Theoretical Investigation of the Reaction Paths of the Aluminum

Article pubs.acs.org/JPCA

Theoretical Investigation of the Reaction Paths of the Aluminum Cluster Cation with Water Molecule in the Gas Phase: A Facile Route for Dihydrogen Release Jerzy Moc* Faculty of Chemistry, Wroclaw University, F. Joliot-Curie 14, 50-383 Wroclaw, Poland W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: The gas-phase reaction of the Al6+ cation with a water molecule is investigated computationally by coupled cluster and density functional theories. Several low-energy paths of the mechanism for dihydrogen production from H2O by the positively charged aluminum cluster are identified. This reaction involves the initial formation of the association complex, exothermic by 25 kcal/mol, followed by the water dissociation and H2 elimination major steps, yielding the Al6O+ product oxide with either the nonplanar or planar structure. The H2O dissociation on Al6+ is the rate-determining step. Of the paths probed, the one kinetically most preferred leads from the O−H bond dissociation transition state lying below the separated reactants to the immediate HAl6OH+ intermediate of the “open” type and involves further the more compact intermediate from which H2 is eliminated. The other reaction paths explored involve the activation enthalpy (at 0 K) for the rate-determining step of less than 2 kcal/mol relative to the Al6+ + H2O. Natural population analysis based charges indicate that forming of H2 along the elimination coordinate is facilitated by the interaction of the hydridic and protic hydrogens. For the kinetically most favorable route detected, the coupled cluster singles and doubles with perturbative triples (CCSD(T)) relative energies calculated with the unrestricted and restricted HF references are in a good agreement. This investigation is relevant specifically to the recent mass spectrometric study of the reactivity of Aln+ with water by Arakawa et al., and it provides a mechanistic insight into the formation of the observed AlnO+ product oxide with n = 6. water occurred to produce AlnO+. This reaction was not observed for the Aln+ clusters with n = 3−5, which result was attributed to their planar-type lowest-energy geometries.8 The combined experimental and theoretical work on the Aln−/ H2O systems1,2 mentioned above demonstrated that only the relatively large Aln− anionic clusters (16 ≤ n ≤ 18) were reactive at room temperature. The operating mechanism1,2 put forward for the elementary reactions Aln− + 2H2O → Aln(OH)2− + H2 was a dissociative chemisorption of the water molecules upon the clusters’ adjacent sites, which served as a Lewis acid and a Lewis base, thus facilitating the O−H bonds’ breakage and H2 formation. As first noticed by Arakawa et al.,8 compared to the size of Aln−, the size range of Aln+ capable of reacting strongly with H2O was strikingly wider; furthermore, at a molecular level, the involvement of a single H2O was suggested in the latter case. Undoubtedly, the mass spectrometry based investigation8 offered novel pieces of knowledge on the size-selective reactivity of Aln+ with H2O. Nevertheless, the information concerning the structure of the cluster−adsorbate species formed in various steps of the reaction are not generally provided by such techniques (see, e.g., ref 9), and the same holds true for the

1. INTRODUCTION Nowadays an increased interest in studying reactions of aluminum clusters with water is noticed. From the basic research and practical viewpoints, these studies have been undertaken to reveal the relevant sizes and charge states of the Al clusters which are able to generate hydrogen from water and to indicate mechanisms involved.1−6 A notable example of such research is that of size-selective reactivity of Aln− anionic clusters (n = 7−18) with water reported by Castleman and co-workers1,2 who showed that such negatively charged clusters of specified size could react intensively with H2O to break the O−H bonds and yield H2. Recently, a series of small aluminum cluster cations Aln+ (with n up to 15) were detected in the mass spectrometric investigation of Al in helium droplets by Spence et al.7 In another recent work using mass spectrometry and involving small aluminum cluster cations, Arakawa et al.8 looked at a size-dependency of the reactivity of Aln+ (n = 3−19) with water. Under single collision conditions, these authors detected the Aln(H2O)+ and/or AlnO+ species as major reaction products. More specifically, under pressure conditions designated as “A” in ref 8, for 6 ≤ n ≤ 13, either the former or the latter product species were selectively observed, whereas the two kinds of products were detected for 14 ≤ n ≤ 19. The aluminum hexamer cation (n = 6) was revealed to be the smallest Aln+ cluster cation for which the reaction with © 2015 American Chemical Society

