1 Introduction

Studying of adsorption/dissociation of molecular hydrogen on the surface of bare transition metal clusters has been an active research area and is well documented (see, e.g. [1–5]). The important rationale behind these studies is that gas-phase transition metal clusters have served model systems for catalysis [6]. By contrast, hydrogen activation by main group metal clusters has been investigated on a smaller scale. A recent experimental example is provided by the reaction of lithium atoms in solid H2 to form on annealing lithium hydride dimer (LiH)2 [7]. Turning to the main group 13, nanosized aluminium-hydride clusters have recently attracted some attention because of their potential application as the hydrogen storage media [8]. Sub-nanosized Al13 cluster was investigated in that direction using density functional theory (DFT) with the aim of determining its hydrogen storage capacity [9, 10] and kinetic barrier for the dissociative chemisorption of hydrogen on its surface [9, 11].

The relevant gas-phase experimental study of the reactions of Al n clusters (n ≤ 30) with deuterium molecules under mild conditions was conducted by Cox et al. [12]. In that study, which revealed a strong dependence of the reactivity on cluster size, the largest relative rate constant was determined for n = 6 (aluminium hexamer). The subsequent quantum chemical studies of the Al6 + H2 reaction by Moc [13] and Pino et al. [14] were consistent with the experimental outcome [12]. Furthermore, the reported [13–17] theoretical studies of the Al n  + H2 reactions with n = 2–6 have demonstrated that Al6 behaves uniquely, if one judges the ability of the aluminium cluster in the ground electronic state to activate H2. Indeed, for the H2 addition to Al2 dimer [14, 15, 17] and Al4 tetramer [14], whose ground electronic states are the triplets, the prior crossing between the triplet and singlet potential energy surfaces (PESs) is required along the reaction coordinate to reach the lower energy singlet energy surface of the H2 dissociation transition state and hydrogenation product. Also, the H2 addition to Al3 trimer [14, 16] and Al5 pentamer [14], whose ground electronic states are the doublets, present the reactions with significant energy barriers for hydrogen dissociation, unlikely accessible under mild conditions.

Recently, by using anion photoelectron spectroscopy (PE) combined with DFT calculations, Li et al. [18, 19] investigated novel Al n H − m cluster anions (4 ≤ n ≤ 8, 0 ≤ m ≤ 10) formed by the reactions of Al − n with atomic hydrogen. By analysing the cluster anion PE spectra, it was recognized [19] that neutral clusters of formula Al n H n+2 (5 ≤ n ≤ 8) had significantly large HOMO–LUMO gaps indicative of their increased stability. The following DFT pseudopotential study of Martinez and Alonso (ML) [20] using the PBE functional and plane wave basis set examined the structures, stability and bonding of the Al n H n+2 clusters (n = 4–11). In the related DFT work [21], similarities between the Al n H n+2 (n = 4–12) alanes and corresponding boranes were traced, especially the question of to what extent the so-called Wade’s rules could be applied to predict the alanes’ ground state structures. We note, however, that mechanistic aspects of the hydrogenation of Al n clusters leading to the Al n H n+2 alanes with n ≥ 6 (via the H2 addition reactions), including the kinetic barriers, were not addressed so far.

In the current work, we extended our theoretical studies to explore the reactivity of Al6 hexamer towards multiple hydrogen molecules. Our work aims at identifying the low-energy paths for the consecutive dissociative addition of H2 to the clusters Al6H2k−2 to form the clusters Al6H2k with k = 1–4. In particular, we investigated the viability of formation of Al6H8, considered the ‘target’ alane for the reasons given above.

2 Computational methods

According to the most accurate and comprehensive theoretical studies reported [14, 22], Al6 is the smallest aluminium cluster adopting a three-dimensional (3D) structure of lowest energy. To model adequately the reactions of multiple H2 addition to a 3D metal cluster in the gas phase, an extensive exploration of the underlying potential energy surfaces is crucial [5]. In search of the low-lying paths for H2 dissociation on the aluminium-hydride clusters, we have probed both the octahedron- and trigonal prism-like structures. The reason for this is that, for bare Al6, the octahedral and prism geometries lie close in energy [13, 14, 22].

