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Reaction Mechanisms and Dynamics of H Generation in Micro-Hydrated Al Clusters: the Role of OxoHydroxyl and Dioxo Structures in the Al ·(HO) System. 17(-)

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Sonia Alvarez-Barcia, Uxía Rivero-González, and Jesús R. Flores J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b04430 • Publication Date (Web): 02 Sep 2015 Downloaded from http://pubs.acs.org on September 8, 2015

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The Journal of Physical Chemistry

Reaction Mechanisms and Dynamics of H2 Generation in Micro-Hydrated Al Clusters: The Role of OxoHydroxyl and Dioxo Structures in the Al17(-)·(H2O)2 System

Sonia Álvarez-Barcia, Uxía Rivero-González and Jesús R. Flores* Departamento de Química Física, Facultade de Química, Universidade de Vigo, E-36310-Vigo (Pontevedra), Spain KEYWORDS: Al clusters, H2 production, Grotthuss mechanisms, water catalysis, water splitting. Supporting Information

ABSTRACT: The dynamics of the Al17(-)·(H2O)2 system has been studied by means of potential energy surface computations combined with quasi-classical molecular dynamics simulations and transition state theory computations. The complete process of H2 generation has been analyzed. The system first undergoes water-splitting steps, generating HAl17OH(-)·(H2O) and H2Al17(OH)2(-) species. The cluster flexibility plays a major role in the dynamics, because it allows for a quick allocation of the energy excess of the hydrogen atom that splits from water. The result appears to be that H2 production is significantly delayed by the complexity of the potential energy surface and the presence of long-lived intermediates. It turns out that the di-hydroxyl structures H2Al17(OH)2(-) can easily undergo further O-H bond breaking to generate double and triple bridged oxo structures H3Al17O(OH)(-) or H4Al17O2(-). Based on the dynamics computations new mechanisms for H2 generation are proposed in which the di-oxo ACS Paragon Plus Environment

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structures play an important role. It is also shown that some intermediates have distorted forms of the Al frame which can be traced back to low-lying structures of the Al17(-) cluster. Tunneling does not appear to play a critical role, except in the first reaction steps, the water-splitting processes. The impact of the variation of the total energy of the system on the onset of H2 production and on the mechanism is discussed. Some conclusions could be applicable to the reaction of many other Al clusters with water.

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1.


INTRODUCTION The

reaction

of

individual

Al

atoms

and

water

molecules

has

been

studied

both

experimentally1.2,3,4,5,6,7,8 and theoretically.9,10 The reaction with just one water molecule is hindered by an activation barrier; however tunneling speeds up considerably the water-splitting process which leads to the formation of a HAlOH species, which, in turn, generates AlOH + H as the main product. The reaction of a micro-hydrated Al atom, which has also been studied quite intensely,11,12,13 benefits from relay (Grotthuss-type) mechanisms. It should perhaps be pointed out that catalysis by water is important in atmospheric and astrophysical chemistry.14 Some Aln(-) clusters have been found to react (in the gas phase) with water molecules in the flow experiments by Reber et al. 15 and Roach et al.; 16 H2 is generated in many cases (including n=17). Recently, Arakawa et al. have experimentally studied the reactivity of Al cluster cations with water, where H2 is also formed.17 H2 formation from Al nanoparticles has been studied too;18,19,20,21,22,23.24,25 clusters are thought to be models of larger systems in some respects. The reactivity of Alm(-) clusters has been interpreted by geometric and electronic structure arguments;15,16,26 the existence of neighboring Al atoms with Lewis acidic and basic properties would lead to favorable dissociative adsorptions (water splitting) which, in turn, would lead to the generation of H2. The reactivity then appears to depend on geometric features rather than on the electronic shell structure.15,16 The purpose of the present work is to analyze the effect of distorted forms of the cluster throughout the reaction coordinate of the H2 elimination process, to characterize alternative H2 generating structures, and to assess the impact in the reaction dynamics of water adsorption on different sites. Special attention is paid to the role of the energy flows from the splitting water to the rest of the system including the cluster frame. The dynamics of the whole reaction is analyzed in a schematic way by means of RRKM theory in combination with a master equation. We have taken on the Al17(-)·(H2O)2 system but some conclusions are likely to be applicable to many other similar systems. Al17(-) is a good ACS Paragon Plus Environment

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choice for several reasons. First, it has a rather symmetric structure so there are few chemically distinct atoms, which still are significantly different from the point of view of their charges.56,57,15 In fact, it presents a prototypical situation with adjacent sites having acidic and basic properties that facilitate dissociative adsorption; the adducts react to provide H2 deficient products in the experiments but only with partial efficiency.16 Although the bare cluster can be considered to have a compact icosahedral Al13 core, as we will see, it has enough floppiness as to geometrical distortions of the cluster frame to play an important role. Finally, its structure and the reaction to water molecules has been, at least, partially studied in some former works and that allows for comparison.15,26 Finally, we should refer to some relevant previous work. For instance, the studies by Krasnokutski and Huisken,27,28 about the reactivity of Al atoms towards water and water clusters in He droplets. A recent study finds not just atoms but Al clusters involved in the reaction within the droplet. 29 Also some relatively

old

studies

on

the

adsorption

power

of

Al

clusters

towards

simple

molecules.30,31,32,33,34,35,36,37,38 There are a number of other electronic structure studies on the Al(H2O)n systems,39,40,41,42,43 in addition to the more recent ones cited above. There are many structural studies on a number of Al clusters, 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 and their interaction with several ligands58,59,60,61,62,63,64 including water,65 also on its reaction with water.66,67,68,26,15,16 There are also some Molecular Dynamics (MD) simulation studies applied to Alm clusters (m={12,17}) surrounded by several hydration shells.69,70,71 The interaction with water molecules of a Al100 cluster has been modeled by means of a Reactive Force Field by Russo et al. 72 who conclude that catalysis by water is an important effect. Two of the present authors have also concluded that water catalysis by Grothhuss-like mechanisms very much favors the water-splitting process in some Alm·(H2O)n systems.73,74 Finally, the dynamical aspects of H migration on the HAl17OH(-) system have been studied by two of the present authors.75 Note again that Al17(-) has been experimentally demonstrated to produce H2.15,16

2.

