponding to the case of strong field with low spin (i.e. t_2g⁶e_g configuration with S = 1/2). This point is also suitably supported by the band structures and DOS for Fe and Ru doped systems in Figures 2c,d and 3c,d, respectively.

Figure 4:

The electronic spin configuration of d⁷ transition-metal ions Fe⁺(t_2g⁵e_g²; high-spin) and Ru⁺(t_2g⁶e_g; low-spin) in an octahedral ligand field. Based on the crystal field theory, the high- or low-spin depends on a competition between the crystal field stabilization energy (Δ) and the intra-orbital electron pairing energy (Π).

3.4 Charge density

The charge distribution in both pure and doped LiH systems can be analyzed here. On the Pauling scale, H has a higher electronegativity of 2.20, while Li has a lower value of 0.98. Thus, in LiH, atomic H has a more potential to attract electrons than atomic Li and induce Li⁺ cation and H⁻ anion. The 2D charge density plot of Li_1−xM_xH is shown in Figure 5, which clearly shows the charge density surface around H and TM (Fe and Ru) atoms. These charge density contours exhibit the ionic character of LiH and covalent nature of Li_1−xM_xH, respectively.

Figure 5:

Electron density of Li_1−xM_xH. The central atoms of the plane are Li or M atom. The colors are corresponding to different densities: red-higher; blue-lower. (a) LiH, (b) Li_1−xAl_xH, (c) Li_1−xFe_xH, and (d) Li_1−xRu_xH.

The electronegativity values of Al, Fe, and Ru are 1.61, 1.83, and 2.20, respectively. Thus, H and M (=Al, Fe, and Ru) may show affinity for electrons. This point is also verified by the Mulliken charge of M in Table 3. Hydrides of Al are well-known covalent compounds [59], [60] in view of Al electronegativity larger and smaller than Li and H, respectively. Thus, the Al–H bond is expected to be more covalent than the host Li–H one from the lower difference in electronegativity of the former, as pointed out for complex metal aluminum hydrides [5]. From the contours in Figure 5, Li continues to show absence of charge density after doping. The electron density is directed along the six principal M–H bonds, validating the presence of covalent bonding. Meanwhile, the overlap populations (OP) in Table 3 reaffirm the significant covalency of Fe–H and Ru–H bonds and mild covalency of Al–H bonds as well.

3.5 Optical Properties

The imaginary part ε_Im(ω) is calculated from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules. The real part ε_Re(ω) is obtained from the Kramers-Kronig relationship [61]. Then the other linear optical properties [i.e. electron energy loss spectrum L(ω), absorption coefficient α(ω), reflectivity R(ω), refractive index n(ω), and extinction coefficient k(ω)] can be further obtained [62]. The related results are presented in Figures 6 and 7 for the energy range up to 15 eV.

Figure 6:

Absorption coefficient α(ω) of LiH with and without the dopants. All absorption peaks show some red-shifts for the doped systems related to those for pure LiH.

Figure 7:

Linear optical properties for LiH with and without the dopants. (a,b) dielectric function, (c,d) conductivity, (e,f) refractive index, (g) reflectivity, (h) loss function.

3.6 Thermodynamic Properties and Hydrogen Storage

The reactions related to the formation of LiH and Li_xM_1−xH are as follows:

To calculate the formation heat of these reactions, the total energies of element Li, metal-atom M, and hydrogen molecule are subtracted from the hydrides LiH and Li_xM_1−xH with x = 1 and x = 0.96875:

The total energies obtained with the optimized structures of LiH, Li, and Ru are used for the studied systems. The total energy of hydrogen molecule is E_tot(H₂) ≈ −2.332 Ry, adjacent to −2.330 Ry in [70] and −2.320 Ry in [7]. The computed formation enthalpy is listed in Table 3. The formation heat −94.06 kJ/mol H of LiH is actually close to the experimental values (≈−90.5 kJ/mol H [47] and −116.3 kJ/mol H [71]) and the previous theoretical results (≈−89 kJ/mol H [7], −87 kJ/mol H [72], −81 kJ/mol H [73], and −85 kJ/mol H [6]) obtained with different methods. The slight discrepancies can be ascribed to the different calculation methods. Importantly, the addition of metal M to LiH reduces the stability of LiH and may consequently improve the dehydrogenation process. The order (Al < Fe < Ru) of the magnitude of ΔH can be illustrated by the stronger crystal fields of the d⁷ clusters, especially the low spin (S = 1/2) Ru⁺[t_2g⁶e_g] group as compared with the high spin (S = 3/2) Fe⁺ [t_2g⁵e_g²] one [58]. Therefore, the destabilization effect is enhanced with metal dopants without obviously sacrificing the storage capacities.

The thermodynamic properties of the hydrides can be described with the standard Gibbs free energy ΔG = ΔH − TΔS. For the standard zero Gibbs free energy at the decomposition temperature and a constant pressure [18], the temperature can be estimated from enthalpy and entropy changes by using ΔH = TΔS. As the entropy changes of a solid are much smaller than that of the corresponding gas during heating, the entropy change in the decomposition reaction is dominated by the entropy loss of the gaseous hydrogen. For most metal hydrides, the entropy change (corresponding to a mole of gas transforming into the solid) is ΔS ≈ 130.7 J/mol K [74; 75] at the standard pressure and temperature. From the thermodynamic relation T_dec = ΔH/ΔS, the temperature of dehydrogenation can be estimated from the calculated ΔH(H₂). This yields the significantly overestimated decomposition temperature of 1439 K for pure LiH, as compared with the experimental value 993 K [71]. The calculated T_dec may display a slight or significant decrease with dopants, as mentioned for similar doped hydrides [8]. From [21], the entropy change is estimated in the range of 95–140 J/mol K for most dehydrogenation reactions. Adoption of the upper limit of 140 J/mol K and the above enthalpy change yields T_dec ≈ 1343 K, which is still higher than but closer to the measured 993 K [71].

The destabilization of LiH with M dopants so as to reduce the dehydriding temperature may be an important method for practical applications. From Table 3, ΔH decreases from pure LiH to doped systems and shows the order Ru > Fe > Al, corresponding to the dehydriding temperatures of 606, 570, and 522 K for Ru-, Fe-, and Al-doped systems, respectively, with the upper limit of entropy change. So, the Al-substituted system is possibly the most suitable candidate for hydrogen storage due to the high hydrogen content and low dehydriding temperature, which is consistent with the various studies on the complex alkali metal hydrides [1; 75]. It is noted that increasing concentration of M dopants would induce new complex metal hydrides and hence further decreases of ΔH, as mentioned in [5].