The correlation-consistent aug-cc-pVTZ basis set [23] of triple-zeta quality was used throughout. All the geometries were optimized and characterized as minima or transition states using the B3LYP density functional [24, 25], where connectivity of the H2 dissociation transition states with the reactants and products was assured by calculating the intrinsic reaction coordinate [26]. The energetics of the H2 addition reactions was determined subsequently using the coupled-cluster singles-doubles-perturbative triples (CCSD(T)) [27]. In addition to the relative energies, the enthalpy differences (ΔH) and the corresponding free energy differences (ΔG) (at T = 298 K) have been determined at the latter level, where these thermodynamic values were obtained by including the zero-point energy, thermal and entropic corrections estimated with the help of the B3LYP/aug-cc-pVTZ vibrational frequencies. For testing purposes, the multilevel G4 scheme [28] was used as justified by the recent encouraging G4 versus coupled-cluster comparison for the predictions of reaction and activation energies [29, 30]. All the calculations were carried out with Gaussian 09 [31].

3 Results and discussion

Here, the low-lying paths for the consecutive H2 dissociations Al6H2k−2 + H2 → Al6H2k (k = 1–4) are presented and discussed. The path of the Al6 + H2 → Al6H2 reaction (k = 1) has been examined before [13, 14], but we summarize and ‘extend’ it in the next sub-section. The bulk of this report is devoted to the reaction steps with k = 2–4, not investigated so far. The transition states involved in the dissociation of the second (S), third (T) and fourth (F) H2 are labelled TS(2)j, TS(3)j and TS(4)j, respectively, where j = 1, 2, 3, …, indicate the TS number, with the ensuing hydrogenated clusters Al6H2k termed Sj (Al6H4), Tj (Al6H6) and Fj (Al6H8). The prismatic-like transition states are differentiated from the octahedral-like ones by adding the subscript ‘pr’.

3.1 k = 1

Previously [13], we found the singlet state distorted octahedron Al6(D3d,1A1g) to be this metal cluster lowest energy structure at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level, the result confirmed recently by the CCSD(T) geometry optimization of Al6 by Pino [14] (at the B3LYP level, the lowest energy Al6 is the triplet (\(^{3} {\text{A}}_{1}^{\prime }\)) trigonal prismatic (D3h) structure). The CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ energy profile of H2 dissociation on singlet Al6 is depicted in Fig. 1. The kinetically most favoured path obtained from the B3LYP calculations [13, 14] involves the singlet transition state TS(1) (see Fig. 2). The H2 dissociation on the singlet Al6 is kinetically favoured (in terms of the energy barrier) due to the favourable interaction of one of the two degenerate highest occupied molecular orbitals of eg symmetry of Al6 with the unoccupied molecular orbital \(\sigma_{u}^{*}\) of H2 [14]. On the B3LYP PES, the TS(1) rearranges to the Al6H2 hydride 1, where one H atom is threefold bridged and the other H atom is twofold bridged (Fig. 2).

Fig. 1
figure 1

Schematic enthalpy/free energy profiles (values in kcal/mol) for dissociation of H2 on singlet Al6(1A1g) calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ and G4 levels. The ΔH and ΔG (T = 298 K) values shown are relative to the global minimum reactant asymptote Al6(1A1g) + H2

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Fig. 2
figure 2

B3LYP/aug-cc-pVTZ and G4 optimized geometries (distances in Å) of the transition state TS(1) (with the imaginary frequency) for dissociation of the hydrogen molecule on the singlet octahedral-like Al6 cluster to form doubly H-bridged Al6H2(1) cluster, along with the other di-bridged Al6H2 isomers (2–4) and transition states for their interconversion (TS1–2, TS1–3, with the imaginary frequencies) along with the prismatic-like isomer Al6H2(1′); the G4 parameters are given within the square brackets. The B3LYP/aug-cc-pVTZ results are from [13]

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At the geometry optimization B3LYP level, there is a tiny energy barrier to H2 dissociation on singlet Al6 with respect to the Al6(\(^{3} {\text{A}}_{1}^{\prime }\)) + H2(\(^{1} \Upsigma_{g}^{ + }\)) system of 1.7 kcal/mol [14] and 0.3 kcal/mol using the 6–311 + G * and aug-cc-pVTZ basis sets, respectively. At the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level [13], the TS(1) energy drops below the correct Al6(1A1g) + H2(\(^{1} \Upsigma_{g}^{ + }\)) asymptote, and therefore, no enthalpy barrier is found for H2 dissociation (Fig. 1). This suggests that TS(1) may not be a true transition state on the PES at the ab initio correlated level. The free energy barrier of 5.3 kcal/mol (Fig. 1) is due to the entropic contribution.