THEORETICAL DETAILS


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The potential energy surfaces have been computed by DFT, (Density Functional Theory). We have employed the M06/6-311++G**//M06/CEP-31G*+ZPE method,76 which is quite adequate to deal with Al cluster structures.26 The G0977 computer program has been used for this purpose. The CEP-31G*78 basis (which includes a pseudopotential) is the one employed for the geometry optimization, the vibrational frequencies and zero-point energy (ZPE) computations. Using the M06/CEP-31G* geometries, single-point energy computations are performed with the 6-311++G** basis,79,80 also using the M06 functional. The ZPE values have been scaled by a factor of 0.95. The intrinsic reaction coordinates (IRC) have been computed by the method of Hratchian and Schlegel.81 Molecular Dynamics simulations of the, sometimes called, Born-Oppenheimer type, have been carried out by the method implemented in G09 in order to monitor the energy flows from the splitting water to the cluster frame. In order to provide an (admittedly crude) picture of the importance of the various reaction mechanisms and the dynamics of H2 formation we have employed RRKM theory in combination with the master equations: −

= − 1

Where {Pi(t)} are the fractions of the intermediates and kij(E) is the RRKM rate for the formation of intermediate j from i; the {kij(E)} values are determined with the utilities of Multiwell.82 Those values include a tunneling coefficient computed by an asymmetrical Eckart barrier model.82,83 Note that microcanonical rates are adequate for conditions of micro-hydration in which the (large) excesses of vibrational energy are unlikely to be efficiently transferred to the environment. Note too, that the many elementary reactions are taken into account at the same time; that is needed for an adequate description of the complete process.


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3.

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RESULTS AND DISCUSSION

3.1 Potential Energy Surfaces A relatively simple mechanism for H2 production from Al17(-)·(H2O)2 has been proposed by Reber, Roach et al.,15,16 although they have explored several other alternatives. It is based on the two water molecules undergoing sequential dissociative adsorption on the (equivalent) positions 1 and 4, so two H atoms go to the neighbouring Al atoms, 2 and 3, and undergo a (Langmuir-Hinshelwood, LH) H2 elimination step. The energy profile of that mechanism (computed at the M06/6311++G**//M06/CEP-31G*+ZPE level) is displayed in figure SM_F1 of the supporting information, (see also figure SM_F2). Our DFT computations reveal that, in addition to that basic route, there is a very complex landscape where distorted forms of the cluster and O-bridged structures play an important role in the dynamics. Besides, we have found that some of the intermediate structures correlate with species that would be formed in water-splitting processes of molecules adsorbed on other positions, such as 1 and 3 (adsorption on those positions gives rise to what we call (1,3) “paths”). As an example, we display together the (1,4) and a (1,3) path in figure 1. A more complete picture of all the energy profiles will be presented in figure 2 and the most relevant minima will be displayed in figure 3.


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Figure 1. Comparison between the reaction coordinate and energy profile of the (1,4) path15,16 (black) supplemented with additional structures (green), and a possible simple (1,3) path (dark red). ∆E0 represents the relative energies with respect to Al17(-) + 2 H2O (kcal/mol) computed at the M06/6311++G**//M06/CEP-31G*+ZPE level for all structures ((1,4) and (1,3)). Some structures of the (1,3) path are embedded in the figure. Note the connection between both paths. See a more complete picture in of the (1,3) paths in figure SM_F2 of the supporting material.

The energy profiles displayed in figure 1 (“paths” (1,4) and (1,3)) are only part of what we call the “di-hydroxyl route”, where we have structures with two –OH groups (we may also refer to them hereafter as A2H2 or H2Al17(OH)2(-) structures). In addition, some of the di-hydroxyl (A2H2) structures may undergo H migration from one of the –OH groups to an Al atom (i.e. by a O-H breaking process), giving oxo-hydroxyl structures H3Al17O(OH)(-), which we have named AEH3. Finally, the oxo-hydroxyl structures may undergo a further O-H splitting step from the remaining hydroxyl group giving dioxo-type structures, H4Al17O2(-) or E2H4. So let us summarize the notation ACS Paragon Plus Environment

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as follows

A2H2 : H2Al17(OH)2(-),

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AEH3 : H3Al17O(OH)(-) and E2H4 : H4Al17O2(-). The A2H2

structures give rise to what we call the AA “route” or the AA zone of the PES, the AEH3 structures relate to the AE route and zone and the E2H4 structures to the EE route and zone. Schematically we have a first general mechanism (the AA route) Al17(-) + 2 H2O ⇌ Al17(-)·(H2O)2 → H2Al17(OH)2(-)

(2)

H2Al17(OH)2(-) → HAl17O(OH)(-) + H2

(3)

where we have already taken into account that, by our calculations, the H2 elimination processes requiring the least energy tend to be those involving one H atom from the hydroxyl group, the other being bonded to a neighbouring Al. As said, H2Al17(OH)2(-) is a A2H2 structure; HAl17O(OH)(-) is a AEH structure. In other words, step (3) can be rewritten schematically as follows A2H2 → AEH+ H2

(4)

It must be noted that the basic mechanism of Reber, Roach et al.16,15 involves a A2H2 → A2 + H2 step (H2Al17(OH)2(-) → Al17(OH)2(-) + H2 ) as the hydrogen generation process. Still, they pointed to other options for the H2 generating step, as well as Day et al..26, and Vashishta et al.71 for the neutral cluster. Other H2 generating mechanisms have also been proposed for the reaction of Al6+ 68 and Al1367 with water. The mechanism of reactions (2)-(3) can branch to a route involving oxo-hydroxyl structures (the AE route) before H2 is generated: A2H2 ⇌ AEH3→ E2H2 + H2

(5)

And then to dioxo structures (the EE route) AEH3 ⇌ E2H4 → E2H2 + H2

(6)

3.1.1. The AA route Figure 2 presents a simplified representation of the AA part (sheet or valley) of the PES in which ACS Paragon Plus Environment

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the most relevant minima and saddle points are included and distributed into several energy profiles. A selection of the local minima of figure 2 (their structures) is presented in figure 3.

