How Fast Do Microhydrated Al Clusters React: A ... - ACS Publications

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How Fast Do Microhydrated Al Clusters React: A Theoretical Study
lvarez-Barcia and Jes
us R. Flores* Sonia A Departamento de Química Física, Facultad de Química, Universidade de Vigo, E-36310-Vigo Pontevedra, Spain

bS Supporting Information ABSTRACT: The dynamics of the first step of the reaction of small Alm clusters m = {3,13} with up to four water molecules has been studied. The first stage in the reaction, which may ultimately result in the production of H2, is the generation of a HAlmOH 3 (H2O)n
1 species, which can take place through transition states of the relay type, in which the water molecules may play different catalytic roles; namely, they can be involved directly in a Grotthuss-like mechanism by forming a relay bridge, or they may lower the saddle point energy by interacting with the molecules of the relay bridge. Rate coefficients have been computed with the inclusion of tunneling effects. The results indicate that the optimal configuration (the one giving the highest values of the rate coefficient for 50 K < T < 500 K) in the case of the Al3 3 (H2O)n system involves three water molecules in the relay bridge. In the case of the Al13 cluster, the two-water system is the most efficient. It is remarkable that Al3 delivers much higher rates than Al13 or a single Al atom. It is argued that Al13 and Al have, somehow, a similar behavior from the point of view of the rates, the Gibbs activation energies, and the tunneling transmission coefficients, which gives some dynamically based support to viewing the Al13 cluster as a kind of “superatom”.

1. INTRODUCTION The reaction of Al atoms, Al clusters, and Al metal with water is the subject of intense research. Apart from the general chemical interest, the production of H2 from Al materials is of technological relevance. For instance, several techniques have been developed to overcome the difficulty of the appearance of the oxide layer in solid Al exposed to water.1
5 Mechanically formed Al composites also offer a way to relatively fast hydrogen production.6 Al powder and individual atoms have been found to react with water molecules in the gas phase, producing a chemiluminiscent glow.7
10 Such emission was attributed by Oblath and Gole to a HAlOH species.8 The reaction of Al powder with water is also important in areas like rocket propulsion or explosives,11
13 where the behavior of Al particles is different from bulk Al metal. There are a number of condensation and matrix isolation experiments in which the species resulting from the interaction of Al atoms and water molecules are trapped in an inert gas matrix and subjected to spectroscopic studies; those studies suggest the formation of HAlOH.14
16 The gas-phase Al + H2O reaction has been the subject of a LIF (laser-induced fluorescence)10 and a theoretical study,17 which are quite coincident in their results for the rate coefficients. The theoretical study indicates that tunneling plays a crucial role in the reaction and that the major product is AlOH + H, which results mostly from the fragmentation of HAlOH. Basically, there are two molecular mechanisms Al þ H2 O f Al 3 ðH2 OÞ
½TS12 f HAlOH f AlOH þ H

ðaÞ Al þ H2 O f Al 3 ðH2 OÞ
½TS1H f AlOH þ H r 2011 American Chemical Society

ðbÞ

Al 3 (H2O) represents a weakly bonded Al
OH2 complex;18,19 TS1H is the saddle point for H-atom elimination; and TS12 corresponds to the H migration process. The first mechanism turns out to be dominant. It must be noted that the AlOH molecule has been detected in the space.20 In our studies of the interaction of an Al atom with one and more water molecules, we have found that the presence of some additional waters enables relay (or Grotthuss-like) molecular mechanisms, which may have a catalytic effect.21,22 The situation is, however, complex; in a recent dynamical study of the Al 3 (H2O)n
[TS12 3 (n
1)H2O] f HAlOH 3 (n
1)H2O process (n = {1
8}),23 where the Al 3 (H2O)n systems are intended to be models of more hydrated systems, we have concluded that catalysis by water may only be effective for some temperature ranges, the reason being that the relay mechanisms tend to present lower tunneling transmission factors than the simple one, which involves one water molecule. It must be noted that the HAlOH 3 (n
1)H2O and AlOH 3 (n
1)H2O systems (n = 1
4) may evolve to higher hydroxides, with H2 elimination, by mechanisms involving neutral intermediates, and without an energy barrier relative to Al + nH2O.21 It must be noted that the role of water molecules as a catalyst is very important in several contexts.24 The importance of Al nanoparticles has long been recognized (see, for instance, ref 25). Shape control of Al clusters, through metalloid clusters using different ligands, has been proposed.26 There are a number of studies of the interaction of Al clusters with several molecules, dating back to the late eighties. Among the Received: August 26, 2011 Revised: September 30, 2011 Published: October 31, 2011 24849

