Hydrogen Adsorption on Gallium Nanoclusters - The Journal of

Article pubs.acs.org/JPCC

Hydrogen Adsorption on Gallium Nanoclusters David J. Henry* Chemical and Analytical Sciences, Murdoch University, Western Australia, 6150, Australia ABSTRACT: The reactivity of metal nanoclusters can vary significantly as a function of the valence electronic configuration of the cluster. Hydrogen adsorption provides a simple probe to investigate variations in reactivity of nanoclusters and identify factors that contribute to regioselectivity of interactions. In this study density functional theory is used to investigate the structures, stabilities, and electronic properties of doped gallium nanocluster hydrides, Ga12XH (X = B, C, Al, Si, P, Ga, Ge, and As). Hydrogen adsorption is found to be energetically favorable, but there is significant isomerization with respect to adsorption site. Consequently, adsorption energies vary not only with valence electronic configuration, but also with adsorption site. This regioselectivity of hydrogen adsorption is analyzed in terms of cluster bonding and frontier orbital interactions.

1. INTRODUCTION Cluster-based materials exhibit considerable advantages over bulk materials, including surface features, electrostatic fields, and reactivity that can differ and be varied as a function of both composition and cluster size. Of the smaller clusters of trivalent main group elements, M13 clusters have been shown to have significant stability because they are the smallest clusters that combine a geometric shelllike structure with an almost closed shell “magic” electronic configuration.1−5 While these M13 clusters are quite stable in isolation, the open-shell 39-valence electron configuration may present difficulties in assembling solids from these species. It has been suggested that one approach to stabilize M13 clusters is adsorption of hydrogen, which leads to a closed shell 40 valence electron species. Indeed, both experimental and theoretical studies have shown that the Al13H cluster is particularly stable in the gas phase.6−9 Nevertheless, H atom adsorption can significantly alter bonding in small clusters and therefore the symmetry of the underlying framework. Additionally, Varano et al.10 have recently demonstrated that despite their increased stability, these cluster hydrides are still able to aggregate to form dimers in which 0, 1, or 2 hydrogen atoms link the clusters together. Additional dimers were identified with 3 and 4 H atoms linking the clusters, but these are only stable in the multihydrogenated form. Nevertheless, the study of hydrogen adsorption on aluminum clusters has provided a useful probe of the reactivity and isomerism of these species.11−14 In comparison, there have been relatively few studies of the interaction of hydrogen with gallium-based clusters. Moc et al.15 investigated the structures and stabilities of trimers and tetramers of GaH and GaH3, identifying a wide range of isomers with hydrogen in atop, bridge, and hollow locations. However, within these small systems, the lowest energy structures generally have the majority of hydrogen atoms located in atop positions. Maatallah et al.16 explored the potential energy surfaces of a range of gallanes (GanHn+2, n = 7−9) to determine © 2013 American Chemical Society

if these species satisfy the polyhedral skeletal electron pair theory (PSEPT). They identified many energy minima for clusters in this size range, which generally adopted nido-like polyhedral structures. Again, the majority of hydrogen atoms in these structures occupied atop positions, although several isomers also contained one or two hydrogen atoms in bridge locations. Charkin et al.17 investigated closo-gallane anions (Ga12H122−) complexed with endohedral and exohedral metal cations (Li+, Na+, Cu+, Be2+, Mg2+, Zn2+, Al+, Al3+, Ga+, and Ga3+). This specific gallane anion has an icosahedral structure with a hollow core, and all 12 hydrogen atoms are located in atop positions on the surface of the cluster. Generally the global minimum for each of these structures involves tridentate cation coordination to one of the faces of the anion. However, endohedral isomers with heavy multicharged cations are also predicted to be quite favorable in energy. Calculations also reveal significant charge transfer from the hydrogen shell to the endohedral cation via the Ga12 shell, which generally acts as an electron conductor. While these heavily hydrogenated systems clearly exhibit a general preference for atop adsorption, this is not always the case for less saturated structures. For example, a combined DFT and CCSD(T) study of the interaction of molecular hydrogen with the Ga3 cluster identified a global minimum in which the two hydrogen atoms are adsorbed at 3-fold hollow sites on opposite sides of the cluster.18 Nevertheless, a planar structure in which the H atoms are both in atop positions on different gallium atoms is relatively close in energy. Recent studies have revealed that the binding of hydrogen to aluminum clusters can be significantly modified via doping.8,12 A detailed analysis of the bonding in these clusters revealed that dopants can be used to tune the level of covalency in the surface bonds of the clusters, thereby influencing the Received: July 26, 2013 Revised: October 12, 2013 Published: November 6, 2013 26269

dx.doi.org/10.1021/jp4074366 | J. Phys. Chem. C 2013, 117, 26269−26279

The Journal of Physical Chemistry C

Article

Figure 1. (a) Ga12XH structural isomers; (b) definition of key geometric parameters.

interactions with adsorbents such as hydrogen.19 The incorporation of dopants into the Ga13 cluster has also recently been shown to provide a mechanism by which the structure, stability and bonding within these clusters can be modified.20 In particular, endohedral incorporation of third- and fourthrow p-block dopants was found to significantly stabilize the cluster while preserving the decahedral symmetry. However, endohedral doping of Ga13 with second-row p-block dopants resulted in structural transformation to icosahedral symmetry. It is interesting to note that the closo-gallane anions (Ga12H122−) of Charkin and co-workers17 also exhibit icosahedral symmetry even when complexed with endohedral cations. Furthermore, the structure of [Ga19(C(SiMe3)3)6]− consists of a cuboctahedral Ga13− core with six Ga(C(SiMe3)3) substituents.21 These results suggest that exohedral coordination can also induce a structural transformation of the cluster symmetry. It is therefore of interest to explore the perturbation that hydrogen adsorption has on the underlying structure of the clusters. For both the decahedral and the icosahedral based Ga12X clusters there are a range of adsorption sites. Identifying hydrogen adsorption site preferences on these clusters can be used to determine factors that affect the structural and electronic stability of these species. However, identifying these factors may also have broader applications in understanding the reactivity and catalytic potential of these clusters. This study uses density functional theory to investigate the adsorption of hydrogen on endohedral Ga12X clusters, with X = B, C, Al, Si, P, Ga, Ge, and As. The regioselectivity of hydrogen adsorption on these clusters is investigated and characterized in terms of adsorption energies and structural parameters. Factors contributing to observed regioselectivities are identified in terms of cluster bonding and orbital interactions.