Figure 2. Energy profiles for the evolution of the AA system (di-hydroxyl species H2Al17(OH)(-)). H2 generation processes (· · · ·) and H migration processes giving AE (oxo-hydroxyl) species (- - - - lines) are represented. The H2 generation processes are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F3 for clarity.

As said, the basic mechanism proposed by Reber, Roach et al.15,16 is of the AA type but includes only the structures of figure 2 which are closer to the product of the water-splitting step, being therefore a little more schematic than the AA route presented here. According to that mechanism, H2 elimination would take place from structure AAM24d (green line on the left of figure 2, black line on the right of figure 1), in which the cluster frame is distorted with respect to the C2h structure of the bare cluster, while the (previous) water-splitting steps would take place on a mostly undistorted 9 ACS Paragon Plus Environment


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Al17 frame (see figure SM_F1).15,16 That distorted structure can in fact be connected to a path of distorted structures which can be traced back to a distorted form of the bare cluster lying above the most stable one (C2h) by 20.8 kcal/mol; see figure 4. Moreover we could also find “twisted” frames in some structures (for example the minima

AA

M18a or

AA

M23a), that can also be traced back to a

very low-lying twisted form of the cluster, which, to our knowledge, has not been described before (see figure 4).


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Figure 3. Schematic representation of the most important local minima of the AA part of the PES of figure 2. (di-hydroxyl structures, H2Al17(OH)2(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript “a”, “b” and “c” make reference to minima derived of Al17(-)(C2h) frame (or its corresponding twisted form) in the (1,4), (1,3) and (1,2) paths respectively; the subscript "d" has been used to indicate that the minima derive from a distorted form of the Al17(-) frame (see below, figure 4).


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Figure 4. Some low-lying structures of the Al17(-) cluster. Relative energies (in kcal/mol) with respect to Al17(-)(C2h) computed at M06/6-311++G**//M06/CEP-31G*+ZPE level are shown in brackets.

Perhaps the main difference with respect to the basic mechanism of Reber, Roach et al.15,16 is the inclusion of a number of H2Al17(OH)2(-) structures with an “interstial” hydroxyl group, i.e. an oxygen “bridge” linking two Al atoms, which are very low lying (figure 3). Some of those structures could, in principle, be specially active, in the sense that they can undergo A2H2 → AEH+ H2 processes having relatively low-lying saddle points (recall that in those processes one of the eliminated H atoms comes from a hydroxyl group while the other is bonded to the cluster frame). Note that the many low-lying structures arising from migrations of the interstial hydroxyl groups around or into (bridging) the two Al-H groups go down in energy by approximately 30 kcal/mol (the energy gap between

AA

M2a and

AA

M23a, see figure 3), below the -100 kcal/mol mark. Even

though many of them have relatively low-lying saddle points for H2 production, the H migration processes giving AEH3 structures and most hydroxyl migrations have yet lower-lying saddle points. The hydroxyl migration processes are not “pure” in the sense that they are accompanied by significant distortions of the Al frame. It is evident from figures 2, 3 and 4 that, in general, the structural changes in the frame play a very important role, for they make some migration processes easier and may bring the active groups spatially close. In a way, rather than “intrinsic” Al-OH or Al-H reactive sites, there are also sites which may become reactive with the right frame changes. We have also considered some “deactivation” processes; by that we mean H migrations leading to ACS Paragon Plus Environment

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structures in which that H cannot directly produce H2 or that is only possible by a relatively highlying transition state. As we will see, these “deactivations”, which are mostly considered in the AE and EE routes, should better be seen as giving late or deferred H2 generation. As we will show in section 3.1.3, they are unimportant in the AA route for the really fast process is formation of the AEH3 forms, which means switching to the AE route (see below). Finally, as said, we have considered other options for the adsorption of the second water molecule. As an example, we have considered in the main text the possibility that it gets adsorbed on atom 3 (i.e. (1,3) paths) (see section 3.1.4 and the supporting material for other options), and we have presented a simple mechanim for H2 production in figure 1 based on a (1,3) path (red line) (see a more complete picture, with an additional (1,3) path in figure SM_F2). Note that water splitting leads to structures in which two H atoms are bonded to the same Al atom. It is also readily seen that the saddle point for the (second) water-splitting process is considerably higher in energy than HAl17OH(-) + H2O (but still far lower than Al17(-) + 2 H2O), which will make that (1,3) path (also the additional one shown in figure SM_F2) uncompetitive with (1,4). The point however, is that this (1,3) path can be reached by a –OH migration step from structure AAM3a to structure AAM20b, which connects to structure AAM21b (figures 1 and 3), so both paths shown in figure 1, (1,3) and (1,4), are, as said, linked.

3.1.2 The AE route The AE route is displayed in figures 5 and 6 (for clarity, we have divided the AE valley of the PES in two groups of energy profiles). Figure 7 displays the structures of the most important minima of the AE part of the PES (the most important processes for the H2 generation are shown in figure SM_F4 of the supporting information).


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Figure 5. Energy profiles of the AE route (first part). The relative energies with ZPE differences are shown (kcal/mol). They include the AA → AE transitions (- - - - lines), AE → EE transitions (·-·-·-· lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F5 for clarity.