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The Journal of Physical Chemistry C first works are those of Leuchtner et al., who have studied the interaction of negative27 and positive28 Al clusters with oxygen.29 Ruatta and Anderson have determined cross sections and branching ratios for the reaction of Aln+ (n = 1
9) with O2 and N2O.30 Cox et al. have established an affinity scale of small Al clusters (up to n = 30) toward simple molecules.31 Fukue et al. have also conducted similar studies.32 Jarrold and Bower have studied the reactivity of positively charged Al clusters with molecular oxygen and deuterium.33
35 Hettich has studied charge-exchange, collisional dissociation, and oxidation of negative Al clusters,36 and Cooper et al. have studied their oxidation and photochemical behavior.37 Some aspects of reaction of Al13
with some simple molecules in the gas phase have been reviewed by Burgert and Schn€ockel,38 and the effect of spin conservation in the reaction of that cluster and similar Al clusters with molecular oxygen has been treated in detail by Burgert et al.39 Those experimental studies do not give enough information about the processes that the adsorbed molecules undergo. Microhydrated clusters can be used as models for the interaction of water with Al nano- or microparticles or even with Al surfaces; a dynamical study which considers the different relay mechanisms could add many insights into the present understanding of Al
water interactions. There are a number of other theoretical studies of the AlOH2 system or more hydrated systems (see for instance refs 40
45). The interaction of negatively charged Al clusters with water has been studied more recently by means of a flow method and also theoretically by Reber et al.46 and Roach et al.47 Very recently, the reactivity of Al atoms with O2 and H2O in He droplets has been studied by Krasnokutski and Huisken;48 greater reactivity toward water clusters than to a single molecule has been encountered. Shimojo et al.49,50 have performed Molecular Dynamics (MD) simulations of two Alm clusters (m = {12,17}) and a number of water molecules. They have found that, at 300 K, only six water molecules may bond to the cluster. Their results for the reaction dynamics (1000 K) show the importance of the relay mechanisms and that H2 production, at least that of the first molecule, is fast whenever one has a hydrogen atom bonded to the cluster (i.e., a HAlmOH 3 (H2O)n
1 species). Russo et al.51 have also performed simulations of an Al100 cluster interacting with water molecules using a reactive force field method; their results also suggest that water may act as a catalyst. None of those simulations though takes into account tunneling. As we have mentioned, tunneling plays an important role in the dynamics of hydrated Al atoms (Al 3 (H2O)n systems).23 The purpose of the present work is to gain insight into the dynamical aspects of the interaction of Al clusters with water. We have performed a detailed study of the potential energy surface (PES) of several model systems Alm 3 (H2O)n (m = {3,13}, n = {1
4}) and computed the rate coefficients of the critical reaction step (i.e., production of HAlmOH 3 (H2O)n
1), through transition state theory. Hydrated Al trimers are small enough for benchmarking purposes. Al3 has been the subject of intense experimental and theoretical work.52
57 Al13 is a very stable cluster with nearly icosahedral symmetry,54,58
72 perhaps the first representative of larger systems or Al crystals.

2. THEORETICAL APPROACH We have taken the Al3 3 (H2O)2 system as a prototype and compared, for some significant structures, the relative energies produced by a number of Density Functional Theory (DFT)

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methods with those obtained by relatively high-level ab initio computations (ROCBS-QB373 and ROCCSD(T)74 with several basis sets). We have tried the BHandHLYP density functional (BHHLYP) as defined in the G0375 and G0976 program packages; also B3LYP,77 PBE0,78 BMK,79 M052X,80 M06,81 and M06-L82 in combination with the (effective potential) CEP-31G*,83 6-311++G**,84,85 and aug-cc-pVTZ86,87 basis sets. We will show in the following section that the BHHLYP/6-311 ++G**//BHHLYP/CEP-31G*+ZPE level (where we use the CEP-31G* for optimization and zero-point energies (ZPE) and the 6-311++G** basis set for the single-point computations) is a reasonably good option. The ZPE values have been scaled by a factor of 0.93. Intrinsic reaction coordinates (IRC) have been obtained by the method of Hratchian and Schlegel.88 We have applied transition state theory (TST). The TST rate can be expressed in thermodynamic language as kðTÞ ¼ kðTÞ

kB T
ΔG°, q =RT e h

ð1Þ

The tunneling transmission coefficient k(T) has been obtained as k(T) = k(T)/k(T)nt by using an asymmetrical Eckart barrier89,90 (k(T)nt is the rate coefficient without tunneling). The Gibbs activation energy ΔG°,q(T) includes all contributions except that of rotations. Statistical factors are set to unity. We have employed the Multiwell software.89 For the electronic structure computations, we have employed the G0375 and G0976 programs.

3. RESULTS AND DISCUSSION 3.1. Al3 3 (H2O)2 System: Testing the Electronic Structure Methods. We have three types of structures relevant to the first