different atop sites, either on the axial gallium atoms (A1) or alternatively on any of the gallium atoms in the equatorial five-membered rings (A2). Additionally, three potential bridge adsorption sites exist including bridging between an axial Ga atom and an equatorial Ga atom (B1), bridging between two equatorial Ga atoms of the same ring (B2), and bridging between two equatorial Ga atoms located in opposing rings (B3). Finally, there are two potential hollow adsorption sites on the surface of these clusters that are represented by the triangular (H1) and the square (H2) faces of the clusters, respectively. Key structural parameters are defined in Figure 1b. The strength of hydrogen atom interaction with the clusters was characterized by the adsorption energy (ΔHHads), which is defined as the enthalpy change for the following reaction: Ga12X + H → Ga12XH

The distortion energy (ΔHdist) can be used to “isolate” energy contributions arising from structural changes as a result of adsorption. The distortion energy is defined as the energy of the Ga12X conformation in the cluster hydride (Ga12XH) minus the energy of free Ga12X cluster. Therefore, a positive value for ΔHdist indicates structural destabilization of the gallium framework as a result of hydrogen adsorption, that is, the Ga12X conformation in the cluster hydride is less stable than in the undoped Ga12X cluster.

3. RESULTS AND DISCUSSION Gallium exhibits a strong preference for formation of Ga2 subunits within both the bulk structure and in the structure of small clusters.24 This tendency significantly contributes to the general preference for decahedral symmetry in Ga12X clusters with third- and fourth-row p-block dopants because it facilitates the formation of five Ga2 subunits in the equatorial inter-ring region. However, as observed previously, when X is a second-row p-block element (X = B or C) the cluster undergoes a structural transformation to icosahedral-like symmetry.20 Naturally there are distinct differences in the surfaces of these clusters and the structures of the resulting hydrides. Therefore, for clarity, the structures and properties of the decahedral based systems will be discussed first, followed by the icosahedral-based systems. A. Hydrogen Adsorption on Decahedral-Based Clusters. The pure Ga13 cluster has a 39-valence electron open-shell electronic configuration. Consequently, Ga13 exhibits a Jahn− Teller distortion of the decahedral structure in the form of an elongation of one of the axial X−Gaax bonds and elongation of one of the equatorial Ga2 subunits (Gaeq−Gaeq).20,25−27 Ga13H exhibits significant isomerism, with stable isomers observed for H adsorption at the A2, B2, B3, and H2 sites (Figure 2). The Ga−H bond lengths for these isomers (Table 1) are generally comparable to those found in Al13H analogues.8 However,

2. COMPUTATIONAL PROCEDURES Standard density functional theory calculations were performed using the Gaussian03 and Gaussian09 computer programs.22,23 Hydrogen adsorption on endohedrally doped Ga12X (X = B, C, Al, Si, P, Ga, Ge, and As) clusters was studied with the PBE0 functional using the 6-311G(d,p) basis set. All structures were fully optimized with no geometry restrictions. Vibrational frequency analysis was performed to characterize all stationary points reported here as true minima. Hydrogen adsorption was considered for all symmetrically unique locations on each of the clusters. Gallium clusters (Ga12X) with second-row endohedral dopant atoms (X = B and C) exhibit near icosahedral and icosahedral symmetry, respectively. Therefore, it is generally only necessary to consider adsorption to generic atop (A1), bridge (B1), or triangular hollow (H1) sites (Figure 1a). However, Ga12X clusters with thirdand fourth-row p-block endohedral dopant atoms generally have near-decahedral symmetry, leading to a larger range of potential adsorption sites (Figure 1a). This includes two 26270



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Figure 2. Stable isomers of endohedral-based Ga12XH clusters with symmetry labels.

the corresponding Ga13H structure and retains the Cs symmetry of Ga12Al. The B2 structure of Ga12AlH also has Cs symmetry but there is significant twisting and puckering of the Ga5 rings such that the mirror plane of this isomer is rotated ∼30° relative to the mirror plane of the parent Ga12Al. Nevertheless, only the gallium atoms at the adsorption site show a substantial change in X−Gaeq, while there is a decrease in the length of the axial X−Gaax bonds. Hydrogen atom adsorption at the B3 site of Ga12Al leads to a change in the individual axial bond lengths, but relatively little change in the overall axial dimension. There is also a decrease in X−Gaeq at the adsorption site, but the cluster retains Cs symmetry. The H2 structure of Ga12AlH resembles the H2 isomer of Ga13H with uniform X−Gaax bonds and increased symmetry (C2v). However, for the hollow isomer of Ga13H, the H atom is clearly located outside the Ga12 cage, whereas for the corresponding Ga12AlH isomer, the H atom is embedded in the surface of the cluster within 2.52 Å of the aluminum core. This leads to a slightly greater expansion of the equatorial region of the cluster relative to the Ga13H analogue. Ga12Si has a closed-shell electronic configuration with true D5h symmetry and therefore should provide a less favorable environment for H atom adsorption. Nevertheless, stable isomers are observed for hydrogen adsorption at the A1, A2, B2, and B3 sites, with varying effects on the underlying cluster geometry (Figure 2). For example, in the A1 isomer, the hydrogen does not adsorb directly along the cluster axis, which lowers the symmetry to Cs. Nevertheless, this leads to an elongation of the axial (X−Gaax) bond opposite the adsorption site. In comparison, there is relatively little change in the

