Role of catalysts in dehydrogenation of MgH₂ nanoclusters

Abstract

A fundamental understanding of the role of catalysts in dehydrogenation of MgH₂ nanoclusters is provided by carrying out first-principles calculations based on density functional theory. It is shown that the transition metal atoms Ti, V, Fe, and Ni not only lower desorption energies significantly but also continue to attract at least four hydrogen atoms even when the total hydrogen content of the cluster decreases. In particular, Fe is found to migrate from the surface sites to the interior sites during the dehydrogenation process, releasing more hydrogen as it diffuses. This diffusion mechanism may account for the fact that a small amount of catalysts is sufficient to improve the kinetics of MgH₂, which is essential for the use of this material for hydrogen storage in fuel-cell applications.

There is an increasing trend in the use of fuel cells in vehicles (1, 2) and as replacement for batteries in mobile phones and laptop computers (3, 4). In recent years, complex light metal hydrides (5, 6) have attracted considerable attention as hydrogen storage materials because of their large gravimetric density. The metal–hydrogen bonds in these materials are strong, however, and the poor kinetics and thermodynamics do not make these materials suitable for mobile applications. Therefore, the primary focus of research has been to find ways to improve the kinetic and thermodynamic behavior of these light metal hydrides by weakening the metal–hydrogen bond. Although the high thermodynamic stability [ΔH = −75 kJ (mol H₂)⁻¹] and dissociation temperature (≈400°C) combined with poor kinetics impede the use of MgH₂ for hydrogen storage, it does possess some attractive features. First, it is a low-cost material because of the abundantly available magnesium. Second, it has a gravimetric density of 7.7 wt % and, unlike the alanates, all of this hydrogen can be desorbed. Third, being a binary alloy, the role of catalysts is easier to study than in the ternary alanates. The current research on MgH₂ has focused on reducing the strength of the metal–hydrogen bond by nanostructuring and/or using catalysts. It has been shown that mechanical ball milling can reduce the particle size to ≈10 nm where defects, large surface areas, and grain boundaries help to improve the kinetics and thermodynamics of hydrogen sorption (7). Further milling with transition metal additives such as Ti, V, Fe, Co, and Ni leads to greatly enhanced hydrogen sorption kinetics (8–10). Despite a considerable amount of experimental work, a fundamental understanding of how nanostructuring and/or catalysts improve the kinetics and thermodynamics of MgH₂ is still lacking. It is needless to emphasize that an understanding of where the catalytic atoms reside and how a small amount of catalysts can improve the thermodynamic behavior is necessary for the synthesizing of materials with optimal performance. Here, an attempt to provide such an understanding is made by carrying out first-principles calculations of the electronic structure and total energies of MgH₂ nanoclusters that are interacting with transition metal dopants.

MgH₂ Cluster Model

Typically, the smallest nanoparticle produced during mechanical ball milling is ≈10 nm in size. It presents a problem because first-principles calculations of a 10-nm-size MgH₂ cluster (≈100,000 atoms) are beyond the scope of any present-day computer. Fortunately, systematic studies (11–13) of the evolution of desorption energies and electronic structure of Mg_nH_2n clusters as a function of n have shown that the properties have converged when n is ≈30. Therefore, a 31 formula unit MgH₂ nanocluster was used in the present work to study the effect of doping in nanostructures; and given the recent advances in synthesis of nanoscale particles (14) and the move in the hydrogen storage community toward highly nanostructured hydrogen storage materials (15), clusters of the size considered here may soon become more than model systems.