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Figure 6. Energy profiles of the AE route (second part). The relative energies with ZPE differences are shown (kcal/mol). They include the AA → AE transitions (- - - - lines), AE → EE transitions (·-·-·-· lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. Note that some paths involve some processes that belong more to the EE area than to the AE area. See figure SM_F6 for clarity.

Note that the lowest-lying minima of the AA route appear to be

AA

M14a and

AA

M23a (figures 2

and 3) which have a double –OH bridge connecting the –AlH groups on top of the cluster. Hydroxyl migration from these species would produce back the higher-lying AA structures from which they come from. The lowest-lying saddle points for H migration are lower in energy than their H2elimination counterparts and give two important structures of the AE sheet of the PES, namely AE

M38a and AEM42a, which have both a (double bridging) oxo group (it is the H of a hydroxyl group

the one which migrates). The latter species lie already quite low on the AE valley of the PES, but they are very short-lived intermediates; they may easily evolve (by very low-lying saddle points) to more compact structures where the double bridge becomes, at least formally, triple, namely AE M52a and

AE

M53a respectively (figure 7). The latter forms can be reached as well from other AE

structures (for instance

AE

M34a and

AE

M36a, see figures 5 and 6), which, in turn, can be produced


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by H migration from AA structures (AAM11a and AAM13a, see figures 2 and 3). Note that, in general, the AE part of the PES lies well below the AA part and that, again,

AE

M52a and

AE

M53a appear to

be at its bottom. We have located the saddle points for the H2 elimination, H migration (leading to EE structures) and “deactivating” H migration processes. Again, as in the case of the AA route, the H2 elimination saddle points turn out to be higher in energy than the H migration ones. The “deactivating” migrations (where one H moves away from the active part of the system, i.e. where the other -H or -OH groups are) have been found to have one relatively competitive saddle point leading to structure

AE

M70a (-99.0 kcal/mol see figure 5 –center left- and figure SM_F4 of the

supporting information).

Figure 7. Schematic representation of the most important local minima of the AE part of the PES (oxohydroxyl structures, H3Al17O(OH)(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript "a" indicates that the minima are derived from the Al17(-)(C2h) frame (or its corresponding twisted form).


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3.1.3 The EE route We have also divided the EE route in two energy profiles (figures 8 and 9). Figure 10 displays the structures of the most important minima of this part of the PES (the most important processes for H2 generation are shown in figure SM_F7 of the supporting information).

Figure 8. Energy profiles of the EE route (first part). The relative energies with ZPE differences are shown (kcal/mol). They include the AE → EE transitions (- - - - lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F8 for clarity.


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Figure 9. Energy profiles of the EE route (second part). The relative energies with ZPE differences are shown (kcal/mol). They include the AE → EE transitions (- - - - lines) and H2 elimination processes (direct of deferred) (· · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F9 for clarity.

As it was the case with the AA→AE transition, the lowest-lying AE forms,

AE

M52a and

AE

M53a,

connect to even lower-lying EE structures, EEM59a (figure 8 left), EEM84a (figure 9 left) and EEM61a (figure 8 center), which are already deep on the PES valley corresponding to the EE system. As in the case of the AE sheet, the EE structures connected to the upper PES area (i.e. the AE part of the PES) can still evolve into even more stable EE forms by, typically, very low-lying saddle points. Structure

EE

M84a, however, is about the most stable form according to our computations (see

figures 9 and 10). It is by as much as 144.8 kcal/mol below Al17(-) + 2 H2O. As many other very low-lying EE forms it has two triple-bridged oxo groups.


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Figure 10. Schematic representation of the most important local minima of the EE part of the PES (dioxo structures, H4Al17O2(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript "a" indicates that the minima are derived from the Al17(-)(C2h) frame (or its corresponding twisted form).

Note that, again, the EE part of the PES is, in general, significantly lower in energy than the AE sheet; so we can conclude the overall stability order is EE > AE > AA. Given that the water-splitting steps produce an AA form, one can further envision a very general ACS Paragon Plus Environment

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scheme for the overall H2 generation process, as shown in figure 11. There HD refers to deferred or late H2 formation by structures resulting from “deactivating” H migrations, in which, as said, one H moves away from the active part of the molecule.

Figure 11. Simplified reaction scheme for the H2 generation in the Al17(H2O)2(-) system. HD indicates deferred H2 formation. A and E refers to a hydroxyl group and an oxo group respectively.

3.1.4 Alternative mechanisms Reber et al.,15 and Day et al.26 have studied alternative paths for the formation of H2 in the Al17 (-) + 2 H2O reaction. They distinguish between two types of mechanism (ER -Eley-Rideal- and LH -LangmuirHinshelwood-). Vashishta et al.71 (for the neutral cluster) have considered an ER H2 production mechanism in their studies about the reactivity of Al clusters covered by water shells, in which a surrounding water molecule participates in the mechanism, i.e. they consider a water-assisted process, where the extra water does not belong to the hydration chain. We have also tried alternative adsorption options (see figure SM_F10 and the next figures), some of them previously considered by Reber et al..15 The second water molecule (that of the HAl17OH()

·(H2O)) system may adsorb on different Al atoms or form a hydrogen bond to a hydroxyl group,

giving different paths. Then, it may undergo water splitting, which following the literature we consider part of a LH mechanism, or, if it is sufficiently close to the Al-H bond originated in the first water splitting step, eliminate H2, via a –Al··OH2–Al-H → –Al-OH–Al + H2 process, which we consider an ER-type mechanism. For the LH mechanisms, we can conclude that those alternative water-splitting processes (see figures SM_F11-SM_F14 and figure 1) tend to be less favorable than the

wA

M1a →

AA

M2a step of path (1,4) (see figures 1 and SM_F1). Only when the system evolves to 20 ACS Paragon Plus Environment