reaction step, namely, an Al cluster
water complex (Al3 3 (H2O)n which we will note in general as M1_wk), a HAl3OH 3 (n
1)H2O complex (M2_wk), and the saddle point connecting them (TS_wk, where k = n
1). The most relevant structures of the Al3 3 (H2O)2 system are displayed schematically in Figure SM_F1 of the Supporting Information. Table SM_T1 of the Supporting Information presents the energies of some of those structures relative to Al3 + 2H2O, computed at many DFT and some ab initio levels, as described in Section 2. The critical aspect of that table is the TS_w1/M1_w1 energy difference. It is readily seen that the BHHLYP/6-311++G** and even the BHHLYP/CEP-31G* method are about as accurate (sometimes better) as the other density functionals. The BHHLYP functional, unlike most of the others, also appears to give upper bounds to the TS_w1/M1_w1 energy difference. Moreover, the BHHLYP/6-311++G**//BHHLYP/ CEP-31G*+ZPE level is a good (and much less expensive) “substitute” of BHHLYP/6-311++G** (it gives similar results). Note, also on that table, that the use of the larger aug-cc-pVTZ basis set91 does not improve much the results. For those reasons, and also for consistency with our previous work on microhydrated Al atoms,23 we have chosen the BHHLYP/ 6-311++G**//BHHLYP/CEP-31G*+ZPE approach for all the computations. 3.2. Al3 3 (H2O)n Systems: Reaction Paths. Simplified reaction mechanisms of the first step in the oxidation of Al3 3 (H2O)n systems (n = {1
4}) are displayed schematically in Figures 1
3; they have all been verified by IRC computations. With three and four water molecules, we have two options, namely, a mechanism in which all waters form the relay bridge, noted as (3) and (4), and a mechanism in which the last water acts as a “spectator”, (2 + 1) and (3 + 1), respectively, where its role is stabilizing the rest of 24850

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Figure 1. Reaction mechanisms for the initial step of the reaction of the Al3 cluster with 1 (noted as (1a) and (1b)) and 2 water molecules (noted as (2)). Activation and reaction energy differences are computed with respect to the minimum on the left, at the BHHLYP/6-311++G**// BHHLYP/CEP-31G*+ZPE level.

Figure 2. Reaction mechanisms (3) (relay) and (2 + 1) (assisted relay) for the initial step of the reaction of the Al3 cluster with 3 water molecules. Activation and reaction energy differences are computed with respect to the minimum on the left at the BHHLYP/6-311++G**// BHHLYP/CEP-31G*+ZPE level.

the system. For instance, in the (2 + 1) mechanism, it is the second water which cedes one hydrogen atom to the Al3 frame; it is also characterized by a more extreme charge distribution, where the terminal water stabilizes a partial positive charge of the rest of the waters. For n = 1, we have two transition states which connect to two different M2_w0 isomers as shown by IRC computations; note that in one of them a hydrogen atom is bonded “nonclassically” to the whole Al3 ring, and in the second, there is an oxygen bridge between two Al atoms. For n = 4, the (3 + 1) mechanism includes a relatively highlying form of M1_w3 (M1_w3_b); we are assuming that all forms of M1_wk can easily interconvert because they differ mostly in a few details of the arrangement of the water molecules and that their relative proportions obey equilibrium constants. It must also be noted that for the (2 + 1), (4), and (3 + 1) mechanisms the reaction paths (computed at the BHHLYP/ CEP-31G* level) are a little more complicated because they include a very shallow secondary minimum (see Figure SM_F2 and table SM_T2 of the Supporting Information). However, the BHHLYP/6-311++G**//BHHLYP/CEP-31G*+ZPE energies indicate that those secondary minima either do not exist on

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Figure 3. Reaction mechanisms (4) (relay) and (3 + 1) (assisted relay) for the initial step of the reaction of the Al3 cluster with 4 water molecules. Activation and reaction energy differences are computed with respect to the minimum on the left at the BHHLYP/6-311++G**// BHHLYP/CEP-31G*+ZPE level.

the exact PES or are just very shallow kinks, which do not have a significant effect on the dynamical behavior, so they have not been taken into account in our rate computations. 3.3. Al3 3 (H2O)n Systems: Rate Computations. Figure 4 represents k(T) (s
1) in the interval T = 50
500 K as well as the 1/k(T) values and the ΔG°,q(T) values (in kcal/mol). In the case of mechanism (3 + 1) of Figure 3, we assume, as said, that the two M1_w3 forms involved are in equilibrium proportions, so k(T) includes the corresponding equilibrium constant. It is readily seen that mechanism (3) of Figure 2 has the largest rate coefficient for all temperatures; the (3 + 1) and (4) processes (Figure 3) are next; and all others are much behind. It is readily seen that these three mechanisms have the lowest ΔG°,q(T) values. The fact that the mechanisms involving one water molecule, (1b) and (1a), present the most efficient tunneling does not make them competitive with those involving three and four waters. However, (3) has a more efficient tunneling at low temperatures than (4) and (3 + 1), which helps it to be dominant also at low T’s. The maximum rate coefficient at T = 300 K is 3.1  109 s
1, which points to a lifetime of about 300 ps for the Al3 3 (H2O)3 complex. Comparing with the study of microhydrated (individual) Al atoms,23 the present results are similar in the sense that (3) is normally the dominant mechanism in both cases. However, in the case of the microhydrated atoms, mechanism (1) is quite competitive, and it could be even faster at low T’s because of its good tunneling efficiency. Here it only comes close to be competitive at T = 50 K. Although the Al3 3 (H2O)n systems studied here can be considered models for more hydrated systems, it is interesting to take into account the competition of water elimination in the gas phase, in other words, the reactions Al3 3 (H2O)n h Al3 3 (H2O)n
1 + H2O. The results, together with those of the Al13 systems, are displayed in table SM_T3 of the Supporting Information. It is quite clear that, even at relatively high temperatures, the water partial pressures required to have a unit Al3 3 (H2O)n
1/Al3 3 (H2O)n ratio are very low; for instance, for 24851

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Figure 5. Reaction mechanisms for the initial step of the reaction of the Al13 cluster with 1 (noted as (1)) and 2 water molecules, noted as (2). Activation and reaction energy differences are computed with respect to the minimum on the left at the BHHLYP/6-311++G**//BHHLYP/ CEP-31G*+ZPE level.