the effect of hydrogen adsorption on the cluster framework varies between the isomers. Adsorption of hydrogen at the A2 position leads to a twisting and puckering of the Ga5 rings of the underlying cluster. Although this leads to an increase in the length of the Ga2 subunits (Gaeq−Gaeq) there is only a marginal decrease in the average X−Gaeq bond length. However, the axial X−Gaax bonds are largely unaffected. The A2 isomer of Ga13H has Cs symmetry, but the position of the molecular mirror plane is at an angle of ∼30° to the corresponding symmetry element in the Ga13 parent cluster. Adsorption at the B2 site also leads to a slight puckering of the equatorial Ga5 rings that distorts the cluster away from Cs symmetry. Although there is an increase in the two X−Gaeq bonds at the adsorption site, the average X−Gaeq shows a marginal decrease in length. Again, there is relatively little change in the axial bond lengths (X−Gaax) of the cluster. In comparison, for the B3 isomer, there is relatively little distortion of the cluster which retains the Cs symmetry of the parent Ga13 cluster. In fact, only the Ga2 subunit at the adsorption site is weakened, whereas the remaining Ga2 subunits exhibit a slight decrease in the length, indicating an increase in bonding. The H2 structure exhibits higher symmetry (C2v) than the other Ga13H isomers, with uniform X−Gaax values and a slight contraction of Ga2 subunits but essentially no change in the average X−Gaeq bond length. Ga12Al is isoelectronic with Ga13 and also exhibits a distorted D5h structure.20,25 Not surprisingly, there are significant similarities between the isomers of Ga12AlH and Ga13H. However, overall the A2 isomer of Ga12AlH exhibits less distortion than 26271


2.707− 2.817 2.705− 2.790

2.641− 2.732 3.290, 3.290 1.783, 1.783 1.567

1.571 2.680− 2.774 2.809, 3.059 1.578 2.944 As

2.726

1.578 2.916 P

2.683

2.693 Ge

2.739

1.569

2.658, 2.735 2.702, 2.770 2.755, 3.050 1.566 Si

2.685, 2.743 2.670 Ga

1.567

1.570

1.570

1.566

2.701− 2.742 2.727− 2.774 2.630− 2.737

1.553

X-Gaax

2.689, 2.689 2.688, 2.688 2.061,2.061, 2.061, 2.061 2.071,2.071, 2.071, 2.071

Ga-H X-Gaeq

2.629− 2.783 2.617− 2.777 2.617− 2.717 2.647− 2.742 2.583− 2.690 2.678, 2.828 2.678, 2.817 2.972, 2.972 2.992, 2.992 3.280, 3.280

X-Gaax Ga-H

1.715, 1.875 1.717, 1.862 1.773, 1.773 1.777, 1.777 1.776, 1.776, 2.574− 3.481 2.636− 2.831 2.643− 2.714 2.685− 2.739

X-Gaeq X-Gaax

2.793, 2.800 2.668, 2.749 2.856, 2.966 2.881, 2.977 1.796, 1.800 1.762, 1.862 1.801, 1.801 1.806, 1.806

Ga-H X-Gaeq X-Gaax Ga-H X-Gaeq X-Gaax Ga-H

2.703− 2.789 2.702− 2.796 2.714

X-Gaax

2.721

X

Al

X-Gaeq

equatorial bonds (X−Gaeq), but there is a slight decrease in the inter-ring separation. This suggests a weakening of bonding along the cluster axis but a strengthening of the equatorial Ga2 subunits. In comparison, adsorption at the A2 site leads to a significant warping of the cluster axis and a puckering of both Ga5 rings. Inspection of individual bonds of the A2 isomer reveals a substantial increase in the X−Gaeq bond lengths at the adsorption site and a decrease in the X−Gaeq bond lengths on the opposite face of the cluster. The B2 isomer exhibits Cs symmetry and a significant elongation of both the axial bonds of the cluster and a slight decrease in the average X−Gaeq bond length for the equatorial gallium atoms. Hydrogen adsorption at the B3 site leads to an even greater increase in the length of the axial bonds. Additionally there is lengthening of all Ga2 subunits, but this is accompanied with a slight contraction of the equatorial dimensions, giving this isomer a somewhat oblate shape with C2v symmetry. Generally, the Ga−H bonds of Ga12SiH are marginally longer than the corresponding values for Ga12AlH, suggesting weaker binding of the H atom in these structures. The structures of the Ga12GeH isomers are generally quite similar to their Ga12SiH counterparts. The Ga12P and Ga12As clusters have inherently elongated D5h symmetric structures. Hydrogen adsorption at the A1 site leads to asymmetry of the axial bonds. This arises from a lengthening of the X−Gaax bond adjacent to the adsorption site and a shortening of the opposing X−Gaax bond (Table 1). However, the overall axial dimension is essentially unchanged. Likewise, there is a slight expansion of the Ga5 ring closest to the adsorption site and a slight contraction of the opposing Ga5 ring, but the average equatorial dimensions are relatively unchanged. Two distinct Ga12PH A2 isomers were identified that both have Cs symmetry but lead to inherently different distortions of the structure of the underlying cluster. In the A2a structure, both X−Gaax bonds are substantially shortened relative to the parent Ga12P structure and the Gaax−X−Gaax angle decreases to 160°. The A2a isomer also exhibits a substantial increase in X−Gaeq at the adsorption site, which causes puckering of the Ga5 rings. Despite this, there is only a slight increase in the average X−Gaeq bond length for the cluster. The second of the A2 isomers (A2b) also exhibits substantially contracted axial bonds and the Gaax−X−Gaax angle decreases to 150°. In this isomer, the Ga5 rings are not only puckered, but also staggered relative to one another so that the molecular mirror plane of the hydride is rotated ∼45° relative to the mirror plane of Ga12P. Close inspection of the underlying structure reveals that the A2b isomer corresponds to H adsorption on one of the higher energy metastable conformations of Ga12P rather than the global minimum D5h conformation. The A2b isomer was actually obtained during attempts to locate the B2 isomer and represents a hydrogen-induced structural transformation. Hydrogen adsorption at the B3 site leads to a significant lengthening of both X−Gaax bonds and a decrease in the X−Gaeq bonds at the adsorption site, but little change in the other X−Gaeq bonds. Likewise, while there is a lengthening of the Ga2 bond at the adsorption site, the remainder of the equatorial Ga2 subunits are largely unaffected. The structural variations for the isoelectronic Ga12AsH isomers are identical to those of Ga12PH. In all cases, hydrogen adsorption results in some level of distortion of the structure of the underlying cluster. Hence, the distortion energies for all isomers are positive (Table 2). However, the magnitudes of the distortion energies vary significantly across the different clusters and the different isomers.