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more compact HAl17OH(-) frames (in which the –OH group bridges two Al atoms), we find lowerlying saddle points for the second water-splitting process in position 2 (path (1,2)) (see figure SM_F14(a)). For the ER mechanisms (with two water molecules), we have considered several possibilities (see figures SM_F11-SM_F16). We have obtained that all H2 elimination saddle points are very high-lying, the process being then uncomptetitive. We have also considered ER H2elmination mechanims with the inclusion of a third water molecule (HAl17OH(-)·(H2O)2 systems). The role of this third water could be to participate in a Grotthus-style chain, delivering one of the H atoms of the released H2 or to “assist” the process typically by bonding to the second water, which provides one of the hydrogen atoms of H2. In order to asses the importance of these processes one should take into account competing ones, like water splitting, water elimination (i.e. going back to a two-water system) or H migration. The whole set of results is displayed schematically in figures SM_F11 to SM_F19. The watersplitting steps “compete” generally well with the water elimination steps when water chains are formed that enable Grotthuss-like mechanisms,13,26 by that we mean that the corresponding saddle points are at least comparable in energy than the water-elimination products. However, we have found only one ER H2 elimination saddle point which is comparable in energy with those of the H migration process or with the water elimination product; it is a structure already described by Day et al..26 Saddle points of the type described by Vashishta et al.71 (water assisted –Al··OH2–Al-H → – Al-OH –Al + H2 processes) appear to be quite high in energy. At least in the system with a total of three water molecules they are clearly higher than the water elimination products. A very essential point when judging the effect of additional waters is the comparison between the collision frequency of the intermediates of the already hydrated cluster with additional waters and the lifetime of those intermediates. According to our results of the next sections, conversion of the two-water system to AE and EE forms should be quite fast unless the molecular system evacuates a large proportion of the excess vibrational energy provided by the (very exoergic) water-splitting


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process. We also find that that excess energy is transferred very quickly to the cluster frame.

3.2. Energy flows by Molecular Dynamics simulations We have performed several on-the-fly MD simulations, by the M06/CEP-31G* method, in order to understand the energy flows between the hydrogen atoms and hydroxyl groups and the cluster frame. The simulation which we are going to discuss is started at the saddle point for the second water-splitting process. An excess energy of 35.67 kcal/mol is given to the saddle point structure in the vibrational mode of the imaginary frequency; the rest of the modes have their ZPE. The total energy is that of E0(Al17H2O(-)) + E0(H2O) at 0 K, which could be adequate to the beam experiments.15,16 Three plots are presented showing the results of a typical trajectory. In the first, (figure 12), we display the nuclear kinetic energies of atoms or groups of atoms; we are interested in particular in the H atom which breaks from the second water molecule and bonds to the cluster. In the second, (figure 13), we use normal mode kinetic energies, specially those of the modes having Al-H contributions (note we have two –Al-H bonds after the second water splitting step). In the final plot (total) normal mode energies are used (figure 14). We have employed the criterion of dividing the potential energy between modes in proportion to the corresponding vibrational frequency, which is an arbitrary but perhaps reasonable option that would not underestimate the time the excess vibrational energy resides in the high-frequency modes. It must be noted that to define normal-mode quantities one has to take a particular structure (PES minimum) as reference; we have employed the very first formed in the second water-splitting process. That choice imposes a limit to the maximum time where the normal-mode decomposition is meaningful of a few hundreds of fs. The atom-wise decomposition of the kinetic energy is fully meaningful at any time of the trajectories.


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Figure 12. Atom-wise kinetic energy analysis of the second water-splitting step. The trajectory is started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The kinetic energy is separated into contributions from the migrating H atom, the rest of the atoms or the Al frame.

Figure 13. Normal mode-wise kinetic energy analysis of the second water-splitting step. The normal modes are defined according to the first H2Al17(OH)2(-) structure formed,

AA

M2a. The trajectory is

started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The kinetic energy is separated into contributions from the modes which have Al-H character, and the rest of the modes.


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Figure 14. Normal mode-wise total energy analysis of the second water-splitting step. The trajectory is started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The total vibrational energy is separated into contributions from the modes which have Al-H character and the rest of the modes.

In figure 12, one can clearly see that the large (and of course strongly oscillating) kinetic energy of the H atom which breaks from water very rapidly decreases and, at about 200 fs, it almost reaches its average for the rest of the simulation. Conversely the rest of the atoms, mostly the Al frame takes up the H kinetic energy loss. In figure 13 the kinetic normal mode energy of the normal modes related to Al-H movements (nine) are ploted together with the rest of the modes. One sees that the Al-H modes loose their kinetic energy quite quickly while the other modes gain it; the process appears to be very fast again. When it comes to the total normal mode energies (figure 14) we see again a switch from the Al-H related modes to the other modes, mostly cluster-frame modes, but it takes a little bit longer, almost 500 fs. The reason for this change in time is that the Al-H modes include some of high frequencies (stretching modes) and the criterion employed to divide the potential energy somewhat favors them. Those very simple figures convey that energy randomization is quite fast. The conclusion is that the dynamical preference for H migration or H2 elimination (any process which involves the H atom resulting from the O-H bond breaking) disappears very quickly; the consequence is, of course, that 24 ACS Paragon Plus Environment

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other processes, including cluster distortions could be central to the system’s dynamics. The results also point to the applicability of RRKM theory.