Figure 1 also shows that 1 can easily rearrange to the lower energy Al6H2 isomers 2 and 3 via transition states TS1–2 and TS1–3, respectively, whose B3LYP optimized structures are summarized in Fig. 2 along with those of the singlet Al6H2 isomers 4 and 1′ (the triplet Al6H2 clusters are significantly higher in energy [13, 14]). We note that the low-barrier isomerizations 1 → 2 and 1 → 3 involve the H shift from one bridging site to the other. Both the coupled cluster and G4 calculations predict the Al6H2 isomer 3 with the two hydrogens capping the Al–Al–Al faces which share the Al–Al edge to be of lowest energy. Because with the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ energetics TS1–3 goes below 1, the latter may not be a true minimum at the ab initio correlated level and the H2 dissociation along this Cs path would result directly in 3. As can be further inferred from Fig. 1, the four di-bridged octahedral-like Al6H2 isomers 1–4 lie within an energy range of 3.7 [3.4]/3.1 [3.2] kcal/mol in terms of enthalpy/free energy at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ [G4] levels. In summary, based on the exhaustive search of the Al6H2 PES, we are confident that all the low-lying Al6H2 isomers were established, including the global minimum.

3.2 k = 2

For the Al6H2 + H2 → Al6H4 reaction, we have identified two low-barrier paths involving octahedral-like clusters and another two involving trigonal prism-like species. With path(2)1 (Fig. 3a), the H2 dissociation occurs via transition state TS(2)1 (Fig. 4) which connects to the Al6H2(1) + H2 reactants and Al6H4(S1) product (Fig. 4). In view of the discussion in the previous section, the actual Al6H2 reactant of path(2)1 may be the Al6H2(3) isomer. The second H2 dissociation results in forming of the new terminal and new bridging Al–H bonds in Al6H4(S1) and is accompanied by the H shift from the bridged to the terminal site. Path(2)2 (Fig. 3b) is similar to path(2)1 because it starts with the same reactants, the hydrogen dissociation occurs on the octahedral-like metal core (via TS(2)2) and leads to the Al6H4 product with two terminal and two (differently) edge-bridged hydrogens, S2 (Fig. 4).

Fig. 3
figure 3

Schematic enthalpy/free energy profiles (values in kcal/mol) for dissociation of H2 on Al6H2 calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level for the a path(2)1, b path(2)2, c path(2)3 and d path(2)4. The ΔH and ΔG (T = 298 K) values shown are relative to the global minimum reactant asymptote Al6H2(3) + H2

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Fig. 4
figure 4

Optimized geometries (B3LYP/aug-cc-pVTZ, distances in Å) of the octahedral-TS(2)1, TS(2)2 and TS(2)3 and prismatic-like TS(2)4 pr transition states (with the imaginary frequencies) for dissociation of H2 on Al6H2 to yield Al6H4 clusters S1, S2, S3 and S4, respectively

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The transition state TS(2)3, being part of path(2)3 (Figs. 3c, 4), exhibits a heavily distorted Al6 core with two broken Al–Al edges (r(Al–Al) > 3.5 Å). The associated IRC indicates that this TS links to the higher energy Al6H2(1′) cluster comprising deformed prismatic Al6 (cf. Fig. 2) plus H2. This H2 dissociation path ends with the face- and edge-bridged S3 Al6H4 cluster with the open Al–Al edge (Fig. 4). Finally, in the path(2)4 (Fig. 3d), the dissociative H2 addition, Al6H2(1′) + H2 → TS(2)4 pr  → Al6H4(S4) occurs on the prism edge and requires the prior Al6H2(3) → Al6H2(1′) rearrangement (not examined).

Judging both the energy barriers and exothermicity of the various second H2 dissociation modes in Fig. 3a–d, the path(2)1 and path(2)2 are most favoured, with the very similar energy barriers of 15.0 (22.7) and 12.2 (20.4) kcal/mol in ΔH (ΔG) relative to Al6H2(3) + H2 (for consistency with the k = 1 H2 addition, the energetics quoted for the k = 2–4 reactions has been calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level).