2.562− 2.799 2.506− 2.874 2.574− 3.481 2.646− 3.500 2.632− 3.636 2.657− 3.424 2.683− 3.405 2.653− 3.448

B A A Ga12X

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2.683, 2.744 2.683, 2.750 2.654, 2.671 2.658, 2.806 2.612, 2.700 2.624, 2.786 2.668, 2.746 2.825, 2.675

B3 Ga12XH 2 2 1

Table 1. Structural Properties of Ga12XH Clusters (X = Al, Ga, Si, Ge, P, and As; Å)

1.549

H2

X-Gaeq


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Table 2. Key Energetic Properties of Ga12XH Clusters (eV) A1 ΔHHads

a

A2 ΔHdist

Ga12AlH Ga13H Ga12SiH Ga12GeH Ga12PH

−1.46 −1.46 −2.55

+0.11 +0.15 +0.09

Ga12AsH

−2.52

+0.10

B2

B3

H2

ΔHHads

ΔHdist

ΔHHads

ΔHdist

ΔHHads

ΔHdist

ΔHHads

ΔHdist

−2.45 −2.54 −1.49 −1.40 −2.53a −2.58b −2.52a −2.44b

+0.02 +0.12 +1.18 +0.71 +0.30 +0.32 +0.35 +0.39

−2.33 −2.34 −1.31 −1.33

+0.24 +0.16 +0.53 +0.49

−2.47 −2.46 −1.52 −1.53 −1.82

+0.05 +0.05 +0.84 +0.81 +0.84

−2.24 −2.23

+0.19 +0.11

−1.83

+0.78

Value for A2a isomer. bValue for A2b isomer.

axis. These plots clearly indicate that the variations in ΔHdist relate not only to the level of structural rearrangement, but to the specific nature of the distortion. For example, hydrogen adsorption at the A1 site of Ga12Si leads to a small change in the axial dimension and relatively little change in the equatorial dimensions so that ΔHdist for this isomer is small. In comparison, H atom adsorption at the A2a site leads to significant localized changes to the equatorial dimensions including significant expansion of X−Gaeq at the adsorption site and contraction to other X−Gaeq bonds. These changes make the largest contribution to ΔHdist, with a further contribution from changes in the length of the Ga2 subunits. For the B2 isomer of Ga12SiH, the major contribution to ΔHdist arises from changes in the axial dimensions with a smaller contribution from localized changes in the X−Gaeq at the adsorption site. Similarly, for the B3 isomer, the significant changes in the axial dimensions make the largest contribution to ΔHdist, with smaller localized changes in X−Gaeq and Gaeq−Gaeq at the adsorption site also contributing. A similar analysis of the cluster distortions can be used to explain the magnitudes of the ΔHdist values for the majority of the Ga12XH isomers. The exceptions to this are the highly distorted A2b isomers of Ga12PH and Ga12AsH, which appear to have surprisingly small ΔHdist values. However, as noted earlier, the underlying structures of these species are metastable conformations of the Ga12P and Ga12As clusters, respectively; therefore, they do not represents points in the local vicinity of the decahedral based minima. Adsorption energies (ΔHHads) for Ga12XH clusters are presented in Table 2. Hydrogen adsorption is found to be energetically favorable on all of the investigated clusters, with similar trends generally observed for isoelectronic species. In particular, hydrogen adsorption on the 39 valence electron clusters (Ga12Al and Ga13) leads to a stable closed-shell species and the ΔHHads values for these clusters are generally quite large (−2.33 to −2.54 eV). Nevertheless, there is variation in ΔHHads with adsorption site. For example, in the Ga13H systems, the ΔHHads values indicate that the A2 isomer is the most stable, followed by B3, B2, and then H2 isomers. The adsorption energies for Ga12AlH isomers are almost identical to those of their Ga13H counterparts, except for the A2 isomer, which has a slightly lower ΔHHads. Hydrogen adsorption energies are substantially lower for Ga12Si and Ga12Ge. Among these species, H adsorption is energetically most favored at the equatorial B3 site, followed by the A2, A1, and B2 sites. The ΔHHads values for the Ga12GeH isomers are very similar to their Ga12SiH counterparts. Hydrogen adsorption energies for Ga12P and Ga12As are generally higher than observed for the group-14 doped clusters,

Figure 3. Potential energy surfaces for (a) systematic change of overall dimensions of selected clusters and (b) for specific distortions of Ga12Si cluster dimensions.