Figure 6. Reaction mechanisms (relay and assisted relay) for the initial step of the reaction of the Al13 cluster with 3 water molecules (noted as (3) and (2 + 1), respectively). Activation and reaction energy differences are computed with respect to the minimum on the left at the BHHLYP/ 6-311++G**//BHHLYP/CEP-31G*+ZPE level.

Figure 4. (a) Representations of k(T) (s
1) in the interval T = 50
500 K for the Al3 3 (H2O)n system, with n = {1
4}. (b) Same for ln(k(T)). (c) 1/k(T) values. (d) ΔG°,q(T) values (kcal/mol).

n = 3, p(H2O) = 0.03 Torr (T = 300 K) or p(H2O) = 3  10
21 Torr (T = 100 K). Al3 fragmentation (prior to the reaction with water) cannot be an important process at the temperatures considered. According to the results of Li and Truhlar,92 the rate coefficient for the Al3 h Al2 + Al process is about 2  109 s
1 at T = 2000 K but

decreases rapidly with decreasing temperature (being approximately 1  10
4 s
1 at 500 K). 3.4. Al13 3 (H2O)n System: Reaction Paths. Figures 5
7 display the most relevant structures for the Al13 3 (H2O)n system (n = {1
4}). Of course, there could be many M2_wk structures according to the positions of the
OH and
H groups attached to the Al13 cluster, but we present only those structures in which those groups are bonded to neighboring Al atoms because they are the ones that could be connected to the saddle points. Figures SM_F3 and SM_F4 give complementary information, including a comparison between BHHLYP and PBE0 geometries. The later density functional is considered adequate to describe the structures of Al clusters,68,93 but it does not 24852

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Figure 7. Reaction mechanisms (relay and assisted relay) for the initial step of the reaction of the Al13 cluster with 4 water molecules (noted as (4) and (3 + 1), respectively). Activation and reaction energy differences are computed with respect to the minimum on the left at the BHHLYP/ 6-311++G**//BHHLYP/CEP-31G*+ZPE level.

perform well with barrier heights in the hydrated systems (see above, Section 3.1). M1_w0 has a simple structure with the oxygen atom of water oriented toward an Al atom. TS_w0 presents a four-atom ring where H
Al and Al
O bonds are formed simultaneously at neighboring Al atoms; it connects M1_w0 to M2_w0 according to the IRC. In M1_w1, one of the water molecules is linked to the cluster by an Al
O interaction, while the other is linked to the former water by a hydrogen bond; one of its hydrogen atoms is very loosely interacting with the cluster. TS_w1 involves a relay mechanism and directly connects M1_w1 to M2_w1, according to the IRC. For the Al13 3 (H2O)3 system (Figure 6), we have two TS_w2 structures of very similar energy: TS_w2_b represents an assisted two-water relay mechanism (2 + 1), whereas the lowerlying TS_w2_a is a true three-water relay structure (3). Note that M2_w2_a is, however, considerably higher in energy than M2_w2_b. The situation is similar for the Al13 3 (H2O)4 system (Figure 7) in the sense that we have (4) and (3 + 1) mechanisms. The reaction coordinate of the (4) mechanism is simple, with just TS_w3_a. The (3 + 1) mechanism looks a little more complex at the BHHLYP/CEP-31G* level we have employed. We have a very shallow secondary minimum along the reaction coordinate (see Figure SM_F5 and Table SM_T4 of the Supporting Information), but the BHHLYP/6-311++G**// BHHLYP/CEP-31G*+ZPE reveals that such a minimum is probably not present in the exact PES. The decisive saddle point of the (3 + 1) mechanism TS_w3_b lies by 11.4 kcal/mol above

Figure 8. (a) Representations of k(T) (s
1) in the interval T = 50
500 K for the Al13 3 (H2O)n system, with n = {1
4}. (b) Same for ln(k(T)). (c) 1/k(T) values. (d) ΔG°,q(T) values (kcal/mol).

M1_w3_b; the latter species lies above M1_w3_a by only 1.1 kcal/mol. It should be noted that, although TS_w0 lies above Al13 + H2O by 4.7 kcal/mol, the other saddle points are much lower in energy than the corresponding reference Al 13 + nH 2 O 24853