Received: March 4, 2015 Revised: July 22, 2015 Published: July 22, 2015 8683

DOI: 10.1021/acs.jpca.5b02123 J. Phys. Chem. A 2015, 119, 8683−8691

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The Journal of Physical Chemistry A

Figure 1. (a) Prism R1 and (b) octahedral R2 type isomers of Al6+. With TPSS and PBE0 functionals, the starting Al6+ prism geometry converged to the R3 structure shown in (c). The structures were drawn with ChemCraft.45 For the DFT structure parameters optimized with various functionals, see Figure S1.

derived from trigonal prism and octahedron. This geometric choice is reasonable, because for neutral Al6, the prism and octahedron type isomers were found previously to lie close in energy; besides, the hexamer was identified to be the smallest neutral Al cluster favoring the 3-dimensional ground-state geometry.23,32,33 However, in the recent34,35 computational studies of Al6+, only the octahedral structure was reported. Parts a and b of Figure 1 show the doublet prism R1 (C2v, 2B1) and octahedron R2 (C2h, 2Ag) type isomers of Al6+, with their full DFT structure parameters included in Figure S1 of the Supporting Information and associated relative energies given in Table 1. Our most rigorous CCSD(T) calculations predict the

reaction mechanism involved. The computational scrutiny of the possible mechanistic pathways is therefore necessary to that end, and such investigation is presented in this report employing coupled cluster and density functional theories. We have focused specifically on the case of Aln+ with n = 6, as this was found experimentally8 to be the smallest positively charged Al particle able to react with water under single-collision conditions that the AlnO+ product was observed, i.e., presumably according to the equation Aln+ + H2O → AlnO+ + H2.

2. COMPUTATIONAL DETAILS The augmented correlation consistent polarized valence basis set of triple-ξ quality, aug-cc-pVTZ,10,11 was used throughout. Density functional theory (DFT) employing spin-unrestricted B3LYP functional12,13 was mostly applied for geometry optimization and subsequent calculation of harmonic vibrational frequencies to ensure that stationary points found correspond to local minima or transition states (TSs). To put the B3LYP results in perspective, additional (spin-unrestricted) DFT calculations were also performed for selected stationary points using the PBE,14 BP86,15,16 PBE0,17 TPSS,18 and M05-2X19 functionals. The selection of all six functionals used here was based on their reported performance for the main group metal clusters, including group 13.20−24 For each transition state located, the intrinsic reaction coordinate (IRC)25 was determined (sometimes with subsequent geometry optimization) to confirm the TS’s connection to the appropriate local minima. The density functional calculations were carried out using Gaussian 0926 and GAMESS27 codes. Energies of the stationary points were next refined by singlepoint calculations employing coupled-cluster theory with singles and doubles with perturbatively included triples (CCSD(T)).28 The spin unrestricted version of coupled cluster theory was mostly applied. Because for some stationary points, using unrestricted Hartree−Fock (UHF) determinant for the CCSD wave function resulted in significant spin contamination, the coupled cluster calculations with restricted open-shell Hartree− Fock (ROHF) determinant were also performed to verify the relative energies. The unrestricted CCSD(T) calculations with UHF reference were carried out with the ORCA package.29 The MOLPRO program30 was employed to calculate CCSD(T) energies using restricted reference and restricted method conserving approximate spin-adaptation.31

Table 1. Relative Energy (kcal/mol) of Different Isomers of Al6+ and Al6O+ Calculated at Various Levels of Theorya species Al6+ R1 (C2v, 2B1) Al6+ R2 (C2h, 2Ag) Al6+ R3 (Cs, 2 A′) Al6O+ P1 (C2v, 2A1) Al6O+ P2 (Cs, 2A′) Al6O+ P3 (Cs, 2A′)

B3LYP

TPSS

PBE

PBE0

BP86

M052X

0.0

c

0.0

c

0.0

0.0

3.4

1.0

0.7

0.8

1.7

−2.6

0.0c

CCSD(T)b 0.0 (0.0) −1.9 (−0.3)