It is therefore of interest to investigate what factors contribute to these variations. Figure 3a displays cross sections of the potential energy surfaces for systematic expansion and contraction of the dimensions of the Ga12Al, Ga12Si, and Ga12P clusters. The first point to note from this plot is that the potential energy surfaces for the three clusters exhibit very similar curvature about the energy minima. Second, contraction of the overall cluster dimensions leads to a larger increase in energy than a corresponding expansion of the cluster. In fact, the only noticeable differences between the three curves are that (i) the Ga12Si surface is slightly steeper for increasing expansion of the cluster and (ii) that the Ga12Al curve is slightly shallower for contraction of the cluster dimensions. Figure 3b shows the potential energy surfaces for systematic distortion of the overall dimensions of Ga12Si, and for separate distortion of the equatorial dimensions, the axial dimensions and the length of the Ga2 subunits. It is clear from this plot that distortion of the whole equatorial region leads to a larger increase in energy than an equivalent expansion of the cluster 26273



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Figure 4. Selected eigenvalue spectra for decahedral-based Ga12X and Ga12XH clusters.

these orbitals appears to be dominated by favorable symmetry interactions. Although H atom adsorption leads to a strongly bonded 40-valence electron species, there is not a significant increase in the degeneracies of the bands of orbitals or further development of a Jellium-like electronic structure. Adsorption at the H2 site appears to cause the least disruption to the electronic structure of the cluster. Although Ga12Si has a 40-valence electron configuration and there is increased degeneracy in the bands of orbitals compared with Ga13, it also does not have a fully formed Jellium electronic structure. However, hydrogen atom adsorption on Ga12Si leads to a H-induced bonding state in each of the Ga12SiH isomers and these levels are in fact slightly deeper than the corresponding levels in the Ga13H isomers. Nevertheless, on the whole, the interactions between H 1s and the other hybrid orbitals is less bonding in these isomers compared to the Ga13H species, which accounts for the lower adsorption energies. Very similar trends are observed for the eigenvalue spectra of the Ga12GeH isomers. The 41-valence electron Ga12P cluster exhibits a narrowing of the deeper lying orbital bands but a broadening of the orbital bands close to the HOMO (Figure 4). Hydrogen adsorption on Ga12P leads to a broadening of most of the orbital bands regardless of adsorption site. However, this feature is most pronounced in the B3 isomer, which exhibits significant splitting of energy levels. The energy levels of the A2a and A2b isomers are affected to a lesser extent, while adsorption in the axial A1 position has a relatively small effect on the orbital structure of the cluster. The hydrogen-induced bonding state occurs at a slightly higher level in these species (∼11 eV) than for the Ga12SiH isomers. A significant outcome of the hybridization of the cluster orbitals is a lowering in energy of the HOMO of the hydrides relative to Ga12P. Consequently, the Ga12PH species have larger HOMO−LUMO gaps than the parent Ga12P cluster. As noted above, a range of orbitals are involved in the formation of the Ga12X−H bonds in these clusters. Inspection of the individual orbitals of each of the Ga12XH species reveals different levels of contribution from the frontier orbitals (HOMO and LUMO) of the parent clusters, depending on the clusters electronic configuration and these contributions correlate with the observed regioselectivities for H adsorption. Generally the lowest energy open-shell frontier orbital of the parent cluster has the largest influence on the preferred locations for hydrogen adsorption. For the 39-valence electron decahedral systems, Ga13 and Ga12Al, the HOMO (Figure 5a)

and in some cases, they are comparable to those of the group13 doped species. The A1, A2a, and A2b isomers have similar ΔHHads values, while H binding to the B3 site is considerably weaker. Several factors contribute to the stability and regioselectivity of hydrogen adsorption on metal nanoclusters, including the electronic structure of the cluster, the interactions between H 1s and the orbitals of the clusters, and the degree of charge transfer. For example, Kawamura et al.28 reported that the cluster-hydrogen bond in Al13H exhibits covalent character resulting from deep-lying bound states. In particular, an important hydrogen-induced level was observed at ∼−10 eV formed by electron-transfer from the cluster. Additionally, the exact position of this level was strongly dependent on the adsorption site of the H atom. Mañanes et al.29 also performed an analysis of the bonding in Al13H and found that there was selective overlap of H 1s with the HOMO of Al13 as well as several deeper states of the cluster spanning a range of ∼12 eV. On the basis of this observation, they suggested that hybridization of these orbitals is dominated by favorable symmetry interactions rather than energy matching. They also noted that bonding character was dominant in these hybrid states, which accounts for the stability of Al13H. As already noted, the structure and bonding in the decahedral-based gallium clusters differs from that of Al13, and therefore, it is of interest to investigate the influence of each of these factors on the stability and regioselectivity of hydrogen adsorption on Ga12X clusters. One of the key observations of the previous study of Ga12X clusters was the effect of different dopant atoms on the development of a Jellium-like electronic structure. Ga13 has bands of orbitals corresponding to Jellium 1s, 1p, 1d, 2s, 2p, and 2f shells, but the orbitals comprising each of these bands are not fully degenerate (Figure 4), that is, the cluster has a poorly formed Jellium electronic structure. Nevertheless, the H 1s orbital is close in energy to the 1d band of orbitals, and in each of the Ga13H isomers, there is significant overlap between H 1s and one of these orbitals, leading to a hydrogen-induced bonding state at ∼−11 eV. The exact position of this level varies slightly between isomers, analogous to the observations for Al13H.28 In particular, the hydrogen-induced bonding states for the B2 and B3 isomers are deeper than the corresponding levels in the A2 and H2 isomers. The eigenvalue spectra for the Ga13H isomers reveal that there is also significant interaction between the H 1s and a range of other cluster orbitals. As for Al13H, hybridization of 26274



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Mañ anes et al.29−31 carried out a detailed analysis of the bonding and reactivity of H and Al13 and found that there is stabilization of a sizable amount of electronic charge around the proton site such that the state of the hydrogen can be considered as a negatively charged impurity, screened by the surrounding electron gas. Inspection of the atomic charges of the Ga12XH clusters reveals that the H atom is generally negatively charged, also indicating charge-transfer to the hydrogen. Analysis of the total electron density isosurfaces can provide valuable insight in to the nature of the bonding in clusters. The 0.088 electrons A−3 isosurfaces for decahedral-based Ga12X clusters reveal only isolated charge density around each of the individual atoms.20 Localized bonding is first observed in the Ga2 subunits at a charge density of 0.044 electrons Å−3 for Ga12Si, Ga12Ge, Ga12P, and Ga12As, but at a slightly lower level for Ga13 and Ga12Al. Consistent with the observations for Ga12X clusters, the 0.088 electrons Å−3 isosurfaces for the four Ga13H isomers do not exhibit any localized bonding between Ga atoms (Figure 6a).