3.3. RRKM computations We have considered several RRKM computations by the master equation (1), in an attempt to simulate the time variation of the population (i.e. the relative concentration) of the many structures considered. It must be noted again that, in micro-hydration conditions, one should not expect fast dissipation of the excess vibrational energy produced by the deep lowering of the electronic energy caused by the watersplitting steps and many of the rearrangements leading to AE and EE structures. Therefore, we use Edependent rates (micro-canonical) rather than canonical rates (T-dependent), which would be very different numerically, in equation (1). Still, we consider the effect of a reduction of the total (constant) energy. All RRKM computations presented next, in the main text, start from structure

AA

M2a, after the

water-splitting process (see figures 2 and 3) and then connect to all structures of the AA, AE and EE routes, but we consider other starting options (the wA structures), and the (1,2) path in the supporting material (figures SM_F20 and SM_F21). Note that, as said, the water-splitting process wAM1a ⇌ AAM2a on path (1,4) has a reasonably low-lying saddle point, which is moderately competitive with water elimination. In simulation I, we do not consider any “deactivation” steps by H migration, which implies that deferred H2 formation is not allowed at all, so hydrogen production proceeds exclusively by the H2 elimination saddle points included in the energy profiles (figures 2, 5, 6, 8 and 9). In simulation II we do take into account those deactivation steps in the following way. We have considered deactivation chains consisting of successive migrations, as shown in figure 15. Where RH would be an “active” species (H, hydroxyl, or oxo groups being close together), and SH, TH, etc. “inactive” (the migrating H unable to form H2). Of course, all forms (TH, SH, etc.) are usually able to undergo several migration reactions; we have selected that with the highest ki/k-i ratio, which more or less amounts to having the lowest-lying saddle point combined the lowest-lying product. Some of those ACS Paragon Plus Environment

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chains are sometimes “cyclic”, which means that one intermediate turns out to be an active species; in that case they are connections between active species so they are not classified as deactivation chains. Interestingly, the reverse rates of those chains tend to be significantly higher than their direct counterparts. That can make sometimes the rate of formation of ZH quite small or, at least not as fast as one would naively expect. For example, if we pick k1=k2=..=kn=k and k-1= k-2=..=kn-1= 2k the effective rate coefficient for ZH formation is k/3 (n=2), k/7 (n=3), in general, k/(2m+1), where m is the former denominator in the series. This result is consistent with the finding that long-range H migration is not a very fast process in HAl17OH(-).75 Then, the “deactivation” processes does not fully control the reaction dynamics despite the fact that H migrations normally have lower-lying saddle points than H2 eliminations.

Figure 15. Deactivation scheme. RH would be an “active” species (H, hydroxyl, or oxo groups being close together), and SH, TH, etc. are the “inactive” ones (the migrating H unable to form H2).

The results are shown in figures 16 (I) and 17 (II). It is readily seen in figure 16 that, despite the many structures considered in the three routes, only a handful really matter. Another important conclusion is that virtually no H2 is formed from the AA structures, and very little from the AE structures (mostly from AEM69a). Only the very low-lying EE forms finally deliver H2 (mostly from EEM88a); the onset of its production is about 10-7 s, although this is just a very rough estimate.75 Interestingly, that time is mostly spent in the AA part of the PES. As soon as AE species are formed, they quickly evolve down to the EE sheet of the PES. The whole process can be described very schematically, as shown in figure 18. The structures are collected for clarity in figure 19.


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Figure 16. Population of the most important local minima as a function of the decimal logarithm of t(s). AE_H2 refers to the group of species obtained by direct H2 production from the AE part of the PES; EE_H2 indicates the same but for the EE part.

When the deactivation chains are considered (figure 17) about 95 percentage of the H2 production of figure 16 (which we call direct) transforms to “deferred” of “delayed”, direct formation from AE structures maintains part of the flux. Still, according to our computations, the branching to deferred production occurs mostly on the part of the PES of the AE and EE systems.


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Figure 17. Population of the most important local minima as a function of the decimal logarithm of t(s). AE_H2 refers to the group of species obtained by direct H2 production from the AE part of the PES; EE_H2 indicates the same but for the EE part. AE_HD and EE_HD are related to the “deferred” H2 production from the AE and EE part of the PES respectively.

What is more important is that the onset of H2 production is almost unchanged as well as the composition of the “direct” mechanism, which is, again, basically that shown in figure 18.


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Figure 18. Schematic representation of the most important processes of the AA (dark red), AE (green) and EE (blue) routes, for the process initiated in the (1,4) path. The broken line indicates that there is more than one step connecting the minima.

Because the second water-splitting saddle point in the (1,2) path (see figure SM_F14) is very low lying, we have analyzed the contribution of this alternative path in the RRKM study (see figures SM_F20 and SM_F21). It has a very significant impact in the AA route since the onset for the formation of the AAM10a structure is reduced by a little more than one order of magnitude (and its population gets significantly higher). However, the onset for the formation of H2 (direct or deferred) in the AE and EE areas is almost unchanged. In fact, the main structures of the AE valley are already more or less the same both in the (1,4) and the (1,2) paths, and also quite independently on the starting structure. As said, the AA route is initially quite different depending on the path and the starting structure; still almost no H2 formation from AA structures is observed. The densities and sums of states inherent in the computation of the rate coefficients of equation (1) have been computed by the harmonic approximation (given the size of the system, rotations have not ACS Paragon Plus Environment

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been taken into account). An analysis of anharmonicity effects on a similar system HAl17OH(-) indicates that the nature of the overall H migration process is virtually unchanged.75 We would expect only a moderate impact on the onset of the H2 production. Another important point is that tunneling does not play a very important role. If one would not include tunneling (as we have done by the asymmetrical Eckart barrier model) the results would be virtually unchanged. Although the Eckart model (the only one we could use in this very complex computation) could underestimate somewhat the impact of tunneling we would not foresee major changes if more sophisticated models could be applied in the future (we are excluding of course the water-splitting steps, especially the first, from this statement). This little impact of tunneling has two reasons. First, the system has large amounts of vibrational energy (especially in the AE and EE parts of the PES), which is mostly a consequence of course of two very “exothermic” water-splitting processes, so many saddle points lie very much below the total energy level, and that makes the tunneling transmission factors to be mostly close to one. Whenever the saddle points are not so deep, the corresponding process tends to be unimportant anyway. Second, many of the saddle points, including some H migrations, have low-magnitude imaginary frequencies; basically because they are in reality complex movements in which the cluster frame, not just the migrating H, plays a role. It is interesting then to consider what happens if some energy is removed from the system, which, in the gas phase could happen by collision with an inert gas. We have considered a number of energies ranging from -13.5 kcal/mol to -54.1 kcal/mol (i.e. below that of Al17(-) + 2 H2O at 0 K, see figure 1) and repeated the RRKM simulations. Such an extreme reduction is probably unrealistic with respect to the flow experiments15,16 but still interesting from the theoretical point of view. The energy reduction produces a significant but not dramatic increase in the onset of H2 production. Going from 0 to -36.1 kcal/mol the “induction” time is augmented by a factor of about 700. Those times seem to obey an