0.0c

0.0

0.0

0.0

0.0

0.0

0.0

0.0 (0.0)

−3.8

6.4

5.3

6.3

1.7

4.1

2.8 (0.5)

−8.2

3.5

2.8

1.3

−0.6

−2.5

−3.5 (−3.6)

a

Including ZPE correction estimated at the respective DFT level. bAt the B3LYP geometries with the B3LYP ZPE corrections. Values were obtained using the unrestricted Hartree−Fock reference; results in parentheses were calculated by employing the restricted Hartree−Fock reference. The ROHF-RCCSD T1 diagnostic for the R1, R2, P1, P2, and P3 structures is 0.022, 0.022, 0.023, 0.029, and 0.021, respectively. c With TPSS and PBE0 functionals, the starting prism-like geometry of Al6+ converged to the R3 (Cs, 2A′) structure shown in Figure 1c.

octahedral structure R2 to be more stable, by 1.9 and 0.3 kcal/ mol using the UHF and ROHF references, respectively. The latter result is likely more accurate because the UHF wave function of the prism suffered from large spin contamination (S2 was too high by 1.0). With TPSS and PBE0 functionals, the starting prismatic geometry of Al6+ converged to the distinct R3 (Cs, 2A′) structure (Figure 1c). However, this result has not been confirmed with the other four functionals tried, which provided the R1 optimized structure, including B3LYP used below to locate stationary points of the Al6+ + H2O reaction.

3. RESULTS AND DISCUSSION 3.1. Al6+ and Al6O+. We have begun with predicting the lowest energy geometry of bare Al6+ cluster cation reactant as 8684


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Figure 2. (a) P1, (b) P2, and (c) P3 isomers of Al6O+. For the DFT structure parameters optimized with various functionals, see Figure S2.

In other words, the initially formed Al6−OH2+ complex lies in a quite deep well on the doublet PES of the Al6+ + H2O reaction. Recalling the study of Arakawa et al.8 one notices that under single-collision conditions, the liberation of the initial adsorption energy can cause a substantive heating of the complex,9 thus making it possible to surmount the subsequent activation barriers. The general path of the reaction of H2 release from H2O by Al6+ predicted in this work involves an association complex, TS for H2O dissociation on Al6+ and resulting intermediate, H2 elimination TS, and a weakly bonded product complex between Al6O+ and H2. We have examined additionally the energetics of H atom elimination, Al6+ + H2O → Al6OH+ + H (Table S1). However, the latter process is found to be endothermic, with the TS for H atom elimination (Figure S4) lying about 25 kcal/mol above the entrance channel. In the following, the four paths of the thermodynamically favored reaction Al6+ + H2O → Al6O+ + H2 are described in detail. Unless otherwise noted, the relative energies quoted underneath have been computed using the unrestricted coupled cluster theory including the ZPE corrections (the enthalpies at 0 K), for which the shorthand notation CCSD(T) is used. The unrestricted CCSD(T) reaction profile is depicted in Figure 4, with the relevant energies collected in Tables 3 and 4. For comparison purposes, the (unrestricted) B3LYP energy profile is shown in Figure S6. 3.3. Path A. From the complex 1, the water dissociation can take place on Al6+ via the four-center transition state TS1−2 of Cs symmetry, thus following path A (Figure 5, note a different view of 1 compared to that in Figure 3 to see better the passage from the complex to the TS). Note that the fully annotated version of Figure 5 is included in Figure S7. In TS1−2, the hydrogen H1 migrates from an oxygen atom to the Al center of the Al−Al edge involved, with the coplanar arrangement of the latter with the “water molecule”; the corresponding reaction coordinate vector is depicted in Figure S8. The energy profile in Figure 4 reveals that the H2O dissociation is the rate-limiting step and that the CCSD(T) energy of TS1−2 is found to be only 1.8 kcal/mol higher than the Al6+ + H2O asymptote. At this theory level, the resulting intermediate 2 formation is exothermic by as much as 53.7 kcal/mol (relative to the free reactants) and this excess energy is available for its decomposition. Structurally, the dissociated water fragments H1 and O−H2 occupy in 2 terminal and bridged sites, respectively. From the viewpoint of H2 elimination (the next step) it is relevant to notice the protic