Because of the numerous minima which can exist on the Al6H4 PES, the kinetically most preferred modes of the second H2 dissociation indicated above were not generally expected to provide the thermodynamically most stable Al6H4 product. So, the extensive parallel exploration of this cluster’s PES was performed at B3LYP/aug-cc-pVTZ. We have studied the Al6H4 structures derived from the octahedral, trigonal prismatic and capped tetragonal pyramid Al6 cores. The total 18 low-lying Al6H4 (distinct) isomers found S1–S18 (being within 10 kcal/mol of the global minimum) are gathered in Figure S1 of Supplementary Information. Of these, the three octahedral-based Al6H4 clusters S5–S7 relevant to the k = 3 H2 addition step (see below), including the global minimum S5 are shown in Fig. 5. It is seen that in the latter Al6H4 cluster both bridging hydrogens occupy the neighbouring threefold sites as in Al6H2(3).

Fig. 5
figure 5

Optimized geometries (B3LYP/aug-cc-pVTZ, distances in Å) of the low-energy Al6H4 isomers S5–S7, including the global minimum Al6H4 structure (S5)

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Although we have not studied the rearrangement of our most exothermic Al6H4 products S1 (path(2)1) and S2 (path(2)2) to any of the low-energy S5-S7 clusters, we first note the five species lie within a narrow range of 5.1 (4.4) kcal/mol in ΔH (ΔG) (see Fig. 3a, b for their CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ relative energies). Second, the isomerizations of this type are mostly related to the change of the H-bridging positions which are suggested to be low-barrier rearrangements, judging from those calculated for k = 1.

3.3 k = 3

We have predicted three low-lying paths for this case. The actual Al6H4 reactant of path(3)1 (Fig. 6a) and path(3)2 (Fig. 6b) is the isomer S7, lying 3 kcal/mol above the Al6H4 global minimum S5. The H2 dissociation along path(3)1 proceeds via TS(3)1 (Fig. 7) with the energy barrier of 14.2 (22.2) kcal/mol in ΔH (ΔG) relative to the Al6H4(S5) + H2. On the product side, TS(3)1 connects to the Al6H6 cluster T1 with the threefold-bridged hydrogens separated (Fig. 7). Path(3)2 involves the transition state TS(3)2 which rearranges to the Al6H6 isomer T2 with the different H-bridging pattern than T1. This mode of H2 dissociation requires, however, a higher energy barrier of 18.7 (26.1) kcal/mol and is less exothermic compared to path(3)1.

Fig. 6
figure 6

Schematic enthalpy/free energy profiles (values in kcal/mol) for dissociation of H2 on Al6H4 calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level for the a path(3)1, b path(3)2 and c path(3)3. The ΔH and ΔG (T = 298 K) values shown are relative to the global minimum reactant asymptote Al6H4(S5) + H2

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Fig. 7
figure 7

Optimized geometries (B3LYP/aug-cc-pVTZ, distances in Å) of the octahedral-TS(3)1 and TS(3)2 and prismatic-like TS(3)3 pr transition states (with the imaginary frequencies) for dissociation of H2 on Al6H4 to yield Al6H6 clusters T1, T2 and T3, respectively

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The prismatic-like Al6H4 cluster S4, being 6 kcal/mol less stable than S5, and the transition state TS(3)3 pr (Fig. 7) are engaged in path(3)3 leading to the structurally related Al6H6 cluster T3 (Figs. 6c, 7). As can be inferred from Fig. 6b–c, the path(3)2 and path(3)3 exhibit very similar energy barriers, but the latter requires additionally the Al6H4(S5) → Al6H4(S4) rearrangement (not studied) and results in the higher energy Al6H6 product. Among the three dissociation modes examined, the path(3)1 affording T1 is thus most favoured.

Because of the numerous local minima that can appear on the Al6H6 PES, we anticipated that the latter path might not lead to the thermodynamically most stable Al6H6 product. Therefore, the extensive probe of this cluster’s PES was simultaneously carried out at B3LYP/aug-cc-pVTZ. As for Al6H4, we systematically investigated the Al6H6 structures with different Al6 cores. The outcome of this search is the total 15 distinct Al6H6 isomers T1–T15 (with the 12 structures being within 10 kcal/mol of the global minimum), collected in Figure S2. Of these, the five octahedral-based Al6H6 isomers T4–T7, including the global minimum T4 are shown in Fig. 8, with their CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ energies compared to T1 in Fig. 6a. In the most stable Al6H6(T4) structure, the two bridging hydrogens are positioned in the neighbouring threefold sites as was seen here in the lowest energy isomers of Al6H2 and Al6H4. Also, the structure of Al6H6(T4) is consistent with the Al6H6 global minimum found recently by the global-search-algorithm-for-minima approach [32].