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The Journal of Physical Chemistry C (by
11.9 kcal/mol TS_w1,
21.0 kcal/mol TS_w2_a, and
29.1 kcal/mol TS_w3_a; all the numbers computed at the BHHLYP/6-311++G**// BHHLYP/CEP-31G*+ZPE level). 3.5. Al13 3 (H2O)n Systems: Rate Computations and Comparison to Al3 3 (H2O)n and Al 3 (H2O)n. Figure 8 represents k(T) (s
1) and its logarithm in the interval T = 50
500 K as well as the 1/k(T) values and the ΔG°,q(T) values (in kcal/mol). It is readily seen that the two-water mechanism (2), going through TS_w1 of Figure 5, has the largest rate at all temperatures, with the only exception of T = 500 K where the (3 + 1) mechanism provides a slightly larger rate. This result is in contrast with the behavior of Al3 clusters, where three waters is the optimal bridge. The three-water mechanism becomes competitive only at high temperatures. The reason for the prevalence of the two-water mechanism is mostly the low ΔG°,q(T) values. The three- and four-water mechanisms have comparable k(T) values, which are even larger than the two-water ones at low T’s. In fact, all the relay mechanisms have relatively similar k(T) values, which are significantly lower than their one-water counterparts. Indeed, the one-water mechanism has the largest values of k(T) but also the largest ΔG°,q(T) values, which makes it uncompetitive, except at the very low temperatures. However, in all cases, one can state that, below 200 K, the reaction is basically a result of tunneling. The assisted (2 + 1) mechanism is slower than (3) for T > 200 K but faster at lower temperatures due to the more efficient tunneling. Recall that the (3 + 1) mechanism originates in a local minimum (M1_w3_b) lying by 1.1 kcal/mol higher than M1_w3_a. The structural difference between the two minima is mostly some rotations of the water molecules along the H-bond chain. We have assumed there is an equilibrium M1_w3_a h M1_w3_b and multiplied the (3 + 1) rate constant by the corresponding equilibrium constant, which basically amounts to adding its Gibbs reaction energy to ΔG°,q(T). The assisted mechanism (3 + 1) is always faster than (4), for the whole T range, due to the lower ΔG°,q(T) values; although (4) has higher k(T)’s for T e 250 K, they do not compensate for the higher Gibbs activation energies. The maximum rate coefficient at T = 300 K is 1.9  104 s
1 (n = 2), which would correspond to a time scale of about 50 μs. Considering the Al13 3 (H2O)n h Al13 3 (H2O)n
1 + H2O reactions, as with the Al
trimer systems, the water partial pressures required to have a unit Al13 3 (H2O)n
1/Al13 3 (H2O)n ratio are very low. For n = 2, we have p(H2O) = 0.05 Torr (T = 300 K) or p(H2O) = 5  10
21 Torr (T = 100 K) (see table SM: T3, Supporting Information). Also, as with Al3, cluster fragmentation before reaction with water cannot be an important process in our temperature range. According to the results of Li and Truhlar,92 the rate coefficient for the Al13 h Al12 + Al process is about 6  108 s
1 at T = 2000 K, but it diminishes very rapidly with decreasing T; the 500 K extrapolated value would be 2  10
9 s
1. The Al13 3 (H2O)n f HAl13OH 3 (H2O)n
1 rates are, in general, not very high and very much lower than those of the Al3 cluster (Figures 4 and 8). For instance, the highest Al13 rate at 300 K is 1.9  104 s
1 (n = 2), while its Al3 counterpart (n = 3) is 3.1  109 s
1. Note both are open shell systems, the electronic ground state being a doublet. Of course, Al13 is considered a “magical” cluster,67,68 one significantly stable as compared to the former and next members of the series. To some extent, the electronic structure of the Al13
anion can be interpreted in terms of a closed-shell “jellium” like structure64,94
98 with a valence electron configuration of 1s21p61d102s22p61f14, so the

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Figure 9. (a) Representations of k(T) (s
1) in the interval T = 50
500 K for the optimal Al 3 (H2O)n, Al3 3 (H2O)n, and Al13 3 (H2O)n systems. (b) Same for ln(k(T)). (c) 1/k(T) values. (d) ΔG°,q(T) values (kcal/mol).

neutral system, which appears to be 1f13, can act as both an electron acceptor and donor. It is instructive to compare the Al13 3 (H2O)n and Al3 3 (H2O)n systems with the corresponding (one-Al) Al 3 (H2O)n systems, for which reaction rate coefficients have been reported recently23 and have been computed using a procedure equivalent to the one 24854

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The Journal of Physical Chemistry C employed here. To make them comparable to the Al13 3 (H2O)n and Al3 3 (H2O)n results, we have recomputed those recently reported rates by taking away the effect of rotations (which is small anyway). Figure 9 displays k(T) vs T, ln(k(T)) vs 1/T, k(T) vs T, and ΔG°,q(T) vs T; for each system and temperature, we have chosen the value of n which produces the highest rate. Note, however, that for Al 3 (H2O)n we have two curves, one for n = 1, which produces the largest values of k(T) for T < 250 K, and the other for n = 3, which prevails for T g 250 K. It is readily seen in those figures that the behavior of Al13 3 (H2O)2 and especially Al 3 (H2O)3 is very much alike; at high T’s, the rates are very close in value and even in slope. One could argue that Al13 behaves like Al, although it is somewhat less reactive. Whether Al13 may be viewed somehow as an atom (the “superatom” model) has been widely discussed, although the discussions have been based mostly on electronic structure considerations.99,100 In fact, Castleman has considered Al13 as a superhalogen.99,101 The Al3 3 (H2O)n systems appear to be much more reactive, due precisely to the power of the relay mechanisms to lower ΔG°,q(T). Contrary to the other cases, tunneling only plays a very significant role at low temperatures. We believe their different behavior is not a geometrical effect but rather a result of the different electronic structures. In any case, the present results stress the importance of cluster size in the analysis of reactivity.