For the Al6O+ product oxide, the three low-energy doublet isomers, P1 (C2v, 2A1), P2 (Cs, 2A′) and P3 (Cs, 2A′)36 are found (Figure 2a−c), whose complete DFT structure parameters are shown in Figure S2. The CCSD(T) calculations favor the P3 isomer by 3.5 (3.6) and 6.3 (4.1) kcal/mol with respect to P1 and P2, respectively, employing the unrestricted (restricted) reference. We conclude that regardless of the choice of the reference of the CCSD wave function, the octahedral R2 and nonplanar P3 structures are predicted to be the most stable reactant Al6+ and product Al6O+ species, respectively, at the CCSD(T) level. 3.2. Association Complex. The potential energy surface (PES) of a gas-phase ion−molecule reaction can be elaborate and a reaction of this type is usually initiated by a formation of an ion−molecule complex.37 As detailed below, the reaction of Al6+ with a water molecule does exhibit a rich PES, and it proceeds via the initial formation of the association complex Al6−OH2+. We have been able to identify two forms of this complex: 1 (Cs, 2A′) and 6 (C1, 2A) (Figure 3), formed without a barrier. Notably, the

Figure 3. Two structures of association complex Al6−OH2+, 1 and 6, formed initially in the reaction of Al6+ with a water molecule. For the DFT structure parameters optimized with various functionals, see Figure S3.

formation of 1 appears to be a common starting point of the three distinct low-energy paths, paths A, B, and D, whereas 6 initiates another low-energy path C of the Al6+ + H2O reaction. The optimized structural parameters of 1 and 6 are presented in Figure S3, and the corresponding adsorption energies (Eads) are given in Table 2. According to Table 2, the molecular adsorption of H2O on Al6+ is rather exothermic, with the CCSD(T) calculated Eads of 25.3 and 22.8 kcal/mol, respectively. 8685


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Table 2. Adsorption Energy (Eads, kcal/mol)a of the Al6−OH2+ Association Complexes 1 and 6 Calculated at Various Levels of Theory complex 1 6

B3LYP

TPSS

PBE

PBE0

BP86

d

c

d

c

c

19.4 17.2c

26.1 23.9d

23.8 21.6c

27.5 25.1d

CCSD(T)b

M05-2X e

21.1 19.1c

25.3e (25.0)e 22.8e (21.8)e

20.2 17.4e

a Eads = E(Al6+) + E(H2O) − E(Al6−OH2+) (all the species at their optimized geometries); includes ZPE correction estimated at the respective DFT level. bAt the B3LYP geometries with B3LYP ZPE corrections. Value were obtained using the unrestricted Hartree−Fock reference; results in parentheses were calculated by employing the restricted Hartree−Fock reference. The ROHF-RCCSD T1 diagnostic for 1 and 6 is 0.028 and 0.033, respectively. cWith respect to the prism-like R1 (C2v, 2B1) structure of Al6+ plus H2O. dWith respect to the R3 (Cs, 2A′) structure of Al6+ plus H2O. e With respect to the octahedral-like R2 (C2h, 2Ag) structure of Al6+ plus H2O.

Table 4. B3LYP and CCSD(T) Energy Profiles (Relative to the Al6+ + H2O Reactants, kcal/mol) of the Al6+ + H2O → Al6O+ + H2 Reaction Calculated at the B3LYP Geometries with ZPE (B3LYP) Corrections (Path D) Path D method

1 (2A′)

TS1−11 (2A)

11 (2A)

TS11−8 (2A)

8 (2A)a

B3LYP CCSD(T)b

−19.4 −25.3

0.6 1.6

−42.6 −42.1

−42.8 −42.6

−43.3 −42.7

a

From 8 continued as path C (Table 3). bUsing the unrestricted Hartree−Fock reference.