A stable Mg₃₁H₆₂ cluster was constructed by cutting out a part of the MgH₂ bulk crystal structure and then rearranging the surface hydrogen atoms to attain the correct Mg_nH_2n stoichiometry (see Fig. 1). This cluster preserves the D_2h subsymmetry of bulk MgH₂, which also helps to speed up the computer calculations. Note that in this cluster the central Mg atom is the only one that can be classified as bulk-like, whereas all other Mg atoms are surface atoms. Two kinds of surface atoms were studied: a 6 H-coordinated atom (orange in Fig. 1) and a 4 H-coordinated atom (red in Fig. 1). The former will be designated as the “surface” site, whereas the latter will be designated as the “edge” site for further discussions. The role of catalysts in the dehydrogenation mechanism was studied by using the transition metal elements Ti, V, Fe, and Ni as dopants. The preferred site of these dopants was studied by substituting them at the “center”, surface, and edge sites. The effective alloying content with 1 Mg atom substituted out of 31 amounts to ≈3.2 mol %. The models of the fully dehydrogenated metal clusters were obtained by simply removing all hydrogen atoms from a fully relaxed metal hydride cluster and then performing geometry relaxation with the same symmetry constraints (D_2h for center substitution, and C_s for surface and edge substitution). This yielded metallic clusters with hexagonally close-packed layers, like that of bulk magnesium metal.

Fig. 1.

Ball-and-stick model of a MgH₂ cluster with 31 formula units. Mg atoms are green; hydrogen atoms are white. Three different Mg sites where transition metal atoms are substituted are shown in red (edge site), orange (surface site), and blue (central site).

Results and Discussion

Substitutional Doping.

To establish the preferred substitutional site of the transition metals, energy costs for the various substitutions were calculated from the total energies according to the following equation:

Here, E corresponds to total energies with atomic energies of Mg and the transition metal atoms, M = Ti; V; Fe; Ni, being used as reference. Although such a choice of reference may influence the calculated energetic stability of the alloy, note that the intention here is not to show whether it is energetically preferable to substitute transition metal atoms at the Mg sites, but rather which Mg site (center, surface, or edge; as defined in Fig. 1) is the most favorable site for doping. In this sense, the choice of the reference energies is immaterial. The results are given in Fig. 2. Note that all energies in Fig. 2 are negative, indicating that substitutional doping of clusters is possible, at least with respect to the gaseous metal atoms. More importantly, the surface or edge sites are the most preferred sites for all elements studied. This should explain some of their high catalytic activity, because hydrogen desorption from the surface of MgH₂ has been found to be the rate-determining step (16).

Fig. 2.

Energy gain when substituting Mg by transition metal dopants at various sites of Mg₃₁H₆₂.

The substitution energies in pure magnesium clusters were calculated in a similar manner:

These energies are given in Fig. 3. Once again, these energies are also negative, indicating that it is possible to form these alloyed clusters with pure Mg, at least in the gas phase. However, there are some differences between the results in Figs. 2 and 3. Whereas the transition metal atoms mostly prefer the surface sites in MgH₂, they prefer the edge sites in pure Mg. The exceptions are Ti and Ni. In the Mg cluster, titanium shows very little site preference, whereas in the hydride phase, Ti clearly prefers the surface site, as do the other transition metal atoms. The energy differences between transition metal doped Mg and MgH₂ clusters are further highlighted in Table 1, which shows the gain in energy for the dopant atoms in the most stable surface site compared with the center site. The gain in energy implies that V, Fe, and Ni would always prefer surface or edge sites over the bulk sites in Mg clusters, showing that the migration to the surface is thermodynamically favorable and the transition metal atoms would be found at the surface, forming a catalytic coating. This is in agreement with the fact that most transition metals do not form alloys with Mg at ambient pressure (17–19).

Fig. 3.

Energy gain when substituting Mg by transition metal dopants in Mg₃₁ clusters.

Table 1.

Relative energy (kJ/mol) of the most stable surface site with respect to the center site

M=	Ti	V	Fe	Ni
Mg30MH62	−82	−45	−60	−183
Mg30M	+27	−30	−84	−115

It is also instructive to look at the optimized cluster geometries. The doped clusters kept their overall shape after geometry relaxation but not without local changes in the geometry around the surface and edge transition metal atoms. As a reference, consider the central Mg atom that is bound to 6 H atoms at a distance of 2.0 Å (which is close to the bulk crystal value of 1.96 Å). Now compare the average transition metal–hydrogen bond lengths for the center, surface, and edge transition metal atoms, as plotted in Fig. 4. There is significant contraction in the bond length as Mg is replaced by transition metal dopants. This reflects the local changes in the electronic structure induced by the dopants. The shortest metal–hydrogen bond-length, 1.57 Å, is observed for Ni in the edge site. It can be explained by the special geometry of the Ni doped cluster: one extra hydrogen atom is bound to Ni for a total of five bound hydrogens.