4. CONCLUSIONS We have studied the critical step in the reaction of microhydrated Al3 and Al13 clusters with water. The structures have been optimized at the BHHLYP/CEP-31G* level, and BHHLYP/6-311++G**//BHHLYP/CEP-31G*+ZPE computations have been employed to determine the energy differences. Relatively high-level calculations on the Al3 3 (H2O)2 system have shown that the BHHLYP/6-311++G**//BHHLYP/CEP-31G* +ZPE level is quite suitable for our purposes, as compared to a series of other DFT levels. The most relevant reaction pathways have been determined for Alm 3 (H2O)n systems, m = {3,13} and n = {1
4}. The water molecules may play different catalytic roles; namely, they can be involved directly in the Grotthuss-like relay mechanism, or they may interact with those involved in it, eventually lowering the activation Gibbs energy. The highest rate coefficients (50 K < T < 500 K) for Al3 3 (H2O)n are obtained with n = 3, the three water molecules being involved in the relay bridge. In the case of Al13 3 (H2O)n, the two-water relay system (n = 2) appears to be the most efficient. Tunneling is important (for low T’s the reaction is sustained by tunneling) but perhaps not as crucial as for the Al 3 (H2O)n systems, which we have studied recently. It is remarkable that the Al13 cluster and the Al atom somehow behave in a similar way; the Gibbs activation energies, the tunneling transmission factors, and even the rates are not too far and vary with T similarly (even if the atom is more reactive at low T’s). Al3, however, is much more reactive and appears to benefit more from more extended relay bridges than Al13. At T = 300 K, the Al3 3 (H2O)3 complex has a rate coefficient of 3  109 s
1, while that of Al13 3 (H2O)2 is just 2  104 s
1 (still a fast rate corresponding to a lifetime of 50 μs). We would argue that this different behavior should not be a geometrical, but rather an electronic structure effect. It has been discussed in the literature whether the electronic structure and chemical behavior of Al13 might be understood in terms of the superatom model; in fact, Al13 has been proposed as a prototypical superatom. The fact that

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Al13 and the Al atom are not far from the point of view of their reactivity toward water somehow gives some “dynamicallybased” support to that idea. In any case, it is evident that size effects, perhaps due mostly to their impact in the electronic structure of the cluster, are important to assess the Al
cluster reactivity.

’ ASSOCIATED CONTENT

bS

Supporting Information. Tables of absolute and relative energies, equilibrium constants, and schematic representations of reaction mechanisms. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: fl[email protected].

’ ACKNOWLEDGMENT We acknowledge the financial support of the Xunta de Galicia through the project INCITE09314252PR and the program IN845B-2010/036. S.A.B. acknowledges a FPU grant from the Spanish Ministry of Education. The services provided by the “Centro de Supercomputaci
on de Galicia” (CESGA) are also acknowledged. ’ REFERENCES (1) Inorganic Chemistry; Holleman, A. F., Wiberg, E., Eds.; Academic Press: San Diego, USA, 2001. (2) Zuttel, A.; Schlapbach, L. Complex Metallic Alloys, 2 (Properties and Applications of Complex Intermetallics); World Scientific Publishing Co. Pte. Ltd.: Singapore, 2010; pp 331
363. Soler, L.; Candela, A. M.; Macan
as, J.; Mu~ noz, M.; Casado, J. Int. J. Hydrogen Energy 2009, 34, 8511. Kravchenko, O. V.; Semenenko, K. N.; Bulychev, B. M.; Kalmykov, K. B. J. Alloys Compd. 2005, 397, 58. (3) Hiraki, T.; Yamauchi, S.; Iida, M.; Uesugi, H.; Akiyama, T. Environ. Sci. Technol. 2007, 41, 4454. (4) Watanabe, M. J. Phys. Chem. Solids 2010, 71, 1251. (5) Petrovic, J.; Thomas, G. Reaction of Aluminum with Water to Produce Hydrogen, vs. 1.0; U.S. Department of Energy, 2008. (6) Streletskii, A. N.; Kolbanev, I. V.; Borunova, A. B.; Butyagin, P. Yu. Colloid J. 2005, 67, 631. (7) Oblath, S. B.; Gole, J. L. J. Chem. Phys. 1979, 70, 581. (8) Oblath, S. B.; Gole, J. L. Combust. Flame 1980, 37, 293. (9) Jones, M. R.; Brewster, M. Q. J. Quant. Spectrosc. Radiat. Transfer 1991, 46, 109. (10) McClean, R. E.; Nelson, H. H.; Campbell, M. L. J. Phys. Chem. 1993, 97, 9673. (11) Babuk, V.; Dolotkazim, I.; Gamsov, A.; Glebov, A.; DeLuca, L. T.; Galfetti, L. J. Propul. Power. 2009, 25, 482. (12) Huang, Y.; Risha, G. A.; Yang, V.; Yetter, R. A. Combust. Flame 2009, 156, 5. (13) Henz, B. J.; Hawa, T.; Zachariah, R. J. Appl. Phys. 2010, 107, 024901. (14) Hauge, R. H.; Kauffman, J. W.; Margrave, J. L. J. Am. Chem. Soc. 1980, 102, 6005. (15) Joly, H. A.; Howard, J. A.; Tomietto, M.; Tse, J. S. J. Chem. Soc., Faraday. Trans. 1994, 90, 3145. (16) Douglas, M. A.; Hauge, R. H.; Margrave, J. L. J. Chem. Soc., Faraday Trans. 1983, 179, 1533.
lvarez-Barcia, S.; Flores, J. R. Chem. Phys. 2011, 382, 92. (17) A (18) Agreiter, J. K.; Knight, A. M.; Duncan, M. A. Chem. Phys. Lett. 1999, 313, 612. 24855