envisaged hydrogen molecule elimination product oxide would contain the bridge-bound O atom (cf. P1 in Figure 2a), the forming of the partial H−H bond is viable when it originates from the former intermediate. This happens if the subsequent cleavage of the O−H2 bond and the proton migration toward the hydride occur together with the elongation of the Al−H1 bond, giving rise to TS2−3 with the H1−H2 distance of 1.060 Å and NPA charges on the H1 and H2 hydrogens of −0.14 and +0.18 e, respectively (Figure S5). Although TS2−3 lies 25 kcal/mol above 2, this TS is situated 28.7 kcal/mol below the entrance channel (Figure 4). Finally, the ensuing weakly bonded dihydrogen complex Al6O+···H2 3 and departure of hydrogen molecule complete path A. At the CCSD(T) level, the binding energy of 3 is ∼1 kcal/mol, and the formation of the Al6O+ oxide (observed experimentally8 for Aln+ + H2O with n = 6) according to the overall reaction Al6+ (R2) + H2O → Al6O+ (P1) + H2 is exothermic by 50.4 kcal/mol. We note at this point that the reverse step (to the H2 loss) can be viewed the heterolytic H2

Figure 4. Unrestricted CCSD(T) energy profile for the Al6+ + H2O → Al6O+ + H2 reaction calculated at the B3LYP geometries with ZPE (B3LYP) corrections. (Note that the P1 → P3 and P2 → P3 interconversion TSs were not pursued.)

(+0.27 e) and hydridic (−0.18 e) character of the hydrogen atoms H2 and H1 in 2, respectively (Figure S5), where the atomic charges given in parentheses are based on natural population analysis (NPA).38,39 The NPA prediction is consistent with the electronegativity scales.40 Now, because the proton of the O−H2 group in 2 can be combined with the hydride of the Al−H1 bond, and the

Table 3. B3LYP and CCSD(T) Energy Profiles (Relative to the Al6+ + H2O Reactants, kcal/mol) of the Al6+ + H2O → Al6O+ + H2 Reaction Calculated at the B3LYP Geometries with ZPE (B3LYP) Corrections (Paths A−C) Path A method

1 (2A′)

TS1−2 (2A′)

2 (2A)

TS2−3 (2A)

3 (2A′)

P1 (2A1) + H2

P3 (2A′) + H2

B3LYP CCSD(T)a

−19.4 −25.3

−1.6 1.8

−53.6 −53.7

−28.6 −28.7

−52.1 −51.5

−52.4 −50.4

−60.6 −53.9

Path B method

1 (2A′)

TS1−4 (2A)

4 (2A)

TS4−5 (2A)

B3LYP CCSD(T)a

−19.4 −25.3

−3.3 −6.6

−41.9 −41.0

−35.4 −36.1

method

6 (2A)

TS6−7 (2A)

7 (2A)

B3LYP CCSD(T)a

−17.2 −22.8 method

−1.5 0.5

−43.1 −42.6

B3LYP CCSD(T)a a

5 (2A′) −42.1 −44.4 Path C

TS7−8 (2A)

8 (2A)

−43.1 −43.3 −43.3 −42.7 P2 (2A′) + H2 −56.2 −47.6

TS5−3 (2A′)

3 (2A′)

P1 (2A1) + H2

P3 (2A′) + H2

−22.4 −23.4

−52.1 −51.5

−52.4 −50.4

−60.6 −53.9

TS8−9 (2A)

9 (2A)

−27.6 −28.8

−49.6 −47.1

TS9−10 (2A) −27.4 −20.1 P3 (2A′) + H2

10 (2A) −55.8 −48.3

−60.6 −53.9

Using the unrestricted Hartree−Fock reference. 8686


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Figure 5. Stationary points constituting path A of the Al6+ + H2O → Al6O+ + H2 reaction optimized at the B3LYP level. Imaginary frequencies of transition states are shown. Selected bond distances are reported in angstroms.