expression of type = · exp where A, B and E0 are constants and E is the energy relative to

AA

M2a; in fact E0 can be made zero without loss of accuracy (see figure SM_F22). An important ACS Paragon Plus Environment

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(although not unexpected) change is that the mechanism is considerably simplified. Even fewer local minima have significant populations. For very low energies, it turns out that the system stays for longer times in the AA valley, and mostly in the form of

AA

M3a,

AA

M25d and

AA

M26d (see figure SM_F23).

We have analyzed the effect of the adsorption of an additional water molecule on the evolution of the AA

M3a structure and found that an ER H2-elimination process involving the additional water has a

saddle point lying much higher than AAM3a + H2O (see figure SM_F24). All these results suggest that the actual mechanism for H2 formation is probably not unique, but should vary, perhaps strongly, with the experimental conditions. The role of further water molecules may depend on the water pressure an on the energy of the partially hydrated clusters. The existence of pairs of neighboring Al atoms with Lewis acidic and basic properties favoring dissociative adsorptions in already hydrated clusters would probably be an important factor.


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Figure 19. Schematic representation of some important minima for the whole route (AA, AE and EE structures are presented) according to the RRKM simulations described in figures 16-18. ∆E0 represents the relative energies with respect to Al17(-) + 2·H2O (kcal/mol).

4.

CONCLUSIONS

We have studied the PES of the Al17(-)·(H2O)2 system in order to better understand the mechanisms of H2 generation by Al clusters and possibly by other kinds of clusters. That system had been studied theoretically and experimentally (in the gas phase by flow experiments). We have unveiled that the PES is extremely complicated and that may cause the H2 generation mechanisms to be very complex. We have found that distortions of the cluster frame, and also double and triple bridged oxo and dioxo structures could play a major role. The first step is a water-splitting processes which produces H2Al17(OH)2(-), a di-hydroxyl structure. In accord with previous works, we find two favorable dissociative adsorptions in which the two water molecules are separated by two Al atoms, producing neighboring Al-H bonds on the same plane as the hydroxyl residues. Also in agreement with previous work we have found that the resulting H2Al17(OH)2(-) species is already capable of producing H2 by elimination from the neighboring Al-H bonds, even though that movement is coupled with a cluster distortion. However, we find that hydroxyl migrations are not just possible but less energy demanding (the corresponding saddle points are lower-lying than the H2 elimination structures). Moreover, further splitting of the remaining O-H bonds produces oxo and then di-oxo structures which are much lower in energy than the di-hydroxyl structures; somehow we have a PES with three levels (or valleys): dihydroxyl H2Al17(OH)2(-) (which we call AA), oxo-hydroxyl H3Al17O(OH)(-) (named AE) and di-oxo H4Al17O2(-) (EE) levels. We have performed Molecular Dynamics simulations which show that the energy of the H atom breaking apart from water in the second water-splitting process is very quickly transferred to the cluster; one of the consequences is the lack of an obvious dynamical preference for the H2Al17(OH)2(-) species to undergo H2 elimination instead of other processes. ACS Paragon Plus Environment

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H migrations have also been considered on the AE and EE levels of the PES. Some of them bring an H atom to positions in which it does not have another close enough H, either from a hydroxyl group or bonded to the Al frame, so it cannot immediately form H2. We have considered those movements as causing a delayed formation of H2, in contrast with early or direct formation, which happens near the part of the cluster where the water-splitting steps have taken place. We have performed RRKM computations using a reaction network with a very large number of structures including the three levels of the PES (AA, AE and EE). The energy is that of Al17(-) + 2 H2O at 0 K and it remains constant. For all the PES complexity, there is a relatively limited number of really important structures. Apparently, almost no H2 is generated in the AA level and little in the AE level; it turns out that the process can be described very schematically as AA→AE(H2)→EE(H2). The AE structures formed from AA structures are very close to the bottom of the AE valley of the PES and that is also true for the EE structures formed from the AE species. Although we cannot accurately compute a ratio between direct and delayed H2 production, we have found the onset to be quite independent of the treatment of the H migration processes leading to the delayed formation. Tunneling turns out to have little impact in the outcome of the RRKM computations, mostly because at that energy, only slow (then unimportant) processes have a serious tunneling contribution. A reduction of the total energy employed in the RRKM simulations results in a significant delay of the onset of H2 production. Moreover, the time spent by the system in the AA part of the PES, around just a few structures is moderately increased. Such time increase would make it more likely for additional adsorbed waters to play a role in H2 production by relay type or other mechanisms. However, by our analysis those mechanisms may not be competitive sometimes with water elimination or other processes like H migrations. The precise identity of the mechanism of the H2 production should then be very dependent on the experimental conditions, especially the water partial pressure, the total pressure and the timescale of the experiment. One should expect that AE and EE “routes” to H2 production, i.e. the participation of oxo-hydroxyl and di-oxo structures to be of importance in the case other hydrated Al clusters; although electronic,


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spin and other effects may favor other mechanisms in other cases, those structures should definitively be taken into account. Supporting Information Alternative Mechanisms, Full-Size Figures and RRKM Computations at Reduced Energies This information is available free of charge via the Internet at http://pubs.acs.org

AUTHOR INFORMATION Corresponding Author E-mail: flores at uvigo.es Present address Facultade de Química, Universidade de Vigo, E-36310-Vigo (Pontevedra), Spain Notes The authors declare no competing financial interest

ACKNOWLEDGEMENTS SAB acknowledges a F.P.U. grant from the Spanish Ministry of Education. The services provided by the “Centro de Supercomputación de Galicia” (CESGA) are also acknowledged.