Figure 5. Top and side views of the (a) frontier equatorial orbital and (b) the frontier axial orbital of decahedral Ga12X clusters.

is singly occupied and located in the equatorial region of the cluster. Inspection of the individual orbitals of the Ga13H and Ga12AlH isomers reveals that the open-shell HOMO of these clusters is directly involved in bonding to hydrogen in each of the four hydride isomers (A2, B2, B3, and H2). Figure 5a reveals that the HOMO of these clusters, has a large lobe located on the elongated Gaeq−Gaeq bond that facilitates A2 and B3 type adsorption. Additional lobes on one of the large rectangular faces of the clusters and in the adjacent regions enable H2 and B2 type adsorption, respectively. The absence of lobes on the axial Ga atoms, or the region adjacent to these atoms, means that this orbital cannot facilitate H atom adsorption in the A1, B1, or H1 sites. In comparison, the LUMO (Figure 5b) for these clusters has large lobes on the axial sites, the centers of the Ga2 subunits, and between the ends of the Ga2 subunits that can facilitate adsorption in the A1, A2, B2, and B3 sites. Nevertheless, while there is some overlap between the LUMOs and the H 1s orbital in these isomers, the resulting hybrid orbitals are not occupied in the hydride and therefore do not contribute to bonding to hydrogen. The absence of B1 and H1 isomers can be further understood by recognizing that these sites occur at a nodal plane in the LUMO, which prevents a net stabilizing interaction with the spherical H 1s orbital. Consequently, adsorption at the B1 and H1 sites is only predicted to occur for π-type interactions with molecules that have orbitals with a corresponding nodal plane. The frontier orbitals for the 40-valence electron systems (Ga12Si and Ga12Ge) are almost identical to those of Ga13 and Ga12Al, except that the HOMO (Figure 5a) is doubly occupied. Consequently, the interaction between the HOMO and H 1s of these clusters is energetically less favorable and there is no evidence of a bonding interaction between these orbitals in the Ga12SiH and Ga12GeH isomers. In comparison, the LUMO of these clusters directly interacts with H 1s. As noted above, The axial orbital (Figure 5b) is ideally suited to facilitate hydrogen adsorption in the A1, A2, B2, and B3 sites. In the 41-valence electron clusters (Ga12P and Ga12As), the axial aligned orbital (Figure 5b) now has the role of singly occupied HOMO, while one of the higher energy unoccupied orbitals takes the role of the LUMO. Consequently, this open-shell HOMO plays a significant role in the observed regioselectivity for H atom adsorption on Ga12P and Ga12As, which accounts for the preference for A1, A2, and B3 adsorption. However, the greater electronegativity of the core atoms in these clusters leads to a contraction of the central lobes of the HOMO such that adsorption at the B2 site is no longer favored. The lower energy doubly occupied equatorial orbital (Figure 5a) has essentially no involvement in the bonding to H.

Figure 6. Total electron density isosurfaces for Ga13H isomers at (a) 0.088 electrons A−3, (b) 0.055 electrons Å−3, and (c) 0.044 electrons Å−3.

However, at this charge density, the A2 isomer exhibits a significant region of charge density between hydrogen and the neighboring gallium atom, indicating a strongly localized covalent bond between these atoms. In the B2 and B3 isomers, bonding is first observed between hydrogen and the neighboring gallium atoms at a charge density of ∼0.055 electrons Å−3 (Figure 6b). Consistent with the previous study of nonhydrogenated Ga12X clusters, localized bonding between gallium atoms is first observed in the equatorial Ga2 subunits (Figure 6c). Importantly, Ga2 bonding in Ga13H is observed at a slightly higher charge density (∼0.044 electrons Å−3) than in Ga13 (∼0.040 electrons Å−3), reflecting an increase in overall stability as a result of hydrogen adsorption. However, even at this level of electron density, the H atom of the H2 isomer remains isolated from the rest of the cluster. In fact, it is not until the 0.040 electrons Å−3 isosurface is reached that there is any evidence of bonding between hydrogen and gallium in the H2 isomer. The trends in electron density between gallium atoms are consistent with the trends in bond lengths, that is, shorter stronger bonds are evident at slightly higher charge densities, whereas longer weaker bonds are only observed at lower charge densities. In particular, analysis of the electron density isosurfaces of the B3 26275