Figure 6. Stationary points constituting path B of the Al6+ + H2O → Al6O+ + H2 reaction optimized at the B3LYP level. Imaginary frequencies of transition states are shown. Selected bond distances are reported in angstroms. Notice a different view of 3 compared to that in Figure 5.

dissociation by the Al6O+ oxide. For the recent example of the heterolytic activation of H2 by the oxide cluster cation, see ref 41. As mentioned in section 3.1, P1 is not the most stable isomer of Al6O+ with the CCSD(T) calculations, which predict P3 to be the global minimum (Table 1). Accordingly, the corresponding

exothermicity of the overall H2 elimination reaction (Figure 4) increases to 53.9 kcal/mol (the P1 → P3 interconversion TS was not pursued). 3.4. Path B. The next low-energy route of the Al6+ + H2O → Al6O+ + H2 reaction we have detected is designated as path B 8687


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Figure 7. Stationary points constituting path C of the Al6+ + H2O → Al6O+ + H2 reaction optimized at the B3LYP level. Imaginary frequencies of transition states are shown. Selected bond distances are reported in angstroms.

point for an effective formation of the partial H−H bond by combining the hydridic (−0.14e) and protic (+0.27e) hydrogens (Figure S5). In more detail, the synchronous bending of both kinds of bonds in 5, followed by the significant O−H2 breakage, give rise to the transition state TS5−3 comprising the stretched H2 moiety (with H1−H2 = 1.020 Å and NPA charges of −0.15 and +0.17 e on H1 and H2, respectively). Similarly to path A, the energy barrier for this H2 elimination TS is negative relative to the free reactants. Lastly, the dihydrogen complex 3 is formed and H2 released, so the relevant stationary points are the same as those of path A (Figures 4 and 6). 3.5. Path C. For path C (Figure 7), the Al6−OH2+ complex 6 occurs initially. The following O−H bond breakage involves TS6−7, which lies merely 0.5 kcal/mol higher in CCSD(T) energy than the Al6+ + H2O reactants and results in intermediate 7 formation. As seen from Figure 7, the water dissociation step of

(Figure 6) and it involves the transition state TS1−4 for the water dissociation. Unlike TS1−2 of path A, the “active” Al−Al edge and the dissociating water of TS1−4 are not coplanar (for more structural details, see Figure S9). For path B, the water molecule dissociation leads to the “open” intermediate 4, in which the Al−Al edge engaged in the transition structure is broken. The IRC movie42 of the 1 → TS1−4 → 4 step (and the movie for the step directed backward) in qt format is available. Importantly, the CCSD(T) energy profile (Figure 4) indicates that path B is kinetically more favorable than path A because the rate-determining TS1−4 lies below the starting reactants. The resulting species 4 can then rearrange through TS4−5 (with the energy barrier of 6.5 kcal/mol relative to 4) to yield the more stable “octahedral-like” Cs intermediate 5 with the terminally bound H1 and bridge-bound O−H2 associated with the same Al−Al−Al face. The latter intermediate is a starting 8688


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Figure 8. Stationary points constituting path D of the Al6+ + H2O → Al6O+ + H2 reaction optimized at the B3LYP level. Imaginary frequencies of transition states are shown. Selected bond distances are reported in angstroms.

Table 5. Comparison of the Coupled Cluster Energies (Relative to the Al6+ + H2O Reactants, kcal/mol) for Path B Calculated with the UHF and ROHF References Path B method a

CCSD(T) CCSD(T)b T1c a

2

1 ( A′) −25.3 −25.0 0.028

2

TS1−4 ( A)

2

2

4 ( A)

TS4−5 ( A)

5 (2A′)

TS5−3 (2A′)

3 (2A′)

P1 (2A1) + H2

P3 (2A′) + H2

−6.6 −3.9 0.036

−41.0 −42.5 0.027

−36.1 −35.8 0.025

−44.4 −44.1 0.031

−23.4 −23.0 0.028

−51.5 −51.2 0.022

−50.4 −50.2 0.023

−53.9 −53.8 0.021

UHF-UCCSD(T). bROHF-RCCSD(T). cThe ROHF-RCCSD T1 diagnostic (defined in ref 43).