Fig. 8
figure 8

Optimized geometries (B3LYP/aug-cc-pVTZ, distances in Å) of the Al6H6 isomers T4–T7, including the global minimum Al6H6 structure (T4)

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Our energetically most favoured Al6H6 product T1 obtained via path(3)1 is higher in energy than T4 by 5.4 (5.3) kcal/mol in ΔH (ΔG) (Fig. 6a). We have not studied the isomerization of T1 to T4 or to the other low-energy Al6H6 isomers (Fig. 6a), some of which are relevant to the k = 4 H2 addition step (see below). As before, we expect, however, that most of these rearrangements involving the changes of the H-bridging positions should occur easily.

3.4 k = 4

The calculated routes for the fourth H2 dissociation are depicted in Fig. 9a–c. Path(4)1 involves the Al6H6 isomer T7 which is 7 kcal/mol less stable than the Al6H6 global minimum T4 (Fig. 9a). We have identified this path as kinetically most favoured with the relevant transition state TS(4)1 lying 20.1 (28.1) kcal/mol in ΔH (ΔG) above the Al6H6(T4) + H2 reference. Here, H2 is cleaved on one of the ‘naked’ Al vertices of the octahedral-like metal core to yield the Al6H8 product F1. As seen in Fig. 10, the cluster F1 has three bridging hydrogens, and therefore is not the ground state Al n H n+2 alane (n = 6) according to the Wade’s (n + 1) rule [19, 33, 34].

Fig. 9
figure 9

Schematic enthalpy and free energy profiles (values in kcal/mol) for dissociation of H2 on Al6H6 calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level for the a path(4)1, b path(4)2 and c path(4)3. The ΔH and ΔG (T = 298 K) values shown are relative to the global minimum reactant asymptote Al6H6(T4) + H2

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Fig. 10
figure 10

Optimized geometries (B3LYP/aug-cc-pVTZ, distances in Å) of the octahedral—TS(4)1 and TS(4)2 and prismatic-like TS(4)3 pr transition states (with the imaginary frequencies) for dissociation of H2 on Al6H6 to yield the Al6H8 clusters F1, F2 and F3, respectively. The other Al6H8 isomers F4 and F5 with two hydrogens capping the triangular faces are also shown; F2 is the global minimum Al6H8 structure

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Path(4)2 (Fig. 9b) via TS(4)2 is unique because it leads directly to the most stable Al6H8 product F2. This H2 dissociation involves, however, the deformed Al6H6 isomer T6 (being 11 kcal/mol higher in energy than T4) and significantly larger H2 dissociation barrier of 31.7 (39.3) kcal/mol with respect to Al6H6(T4) + H2. This ‘on the Al–Al edge’ dissociation results in two new terminal Al–H bonds in F2 cluster (Fig. 10), instead of ‘the usual’ terminal plus bridged bond pair. The F1 → F2 isomerization is suggested a more viable way of obtaining the latter Al6H8 cluster when starting with the former (Fig. 9a).

The different active site is seen in the transition state TS(4)3 pr participating in the path(4)3 (Fig. 9c), where H2 is added to the prismatic T3 isomer of Al6H6 to form the structurally related Al6H8 cluster F3 (Fig. 10). As can be inferred from Fig. 9a–c, the path ‘3’ is clearly more energy demanding compared to ‘1’ and ‘2’.

We have identified three Al6H8 isomers F2(C2v), F4(C2v) and F5(D3d) (Fig. 10) which could be the ground state alane Al n H n+2 (n = 6) according to Wade’s rules [19, 33, 34]. The three clusters, being within 6.6 (6.2) kcal/mol in ΔH(ΔG) (their CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ energies are compared to F1 in Fig. 9a), adopt n-vertex polyhedral closo-structures with two threefold-bridged hydrogens and have n + 1 = 7 skeletal bonding electron pairs. Clearly, in such cases, these rules are not sufficient to indicate the ground state isomer. The most stable Al6H8 isomer F2 is in agreement with the previous studies [21, 32] including the global-search-algorithm-for-minima approach [32]. Furthermore, consistent with the Al6H2k (k = 1–3) global minima structures identified above, the Al6H8(F2) cluster exhibits the same ‘H-bridging motif’.