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almost identical changes in energy. In comparison, the potential energy surface for the expansion of Ga12C is somewhat steeper than for Ga12Si, particularly for larger distortions. The contributions from separate axial and equatorial distortions are depicted in Figure 8b and are generally quite similar to those of Ga12Si. As for the decahedral based systems, the distortion energies for hydrogen adsorption on the icosahedral clusters can be understood in relation to these potential energy surfaces. In particular, H atom adsorption at the A1 site of Ga12C leads to very little change in the overall cluster dimensions, and therefore, the distortion energy (Table 4) is quite small. On the other hand, the significant elongation of the cluster axis arising from H atom adsorption at the B1 site leads to a substantial increase in the cluster energy, while the localized changes in the X−Gaeq also contribute to the substantial ΔHdist for this isomer. Hydrogen adsorption on Ga12B generally leads to very localized structural changes in the cluster dimensions and the resulting distortion energies are all quite small. The ΔHHads values for Ga12B indicate that H atom adsorption is equally favored at the bridge and hollow sites and slightly less favored at the atop sites, which resembles the pattern for H adsorption on the isoelectronic and structurally similar Al13H cluster.6,8 The individual ΔHHads values are of similar magnitude to those of Ga13 and Ga12Al. Hydrogen adsorption on Ga12C is a significantly less exothermic process than on Ga12B with the A1 site slightly favored over the B1 site. The ΔHHads values for the Ga12CH isomers are marginally smaller than for corresponding isomers of Ga12SiH and Ga12GeH. The eigenvalue spectrum for Ga12B reveals bands of orbitals corresponding to Jellium 1s, 1p, 1d, 2s, 2p, and 2f shells, but as for the larger Ga13 cluster, the orbitals comprising each of these bands are not fully degenerate (Figure 9). The H 1s orbital is close in energy to the 1d and 2s bands of orbitals and consequently there is significant overlap between H 1s and these orbitals in each of the Ga12BH isomers. This interaction leads to a strongly bonding hydrogen-induced state at ∼−11 eV. However, as noted for the decahedral clusters, the exact position of this state varies across the three isomers (−10.8 to −11.3 eV). Analysis of eigenvalues of Ga12C reveals a Jellium-like eigenvalue spectrum with a high degree of degeneracy (Figure 9), which correlates well with its high stability. In particular, the 1s, 1p, 2s, 1d, and 2p shells have clearly formed, however, as Chandrachud et al.32 noted, the levels near the HOMO are predominantly p-type orbitals rather than fully hybridized Jellium-type orbitals. Hydrogen adsorption on Ga12C leads to formation of a 41-valence electron species and there is a resulting disruption of the Jellium orbital structure, particularly for the B1 isomer (Figure 9). Once again, the open-shell frontier orbitals provide a basis for understanding the observed regioselectivities for H atom adsorption. The HOMO of Ga12B (Figure 10a) is singly occupied and has large lobes on two of the triangular faces of

isomers reveals that much of the charge density for the local Ga2 subunit is redirected to the Ga−H bonds, which accounts for the lengthening of the Ga−Ga bond. Similarly, bonding in Ga2 subunits remote from the adsorption site are generally either unchanged or slightly enhanced by the H atom adsorbent, as shown by localized charge density on the 0.044 electrons Å−3 isosurfaces. The trends for the other decahedral-based Ga12XH isomers are generally similar, with localized bonding to hydrogen in atop isomers observed at high charge densities, bonding to hydrogen in bridge isomers observed at intermediate densities and bonding between Ga atoms present at lower charge densities. Analysis of the electron density isosurfaces also indicates that localized bonding in the Ga2 subunits of these Ga12XH clusters is more pronounced for species with groups 14 and 15 dopants, consistent with the observations for nonhydrogenated Ga12X clusters.20 B. Hydrogen Adsorption on Icosahedral-Based Clusters. Ga12X clusters with second-row endohedral dopants adopt icosahedral-like geometries. Hydrogen adsorption is observed at A1, B1, and H1 sites for Ga12B (Figure 7). The atop

Figure 7. Stable isomers of Ga12BH and Ga12CH clusters.

isomer exhibits a structure that closely resembles the isoelectronic atop isomer of Al13H.6,8 In particular, the X−Ga bond at the adsorption site is contracted (Table 3) and the Gaax−X−Gaax angle decreases to 162°. The bridge isomer also exhibits a contraction of X−Ga bonds at the adsorption site but the axial Ga−X−Ga bond angle remains close to 180°. Finally, hydrogen adsorption at a hollow site leads to very little disruption of the cluster framework. Stable Ga12CH structures were located for the A1 and B1 isomers (Figure 7). Hydrogen adsorption at the atop site of Ga12CH leads to asymmetry in the axial X−Ga bond lengths; however, there is very little change in the overall dimensions of the cluster. In comparison, H atom adsorption on a bridge site of Ga12C leads to a substantial elongation of the cluster axis parallel to the bridge site and significant changes in several other X−Ga bond lengths. Figure 8a depicts the potential energy surfaces for systematic distortion of the dimensions of the Ga12Si and Ga12C clusters. Contraction of the overall dimensions of both clusters leads to

Table 3. Structural Properties of Ga12XH Clusters (X = B and C; Å) Ga12XH A1

Ga12X

B1

H1

X

X-Ga

Ga-H

X-Ga

Ga-H

X-Ga

Ga-H

X-Ga

B C

2.540−2.600 2.547

1.555 1.571

2.363−2.665 2.324−2.783

1.780, 1.780 1.773, 1.779

2.425, 2.644 2.168−3.168

1.918, 1.928, 1.944

2.512−2.660

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Figure 10. Top and side views of the (a) HOMO and (b) LUMO of icosahedral Ga12X clusters.

The HOMO of Ga12C has the same shape as the HOMO of Ga12B but it is doubly occupied, leading to a less favorable interaction with H 1s. The LUMO of Ga12C is therefore the lowest energy open-shell orbital and therefore has the greatest influence on the regioselectivity for H atom adsorption. The LUMO has separate lobes at each of the surface gallium atoms that strongly favors atop adsorption. However, these atop lobes are all of the same phase so that bridge (B1) and hollow (H1) type interactions should be possible. Nevertheless, due to the size of these lobes and the distance between Ga atoms, overlap with the H 1s is quite small such that only the bridge isomer is observed. Previous analysis of the total electron density isosurfaces of Ga12X clusters with first row dopants reveals that bonding between the core and the surface Ga’s occurs at higher or similar isosurface values to that of Ga−Ga bonding, reflecting greater charge transfer between the surface and the core dopant atoms. Analysis of the icosahedral-based Ga12XH isomers indicates that the presence of the hydrogen adsorbent does not significantly impact on the preference for stronger bonding between the core and the surface atoms. In addition to this, the total electron density isosurfaces for Ga12BH and Ga12CH isomers are generally consistent with the trends described for the decahedral-based clusters, with localized bonding to hydrogen in atop isomers observed at high charge densities, bonding to hydrogen in bridge isomers observed at intermediate densities, and bonding between Ga atoms present at lower charge densities. However, bonding between hydrogen and the 3-fold hollow site (H1) of Ga12BH is evident at a charge density of 0.052 electrons Å−3 compared with 0.040 electrons Å−3 for the H2 isomers of Ga13H and Ga12AlH, which have 4-fold hollow sites. Clearly there is less delocalization of the bonding electrons in the H1 isomer, which is also reflected in the higher ΔHHads value.