Figure 1. Comparison between the reaction coordinate and energy profile of the (1,4) path15,16 (black) supplemented with additional structures (green), and a simple possible (1,3) path (dark red). ∆E0 represents the relative energies with respect to Al17(-) + 2 H2O (kcal/mol) computed at the M06/6311++G**//M06/CEP-31G*+ZPE level for all structures ((1,4) and (1,3)). Some structures of the (1,3)


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path are embedded in the figure. Note the connection between both paths. See a more complete picture in figure SM_F2 of the supporting material.

Figure 2. Energy profiles for the evolution of the AA system (dihydroxyl species H2Al17(OH)(-)). H2 generation processes (· · · ·) and H migration processes giving AE (oxo-hydroxyl) species (- - - - lines) are represented. The H2 generation processes are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F3 for clarity.

Figure 3. Schematic representation of the most important local minima of the AA part of the PES of figure 2. (di-hydroxyl structures, H2Al17(OH)2(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript “a”, “b” and “c” make reference to minima derived of Al17(-)(C2h) frame (or its corresponding twisted form) in the (1,4) path, (1,3) path and (1,2) path respectively; the subscript "d" has been used to indicate that the minima derive from a distorted form of the Al17(-) frame (see below, figure 4).

Figure 4. Some low-lying structures of the Al17(-) cluster. Relative energies (in kcal/mol) with respect to Al17(-)(C2h) computed at M06/6-311++G**//M06/CEP-31G*+ZPE level are shown in brackets.

Figure 5. Energy profiles of the AE route (first part). The relative energies with ZPE differences are shown (kcal/mol). They include the AA → AE transitions (- - - - lines), AE → EE transitions (·―·―·―· lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F5 for clarity. ACS Paragon Plus Environment

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Figure 6. Energy profiles of the AE route (second part). The relative energies with ZPE differences are shown (kcal/mol). They include the AA → AE transitions (- - - - lines), AE → EE transitions (·―·―·―· lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. Note that some paths involve some processes that belong more to the EE area than to the AE area. See figure SM_F6 for clarity.

Figure 7. Schematic representation of the most important local minima of the AE part of the PES (oxohydroxyl structures, H3Al17O(OH)(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript "a" indicates that the minima are derived from the Al17(-)(C2h) frame (or its corresponding twisted form.

Figure 8. Energy profiles of the EE route (first part). The relative energies with ZPE differences are shown (kcal/mol). They include the AE → EE transitions (- - - - lines) and H2 elimination processes (direct of deferred) ( · · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F8 for clarity.

Figure 9. Energy profiles of the EE route (second part). The relative energies with ZPE differences are shown (kcal/mol). They include the AE → EE transitions (- - - - lines) and H2 elimination processes (direct of deferred) (· · · · lines). The latter are drawn with horizontal lines, but the real energy of the products is shown on the right. See figure SM_F9 for clarity.


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Figure 10. Schematic representation of the most important local minima of the EE part of the PES (dioxo structures, H4Al17O2(-)). Relative energies with respect to Al17(-) + 2 H2O are given in kcal/mol. The subscript "a" indicates that the minima are derived from the Al17(-)(C2h) frame (or its corresponding twisted form).

Figure 11. Simplified reaction scheme for the H2 generation in the Al17(H2O)2(-) system. HD indicates deferred H2 formation. A and E refers to a hydroxyl group and an oxo group respectively.

Figure 12. Atom-wise kinetic energy analysis of the second water-splitting step. The trajectory is started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The kinetic energy is separated into contributions from the migrating H atom, the rest of the atoms or the Al frame.

Figure 13. Normal mode-wise kinetic energy analysis of the second water-splitting step. The normal modes are defined according to the first H2Al17(OH)2(-) structure formed,

AA

M2a. The trajectory is

started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The kinetic energy is separated into contributions from the modes which have Al-H character, and the rest of the modes.

Figure 14. Normal mode-wise total energy analysis of the second water-splitting step. The trajectory is started at TS 1-2 and has an energy of 35.67 kcal/mol in excess of the TS 1-2 ZPE. The total vibrational energy is separated into contributions from the modes which have Al-H character and the rest of the modes


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Figure 15. Deactivation scheme. RH would be an “active” species (H, hydroxyl, or oxo groups being close together), and SH, TH, etc. are the “inactive” ones (the migrating H unable to form H2).

Figure 16. Population of the most important local minima as a function of the decimal logarithm of t(s). AE_H2 refers to the group of species obtained by direct H2 production from the AE part of the PES; EE_H2 indicates the same but for the EE part.

Figure 17. Population of the most important local minima as a function of the decimal logarithm of t(s). AE_H2 refers to the group of species obtained by direct H2 production from the AE part of the PES; EE_H2 indicates the same but for the EE part. AE_HD and EE_HD are related to the “deferred” H2 production from the AE and EE part of the PES respectively.

Figure 18. Schematic representation of the most important processes of the AA (dark red), AE (green) and EE (blue) routes. The broken line indicates that there is more than one step connecting the minima.

Figure 19. Schematic representation of some important minima for the whole route (AA, AE and EE structures are presented) according to the RRKM simulations described in figures 16-18. ∆E0 represents the relative energies with respect to Al17(-) + 2·H2O (kcal/mol).


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