dx.doi.org/10.1021/jp208258j |J. Phys. Chem. C 2011, 115, 24849–24857

The Journal of Physical Chemistry C
lvarez-Barcia, S.; Flores, J. R. Chem. Phys. Lett. 2009, 470, 196. (19) A (20) Tenebaum, E. D.; Ziurys, L. M. Astrophys. J. 2010, 712, L93.
lvarez-Barcia, S.; Flores, J. R. Chem. Phys. 2010, 374, 131. (21) A
lvarez-Barcia, S.; Flores, J. R. J. Chem. Phys. 2009, 131, 174307. (22) A
lvarez-Barcia, S.; Flores, J. R. J. Chem. Phys. 2011, 134, 244305. (23) A (24) Vaida, V. J. Chem. Phys. 2011, 135, 020901. (25) Chowdhury, M. H.; Ray, K.; Gray, S. K.; Pond, J.; Lakowicz, J. R. Anal. Chem. 2009, 81, 1397. (26) Xiang, H.; Kang, J.; Wei, S.-H.; Kim, Y.-H.; Curstis, C.; Blake, D. J. Am. Chem. Soc. 2009, 131, 8522. (27) Leuchtner, R. E.; Harms, A. C.; Castleman, A. W., Jr. J. Chem. Phys. 1989, 91, 2753. (28) Leuchtner, R. E.; Harms, A. C.; Castleman, A. W., Jr. J. Chem. Phys. 1990, 94, 1093. (29) Leuchtner, R. E.; Harms, A. C.; Castleman, A. W., Jr. J. Chem. Phys. 1991, 94, 1093. (30) Ruatta, S. A.; Anderson, S. L. J. Chem. Phys. 1988, 89, 273. (31) Cox, D. M.; Trevor, D. J.; Whetten, R. L.; Kaldor, A. J. Phys. Chem. 1988, 92, 421. (32) Fukue, K.; Nonose, S.; Kikuchi, N.; Kaya, K. Chem. Phys. Lett. 1988, 147, 479. (33) Jarrold, M. F.; Bower, J. E. J. Chem. Phys. 1986, 85, 5373. (34) Jarrold, M. F.; Bower, J. E. J. Chem. Phys. 1987, 87, 5728. (35) Jarrold, M. F.; Bower, J. E. J. Am. Chem. Soc. 1988, 110, 70. (36) Hettich, R. L. J. Am. Chem. Soc. 1989, 111, 8582. (37) Cooper, B. T.; Parent, D.; Buckner, S. W. Chem. Phys. Lett. 1998, 284, 401. (38) Burgert, R.; Schn€ockel, H. Chem. Commun. 2008, 2075. (39) Burgert, R.; Scn€ockel, H.; Grubisic, A.; Li, X.; Stokes, S. T.; Bowen, K. H.; Gantef€or, G. F.; Kiran, B.; Jena, P. Science 2008, 319, 438. (40) Kurtz, H. A.; Jordan, K. D. J. Am. Chem. Soc. 1980, 102, 1177. (41) Sakai, S. J. Phys. Chem. 1992, 96, 8369. (42) Sakai, S. J. Phys. Chem. 1993, 97, 8917. (43) Jursic, B. Chem. Phys. 1998, 237, 51. (44) Watanabe, H.; Aoki, M.; Iwata, S. Bull. Chem. Soc. Jpn. 1993, 66, 3245. (45) Cobos, C. J. J. Mol. Struct: THEOCHEM. 2002, 581, 17. (46) Reber, A. C.; Khanna, S. N.; Roach, P. J.; Hunter Woodward, W; Castleman, A. W., Jr. J. Phys. Chem. A 2010, 114, 6071. (47) Roach, P. J.; Hunter Woodward, W.; Castleman, A. W., Jr.; Reber, A. C.; Khanna, S. N. Science 2009, 23, 492. (48) Krasnokutski, A. A.; Huisken, F. J. Phys. Chem. A 2011, 115, 7120. (49) Shimojo, F.; Ohmura, S.; Kalia, R. K.; Nakano, A.; Vashishta, P. Phys. Rev. Lett. 2010, 104, 126102. (50) Ohmura, S.; Shimojo, F.; Kalia, R. K.; Kunaseth, M.; Nakano, A.; Vashishta, P. J. Chem. Phys. 2011, 134, 224702. (51) Russo, M. F., Jr.; Li, R.; Mench, M.; Van Duin, A. C. T. Int. J. Hydrogen Energy 2011, 36, 5828. (52) Hamrick, Y. R.; Zee, R. J. V.; Weltner, W., Jr. J. Chem. Phys. 1992, 96, 1767. (53) Li, S.; Van Zee, R. J.; Weltner, W., Jr. Chem. Phys. Lett. 1996, 262, 298. (54) Pettersson, L. G. M.; Bauschilcher, C. W., Jr.; Halicioglu, T. J. Chem. Phys. 1987, 87, 2205. (55) Villalta, P. W.; Leopold, D. G. J. Chem. Phys. 2009, 130, 024303. (56) Miller, S. R.; Schultz, N. E.; Truhlar, D. G.; Leopold, D. G. J. Chem. Phys. 2009, 130, 024304.  ivn
y, O. Chem. Phys. Lett. 2011, 512, 40. (57) Czernek, J.; Z (58) Cheng, H.-P.; Berry, R.; Whetten, R. L. Phys. Rev. B. 1991, 43, 10647. (59) Yi, J. Y.; Oh, D. J.; Bernholc, J.; Car, R. Chem. Phys. Lett. 1990, 174, 461. (60) R€othlisberger, U.; Andreoni, W.; Giannozzi, P. J. Chem. Phys. 1992, 96, 1248. (61) Akola, J.; H€akkinen, H.; Manninen, M. Phys. Rev. B 1998, 58, 3601. (62) Yang, S. H.; Drabold, D. A.; Adams, J. B.; Sachdev, A. Phys. Rev. B 1993, 47, 1567.