3.5 The trends in H2 activation barriers and reaction energies versus k

Plots in Fig. 11a, b illustrate, respectively, the barriers and energies of the reactions Al6H2k−2 + H2 → Al6H2k (k = 1–4) versus k in terms of ΔH and ΔG. These profiles correspond to the lowest H2 dissociation TSs and thermodynamically most stable Al6H2k−2 and Al6H2k clusters reviewed above. Figure 11a shows that the dissociation barrier increases from k = 1 to k = 2–4 by about 15–23 kcal/mol and that the entropy contribution (−TΔS) to the free energy barrier is about 8 kcal/mol per H2. The barrier changes are parallelled sensibly by those of the HOMO–LUMO (H–L) gap of the Al6H2k−2 reactants (in Fig. 12a).

Fig. 11
figure 11

Plots of the a enthalpy and free energy barriers and b enthalpies and free energies of the reactions Al6H2k−2 + H2 → Al6H2k (k = 1–4) versus k

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Fig. 12
figure 12

A plot of the HOMO–LUMO energy gap of the most stable a Al6H2k−2 and b Al6H2k clusters (k = 1–4) versus k from the B3LYP/aug-cc-pVTZ calculations

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The larger exothermic effect of formation of Al6H2 (k = 1, Fig. 11b) compared to those associated with forming Al6H4 (k = 2), Al6H6 (k = 3) and Al6H8 (k = 4) can be related to the ‘magic’ 20 valence electron count of the first cluster [35]. Among the four product clusters, Al6H8 is predicted to be most stable (least reactive) as supported by its significantly larger H–L gap (in Fig. 12b) in accordance with the earlier reports [19, 20].

The ‘global’ free energy profile for the reaction of Al6(1A1g) with multiple H2 to yield the ‘target’ Al6H8 alane is given in Fig. 13. This profile which uses the lowest H2 dissociation TSs and thermodynamically most stable clusters Al6H2k−2 and Al6H2k first reveals the ΔG of the overall reaction Al6 + 4H2 → Al6H8(F2) is −58.6 kcal/mol. Second, it shows a small free energy dissociation barrier (of 1.1–5.3 kcal/mol) for k = 1, 2, with no barrier for the addition of the third and fourth H2 due to the strongly increasing exothermicity of the total Al6 hydrogenation reaction.

Fig. 13
figure 13

Schematic free energy profile for the reaction of Al6(1A1g) with multiple H2 to give the ‘target’ Al6H8 alane including the lowest energy TSs for H2 dissociation on the Al6H2k−2 clusters and thermodynamically most stable Al6H2k clusters calculated at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level. Values shown are relative free energies, with enthalpies given within square brackets (all in kcal/mol)

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3.6 The effect of charge on the H2 dissociation

As mentioned above, novel Al n H − m cluster anions (4 ≤ n ≤ 8, 0 ≤ m ≤ 10) were recently generated in the gas phase [18, 19]. Here, we have studied the effect of charge on H2 dissociation on the alanes by investigating the Al6H6 − + H2 → Al6H8 − reaction. The geometries of the two open-shell anions, not reported so far, were calculated by adding charge to the respective neutral clusters, followed by relaxation. The (U)B3LYP/aug-cc-pVTZ calculated structures of Al6H6 − (R1–R15) and Al6H8 − (AN1–AN8) (all verified as minima) are summarized in Figures S3 and S4. The results show that the lowest energy Al6H6 − anion is octahedral-based R4(2B3g) with six terminal Hs, and the most stable Al6H8 − is prism-like AN4(2A) with two bridging Hs on the opposite edges, thus differing from the most stable neutrals (see the bottom of Fig. 15).

The energy profile of the kinetically most preferred route identified for the Al6H6 − + H2 → Al6H8 − reaction is depicted in Fig. 14, with the energetics calculated at the (U)B3LYP/aug-cc-pVTZ level. Here, the IRC-confirmed Al6H6 − reactant is di-bridged R1(2A). Note that the required R4 → R1 isomerization (not studied) moves 2Hs from the terminal to bridge sites, with the higher energy Al6H6 − isomer having two ‘naked’ Al centres, thus being more reactive towards hydrogenation. The H2 dissociation transition state TS(4)1AN( 2A) (Fig. 15) can be viewed the charged analogue of the neutral TS(4)1 (Fig. 10) with the more stretched H–H bond (by 0.12 Å). Figure 14 shows that relative to the Al6H6 −(R4) + H2 reference, the H2 dissociation barrier of 25.7 (34.5) kcal/mol in ΔH (ΔG) is about 10 kcal/mol higher than that involved in the corresponding neutral path(4)1 (note that the B3LYP barriers are compared). This can be linked to the significantly higher H–L gap of the Al6H6 − anion (3.5 eV) compared to the Al6H6 neutral (2.4 eV). The transition state TS(4)1AN( 2A) rearranges to the Al6H8 − cluster anion AN1(2A), which lies about 11 kcal/mol above the Al6H8 − lowest energy isomer AN4(2A) (Fig. 14). The two kinetically less favoured routes for H2 dissociation on Al6H6 −, not discussed in detail, are included in Figures S5 and S6. They can be regarded as the anion counterparts of path(4)2 and path(4)3, respectively, with the relevant anion structures displayed in Fig. 15.