Fig. 4.

Average bond lengths between Mg/transition metals and nearest-neighbor hydrogens.

Complete Hydrogen Desorption.

To see whether this small amount of alloying would destabilize the cluster as a whole and affect the temperature of hydrogen desorption, the reaction enthalpies of full dehydrogenation for both the pure and transition-metal-doped MgH₂ cluster were calculated by using the following equations:

and

These results are given in Fig. 5 and represent the average energy required to remove H₂ molecules. Enthalpies for all systems fall in the range of 70–80 kJ (mol H₂)⁻¹ with the smallest values for Fe and Ni. Thus, the doped Mg clusters all give enthalpies close to the undoped case, as expected for only 3.2% of alloying. Of course, the effects would be more pronounced with a higher amount of alloying, but too much alloying of heavier elements is disadvantageous from a practical point of view because it would lead to lower gravimetric density of stored hydrogen.

Fig. 5.

Average hydrogen desorption energies for Mg₃₀MH₆₂ clusters with dopants at three different sites as compared with a pure Mg₃₁H₆₂ cluster.

Single-Site Hydrogen Desorption.

The optimized cluster geometries showed only local changes around the transition metals, so even though the average desorption energy is largely unchanged, there might still be changes in individual hydrogen desorption energies, especially those corresponding to hydrogens that are bound close to the transition metal atoms. Presumably, hydrogen release takes place at the surface, so one way to probe this effect is to calculate desorption energies of individual hydrogen atoms bound to the transition metal surface and edge sites. Setting E(H) = 0.5E(H₂) gives the following relation for single-site hydrogen removal (normalized to the energy required per H₂ molecule):

The resulting energies (shown in Fig. 6) reveal the local effects of the transition metal catalysts. In nanocluster MgH₂, the removal of hydrogen bound to edge-site atoms costs energy whereas the process is exothermic for the surface atom. This is consistent with several experimental observations that nanostructuring can by itself lower the temperature required for the onset of hydrogen release (10, 20, 21), even without the addition of catalysts. No exothermic hydrogen removal is observed when Ti replaces Mg, but the surface-site energy is still significantly lower than the bulk MgH₂ value. For V, both sites show slightly exothermic hydrogen removal. The most notable cases, however, are Fe and Ni. The removal energies of H atoms from both of the surface sites are remarkably negative, as is removal from the Fe edge site. This kind of exothermic dissociation might lower the minimum temperature needed to initiate hydrogen desorption, especially because an application of the Hammond–Leffler principle would suggest that the corresponding activation energies will be lower as well. Observations of both lower hydrogen release temperatures and activation energies in transition-metal-doped MgH₂ (8, 10) suggest that this is indeed the case.

Fig. 6.

Single-site hydrogen desorption energies for Mg₃₀MH₆₂ clusters at two different surface sites.

In view of the promising energetics in Fe-doped MgH₂, this system was chosen for an in-depth study to see how it evolves as hydrogen atoms are removed successively. As the geometry was relaxed after the removal of the first hydrogen atom from the edge site (Fig. 7A), the iron atom was found to attract another hydrogen atom from the center of the cluster to compensate for the removed hydrogen and preserve the tetrahedral coordination (Fig. 7B). The ability of the iron atom to attract nearby hydrogen atoms remains after removing yet another nearby hydrogen (Fig. 7C) and then two more hydrogen atoms simultaneously (Fig. 7D). The last scenario is probably a more realistic mechanism of desorption (assuming that it happens by H-Mg-H bending modes bringing two hydrogen atoms close together). In the case of the second removed hydrogen atom (Fig. 7C), the final structure even changed into an arrangement where five hydrogen atoms are now close to iron—effectively increasing coordination. Furthermore, when two out of these five hydrogen atoms were removed, and the was structure re-optimized, a FeH₄ tetrahedral arrangement reappeared, facilitated by a displacement of the Fe atom toward the hydrogen-rich core of the cluster. It thus appears that the Fe atom follows the MgH₂/Mg interface during dehydrogenation in its search for hydrogen atoms.