ARTICLE

(63) Fowler, J. E.; Ugalde, J. M. Phys. Rev. A 1998, 58, 383. (64) Rao, B. K.; Jena, P. J. Chem. Phys. 1999, 111, 1890. (65) Calleja, M.; Rey, C.; Alemany, M. M. G.; Gallego, L. J.; Ordej
on, P.; S
anchez-Portal, D.; Artacho, E.; Soler, J. M. Phys. Rev. B 1999, 60, 2020. (66) Alipour, M.; Mohajeri, A. J. Phys. Chem. A 2010, 114, 12709. (67) Ahlrichs, R.; Elliot, S. Phys. Chem. Chem. Phys. 1999, 1, 13. (68) Henry, D. J.; Varano, A.; Yarovsky, I. J. Phys. Chem. A 2008, 112, 9835. (69) Moc, J. Chem. Phys. Lett. 2009, 482, 15. (70) Smith, Q. A.; Gordon, M. S. J. Phys. Chem. A 2011, 115, 899. (71) Aguado, A.; L
opez, J. M. J. Chem. Phys. 2009, 130, 64704. (72) Drebov, N.; Ahlrichs, R. J. Chem. Phys. 2010, 132, 164703. (73) Watts, J. D.; Gauss, J.; Bartlett, R. J. J. Chem. Phys. 1993, 98, 8718. (74) Wood, G. P. F.; Radom, L.; Petersson, G. A.; Barnes, E. C.; Frisch, M. J.; Montgomery, J. A., Jr. J. Chem. Phys. 2006, 125, 094106. (75) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.: Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (76) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr. J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.M; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (77) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (78) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158. (79) Boese, A. D.; Martin, J. M. L. J. Chem. Phys. 2004, 121, 3405. (80) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput. 2006, 2, 364. (81) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Phys. 2006, 123, 194101. (82) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 241, 120. (83) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81, 6026. (84) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639. (85) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. (86) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (87) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (88) Hratchian, P.; Schlegel, H. B. J. Chem. Theory Comput. 2005, 1, 61. (89) Barker, J. R. with contributions by Ortiz, N. F.; Preses, J. M. Lohr, L. L.; Maranzana, A.; Stimac, P. J.; Nguyen, L. T. MultiWell-2009.3 Software; University of Michigan: Ann Arbor, MI, 2009. 24856

dx.doi.org/10.1021/jp208258j |J. Phys. Chem. C 2011, 115, 24849–24857

The Journal of Physical Chemistry C

ARTICLE

(90) Miller, W. H. J. Am. Chem. Soc. 1979, 101, 6810. (91) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (92) Li, Z. H.; Truhlar, D. G. J. Phys. Chem. C 2008, 112, 11109. (93) Schutlz, N. E.; Stazewska, G.; Stazewski, P.; Truhlar, D. G. J. Phys. Chem. B 2004, 108, 4850. (94) Chou, M. Y.; Cohen, M. L. Phys. Lett. 1986, 113 A, 420. (95) De Heer, W. A. Rev. Mod. Phys. 1993, 65, 611. (96) Alonso, J. A. Chem. Rev. 2000, 100, 637. (97) Cha, Ch.-Y; Gantef€or, G.; Eberhardt, W. J. Chem. Phys. 1994, 100, 995. (98) Dologounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V. J. Chem. Phys. 1999, 111, 10762. (99) Castleman, A. W., Jr. J. Phys. Chem. Lett. 2011, 2, 1062. (100) Jung, J.; Kim, H.; Han, Y.-K J. Am. Chem. Soc. 2011, 133, 6090. (101) Bergeron, D. E.; Castleman, A. W., Jr.; Morisato, T.; Khanna, S. N. Science 2004, 304, 84.

’ NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on November 17, 2011. Reference 94 has been replaced. The corrected version was posted on November 29, 2011.

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