reaction Al6+ (R2) + H2O → Al6O+ (P2) + H2 is 47.6 kcal/mol (Figure 4). 3.6. Path D. Path D (Figure 8) provides the fourth lowenergy route detected by us for H2 elimination from H2O by Al6+. Here, the reaction is initiated again by the formation of the association complex 1 and proceeds through the rate-limiting H2O dissociation transition state TS1−11. Within TS1−11, the “active” Al−Al edge and the H2O being decomposed do not make a coplanar arrangement (Figure S11). As shown in the energy profile in Figure 4, this path involves a CCSD(T) activation barrier for the water decomposition (of 1.6 kcal/mol with respect to the Al6+ + H2O) to very similar those determined earlier for paths A and C. The immediate compact intermediate 11 lies relatively high in energy because it features both the H1 and O−H2 water moieties in terminal positions. Its subsequent interconversion through TS11−8 affords the H1-bridged intermediate 8, encountered already for path C. Therefore, starting from 8, the mechanistic scenario ending up with the H2 expulsion is the same as that described above for path C (Figure 4). 3.7. Comparison of the Methods’ Performances. Comparing the CCSD(T) and B3LYP reaction profiles in Tables 3 and 4 (see also Figure S6; these profiles are UHF based)

path C affords a new type of the HAl6OH+ isomer because 7 features the splitted water moieties adopting the “opposite” bridged (H1) and terminal (O−H2) sites. The 7 → 8 O−H2 rotamer’s interconversion occurring next through TS7−8 is predicted barrierless at the CCSD(T) level (Figure 4). The subsequent destroying of the H1-bridge bond in 8 caused by this hydrogen migration to the Al−O−H2 site via TS8−9 is accompanied by both the O−H2 bending toward the adjacent Al center and the rearrangement of the metal core. Although this step requires overcoming the “local” energy barrier of 13.9 kcal/ mol, it yields exothermically the species 9 with the more preferred bonding situation: terminal (H1) and bridged (O− H2). The interaction of the hydridic (−0.17e) and protic (+0.27e) hydrogens, which is viable in 9 (and in the following H2 elimination TS, below, with NPA charges of −0.14 and +0.17e, respectively, Figure S5), contributes to the formation of the partial H−H bond, as recognized before. The actually located TS for H2 loss, which connects to 9, is TS9−10; the latter lies 27 kcal/mol above 9, yet 20 kcal/mol below the free reactants. From the emerging dihydrogen complex Al6O+···H2 10 (bound by 0.7 kcal/mol), H2 is expelled to leave the planar Al6O+ product (cf. P2 in Figure 2b). The calculated exothermicity of the overall 8689


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and involves further the octahedral-like intermediate from which H2 is eliminated. The other paths probed involve the activation enthalpy (at 0 K) for the rate-determining step of less than 2 kcal/mol with respect to the free reactants. The NPA charges indicate that formation of H2 along the elimination coordinate is facilitated by the interaction of the hydridic and protic hydrogens. For the kinetically most favorable path detected, the CCSD(T) relative energies based on the UHF and ROHF references are in a good agreement. Our proposed reaction mechanism is consistent with the recent mass spectrometric study of the Aln+ + H2O reaction systems under single-collision conditions where for n = 6 the AlnO+ product was observed, and it is probably applicable to Aln+ of other sizes, yielding the AlnO+ species.8 Our proposed mechanism for H2 release from H2O by Al6+ can be compared with that of the reaction of H2 elimination from the gas-phase species Al(H2O)m+ (m < 38) activated by blackbody infrared radiation.44 The latter reaction was suggested to occur via a two-step mechanism where H2 is formed by recombining of proton and a hydride, preceded by the formation of the hydride− hydroxide type intermediate HAlOH+(H2O)m−1, predicted to be significantly more stable (by about 48 kcal/mol) than the Al(H2O)m+ species.44