Fig. 14
figure 14

Schematic enthalpy/free energy profiles (values in kcal/mol) for dissociation of H2 on the Al6H6 − cluster anion calculated at the (U)B3LYP/aug-cc-pVTZ//(U)B3LYP/aug-cc-pVTZ level for the kinetically most favoured path. The ΔH and ΔG (T = 298 K) values shown are relative to the global minimum reactant asymptote Al6H6 −(R4) + H2. The B3LYP/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ values within square brackets refer to the neutral counterpart path(4)1

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Fig. 15
figure 15

Optimized geometries ((U)B3LYP/aug-cc-pVTZ, distances in Å) of the deformed octahedral-TS(4)1AN and TS(4)2AN and prismatic-like TS(4)3 pr AN transition states (with the imaginary frequencies) for dissociation of H2 on Al6H6 − to yield the Al6H8 − cluster anions AN1, AN2 and AN3, respectively. The most stable Al6H6 − (R4) and Al6H8 − (AN4) cluster anions are also shown

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A possible way of obtaining Al6H8 − anion is by electron attachment to neutral Al6H8. In the previous section, five Al6H8 isomers were considered. Table S1 of Supplementary Information shows that an ‘instantaneous’ electron attachment (at the neutral’s geometry) occurs easier to the prism-like form (F3) of the Al6H8 neutral than to its octahedral-type structures (e.g. F2) as suggested by the smaller H–L gaps and larger vertical electron affinity of 1.50 eV in the former case (the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ value).

4 Conclusions

In this theoretical investigation at the B3LYP/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ levels, we have considered the viability of multiple H2 dissociation on the 3D main group 13 metal cluster Al6 to form Al6H8, the novel alane proposed experimentally [19]. To this end, the kinetic and thermodynamic aspects of the sequential hydrogenation of Al6 via Al6H2k−2 + H2 → Al6H2k (k = 1–4) have been studied. The minimum energy paths were generated from the located H2 dissociation transition states. Our main conclusions are as follows:

  1. 1.

    The H2 additions to the Al6H2k−2 clusters to give the Al6H2k clusters (k = 1–4) are exothermic, with the enthalpy [free energy] of the overall reaction Al6 + 4H2 → Al6H8 predicted to be −93.2 [−58.6] kcal/mol. The Al6H2k cluster global minima structures exhibit the same ‘H-bridging motif’ with two hydrogens sitting on the neighbouring threefold-bridged sites.

  2. 2.

    Of various H2 addition modes probed including octahedral- and trigonal prism-like clusters, those involving H2 dissociation transition states with the octahedral-like Al6 cores are found kinetically most favoured. A correlation was identified between the dissociation barriers and HOMO–LUMO gaps of the Al6H2k−2 clusters versus k.

  3. 3.

    For k = 1, the H2 dissociation is predicted to have no enthalpy barrier at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level. A good agreement is found between the coupled cluster and G4-calculated energetics. For k = 2, 3 and 4, the lowest enthalpic hydrogen dissociation barriers are determined to be 12, 14 and 20 kcal/mol, respectively, as measured relative to the Al6H2k−2 cluster global minimum isomer plus H2 reactants. According to our calculations, the entropy contribution (−TS) to the free energy dissociation barrier is 8 kcal/mol per H2. Upon adding H2 to the Al6H2k−2 cluster, the relevant van der Waals complex Al6H2k−2 … H2 is first formed (at large intermolecular distances) as noticed earlier for k = 1 [13, 14]. These very weakly bound species were not included in the H2 dissociation reaction profiles because the focus of our study was to calculate the H2 activation barriers.