Fig. 7.

Successive dehydrogenation around the Fe atom. At each step, the blue hydrogen atom(s) is removed and the structure is reoptimized. (A) Mg₃₀Fe-H₆₂. Fe coordinates four hydrogen atoms in a tetrahedral fashion. (B) Mg₃₀Fe-H₆₁. Tetrahedral coordination reformed after removal and optimization. (C) Mg₃₀Fe-H₆₀. Iron now coordinates five hydrogen atoms. (D) Mg₃₀Fe-H₅₈. Iron becomes tetrahedrally coordinated once again.

Such a process may at first appear to be at odds energetically with the doping results of Figs. 2 and 3, where the transition metals were found to prefer surface positions at both the start and the end of the hydrogenation interval. But during dehydrogenation, diffusion of the atom is mainly driven by the local rehydrogenation of the transition metal. Once dehydrogenation is complete, and a metallic cluster has been formed, Fe atoms below the surface may diffuse back to the surface again, where they can act catalytically in the hydrogen absorption process. Again, this should be thermodynamically favorable, judging from the relative energies in Table 1 and also from the experimentally observed poor miscibility of Fe in Mg (18). Furthermore, the mechanism where the Fe atom migrates in search of hydrogen atoms, and then gets recycled back to the surface, can explain why a small amount of catalysts is all that is needed for improving the thermodynamics of complex metal hydrides. Løvvik and coworkers (22) have suggested a similar mechanism for Ti-doped NaAlH₄.

Conclusion

The observed surface effects of transition metals in the cluster model give support to the gateway (or shuttling) hypothesis (23, 24) of dehydrogenation, where transition metals act as catalytic centers for hydrogen atoms by continuously attracting new hydrogen atoms from the rest of the cluster as hydrogen desorbs. In addition, we see evidence of iron diffusion upon dehydrogenation, suggesting that iron, and most probably other transition metals, stays in the MgH₂/Mg interface region, where it continuously catalyzes dehydrogenation.

Methods: Density Functional Theory Calculations

The calculations were performed with Turbomole (25, 26), using atomic-centered Gaussian basis sets. The Mg atoms were assigned a split-valence polarization (SVP) basis set with extra d-functions (27), while the other atoms were treated with the Turbomole standard SVP basis set. Relativistic electronic core potentials (10 electrons in the core) were used for the transition metals. Basis set convergence was investigated for the pure Mg and Fe-doped clusters. It was found that the SVP+d/SVP basis set combination produced reaction energies for Eqs. 3 and 4 (see above) that were within 1 kJ/mol of those obtained with a basis set at the triple zeta polarization level (“TZVP”) followed by quadruple zeta polarization (“QZVP”) singlepoint corrections. Exchange-correlation effects were incorporated with the exchanged correlation functional proposed by Tao, Perdew, Staroverov, and Scuseria (“TPSS”) (28), integrated over the Turbomole “m4” medium-sized multigrid. The resolution-of-the-identity approximation was used to speed-up the calculations. The error introduced with this approximation (29) is too small to be of importance here (typically <0.29 kJ/mol). For the transition metal cases, high damping, level-shifting, and long self-consistent field runs (>100 iterations) were sometimes necessary to converge the initial guess to 10⁻⁶ H (i.e., 2.6 × 10⁻³ kJ/mol). Redundant internal coordinates were used for geometry optimizations. All spin multiplets up to the atomic ground state of the dopant were tested. Zero-point vibrational energies were neglected because calculations of three test cases gave only small (−5 to −1 kJ/mol) ΔE corrections to Eqs. 3–5.