suggests that the energy estimates provided by the two treatments differ mostly for (i) the rate-determining O−H bond dissociation TSs and (ii) the final reaction products (the B3LYP underestimation of the adsorption energy of the initial association complex was already addressed in section 3.2). As to (i), the B3LYP energy barriers for paths A, C, and D are lower compared to the coupled cluster results, the expected tendency, by 1.0−3.5 kcal/mol. This B3LYP “barrier lowering” for the ratedetermining step is large enough to make the DFT predictions qualitatively different from the ab initio results. Indeed, except for path D, B3LYP finds no energy barrier for the rate-determining step (relative to Al6+ + H2O), whereas according to CCSD(T), a small energy barrier exists for paths A and C. Nevertheless, the two computational approaches point clearly to no such barrier for path B. The difference stated in (ii) concerns the more exothermic channels found at the B3LYP level, and it can be traced back (at least partly) to the evaluations of the relative energies of the Al6O+ product oxide isomers by both methods (cf. Table 1). Table 5 compares the UHF and ROHF based CCSD(T) reaction profiles for the kinetically most preferred path B. First of all, a good agreement between both schemes emerges from this table. This result also supports further our using of the unrestricted coupled cluster description of the remaining paths. The other wave function based methodology related issue one should be concerned with here is that of a possible multireference (MR) character of the electronic states21,22,33 and the related reliability of the CCSD(T) results. Most recently, this issue for bare Aln clusters was addressed by Drebov and Ahlrichs21 by comparing (for n = 2−3) the single-reference spin-restricted CCSD(T) binding energies to the MRCISD and MR-ACPF benchmark values (we are not aware of any similar Aln involving high accuracy investigation of the reaction barrier heights). These authors also reported the T1 diagnostic,43 a commonly used indicator of the reliability of the single-reference correlated calculations, which they found for Aln with n = 2−4, 6−8 to be in the range 0.024−0.032 (for n = 5, T1 was 0.042), thus exceeding somewhat the threshold43 of 0.02 in the majority of the cases. As they did not observe a deterioration in the accuracy of the CCSD(T) results compared to the available MR values (for n = 2−3), they projected a similar correspondence would be valid for Aln of larger sizes examined with the comparable deviation of the T1 from the threshold. In the present study, for the path B with the lowest lying rate-determining TS, the T1 diagnostic values from the restricted CCSD(T) calculations are 0.021−0.036 (Table 5), thus in a range very similar to those reported by Drebov and Ahlrichs for bare Aln and viewed acceptable.21 This makes us believe that these our single-reference based relative energies are of reasonable accuracy.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b02123. Full citation for refs 26, 27, and 30. The DFT/aug-ccpVTZ structure parameters of Al6+ (R1), Al6+ (R2), Al6+ (R3), Al6O+ (P1), Al6O+ (P2), Al6O+ (P3) and Al6−OH2+ 1 and 6, optimized using B3LYP, TPSS, PBE, PBE0, BP86, and M05-2X density functionals (Figures S1−S3). The B3LYP optimized transition state TSH for H atom elimination (Figure S4). NPA charges calculated for selected stationary points (Figure S5). Table S1 presenting the energetics of H atom elimination. The B3LYP energy profile for the Al6+ + H2O → Al6O+ + H2 reaction (Figure S6). The fully annotated versions of Figures 5−8 (Figures S7, S9−S11), and the reaction coordinate vectors of the transition states involved in the O−H bond dissociation step of the paths A−D (Figure S8) (PDF) W Web-Enhanced Features *

IRC movies in, qt format, of the 1 → TS1−4 → 4 step and for the step directed backward are available in the online version of the paper.

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4. SUMMARY The current investigation is relevant to the issue of dihydrogen generation from water by the charged aluminum particle. Employing coupled cluster and density functional theories, we have identified several low-energy paths for the gas-phase reaction of the Aln+ cluster cation with H2O to give AlnO+ and H2 (for n = 6). This reaction involves the initial formation of the association complex, exothermic by 25 kcal/mol at the CCSD(T) level, followed by the rate-determining water dissociation on Aln+, and dehydrogenation major steps. Of the reaction paths explored, the one kinetically most preferred involves the water dissociation TS lying below the separated reactants that leads to the “open” HAlnOH+ direct intermediate

AUTHOR INFORMATION

Corresponding Author

*Tel: (48)(71) 375-7267. E-mail address: [email protected]. wroc.pl. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

The author thanks the anonymous reviewer for his valuable comments. He also gratefully acknowledges computational resources provided by the Wroclaw Centre for Networking and Supercomputing, WCSS. 8690


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Theoretical Investigation of the Reaction Paths of the Aluminum

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