Figure 8. Potential energy surfaces for (a) systematic change of overall dimensions of selected clusters and (b) for specific distortions of Ga12C cluster dimensions.

Table 4. Key Energetic Properties of Ga12XH Clusters (eV) A1 Ga12BH Ga12CH

B1

H1

ΔHHads

ΔHdist

ΔHHads

ΔHdist

ΔHHads

ΔHdist

−2.36 −1.39

+0.17 +0.08

−2.49 −1.28

+0.12 +1.28

−2.50

+0.03

4. CONCLUSIONS Hydrogen adsorption on doped gallium clusters Ga12X (X = B, C, Al, Si, P, Ga, Ge, and As) was investigated in this study using density functional theory. The structures and stability of the resulting cluster hydrides (Ga12XH) were also analyzed to identify trends in reactivity and adsorption site regioselectivity. Hydrogen adsorption is found to be energetically favorable on all of the investigated clusters, but adsorption energies vary significantly with valence electron count and with adsorption site. The open-shell 39-valence electron clusters (Ga12B, Ga12Al, and Ga13) generally have the highest adsorption energies, whereas the hydrogen adsorption on the closed-shell Ga12C, Ga12Si, and Ga12Ge clusters is found to be substantially less favorable.

Figure 9. Eigenvalue spectra for icosahedral-based Ga12X and Ga12XH clusters.

the cluster that enable H1-type adsorption. Likewise, there are lobes located between many pairs of Ga atoms that facilitate B1-type adsorption of H atom. These lobes are less well suited to atop adsorption, which requires greater hybridization of the cluster orbitals to enable significant overlap with the H 1s orbital. The LUMO of Ga12B is ideally suited for atop adsorption but analysis of the hydride orbitals reveals that it plays no part in the bonding to hydrogen. 26277



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(7) Khanna, S. N.; Jena, P. Reactivity of Hydrogen with Open and Closed Shell Clusters. Chem. Phys. Lett. 1994, 218, 383−386. (8) Henry, D. J.; Varano, A.; Yarovsky, I. Performance of Numerical Basis Set DFT for Aluminum Clusters. J. Phys. Chem. A 2008, 112, 9835−9844. (9) Burkart, S.; Blessing, N.; Klipp, B.; Müller, J.; Ganteför, G.; Seifert, G. Experimental Verification of the High Stability of Al13H: A Building Block of a New Type of Cluster Material? Chem. Phys. Lett. 1999, 301, 546−550. (10) Varano, A.; Henry, D. J.; Yarovsky, I. Role of Hydrogen in Dimerization of Aluminum Clusters: A Theoretical Study. J. Phys. Chem. A 2011, 115, 7734−7743. (11) Henry, D. J.; Varano, A.; Yarovsky, I. First Principles Investigation of H Addition and Abstraction Reactions on Doped Aluminum Clusters. J. Phys. Chem. A 2009, 113, 5832−5837. (12) Varano, A.; Henry, D. J.; Yarovsky, I. DFT Study of H Adsorption on Magnesium-Doped Aluminum Clusters. J. Phys. Chem. A 2010, 114, 3602−3608. (13) Wang, L.; Zhao, J.; Zhou, Z.; Zhang, S. B.; Chen, Z. FirstPrinciples Study of Molecular Hydrogen Dissociation on Doped Al12X (X = B, Al, C, Si, P, Mg, and Ca) Clusters. J. Comput. Chem. 2009, 30, 2509−2514. (14) Henry, D. J.; Yarovsky, I. Dissociative Adsorption of Hydrogen Molecule on Aluminium Clusters: Effect of Charge and Doping. J. Phys. Chem. A 2009, 113, 2565−2571. (15) Moc, J.; Bober, K.; Mierzwicki, K. Trimers and Tetramers of MH and MH3 (M = Al, Ga): Theoretical Study. Chem. Phys. 2006, 327, 247−260. (16) Maatallah, M.; Cherqaoui, D.; Jarid, A.; Liebman, J. F. Large Gallanes and the PSEPT Theory: A Theoretical Study of GanHn+2 Clusters (n = 7−9). J. Mol. Model. 2012, 18, 3321−3328. (17) Charkin, O. P.; Klimenko, N. M.; Moran, D.; Mebel, A. M.; Charkin, D. O.; Schleyer, P. v. R. Theoretical Study of Complexes of Closo-Borane, Alane, and Gallane Anions with Cations of Light Metals Inside and Outside of Icosahedral Clusters [Al12H12]2− (A = B, Al, and Ga). J. Phys. Chem. A 2002, 106, 11594−11602. (18) Moc, J. Interaction of Ga3 Cluster with Molecular Hydrogen: Combined DFT and CCSD(T) Theoretical Study. Eur. Phys. J. D 2009, 53, 309−317. (19) Henry, D. J.; Szarek, P.; Hirai, K.; Ichikawa, K.; Tachibana, A.; Yarovsky, I. Reactivity and Regioselectivity of Aluminum Nanoclusters: Insights from Regional Density Functional Theory. J. Phys. Chem. C 2011, 115, 1714−1723. (20) Henry, D. J. Structures and Stability of Doped Gallium Nanoclusters. J. Phys. Chem. C 2012, 116, 24814−24823. (21) Schnöckel, H. Formation, Structure and Bonding of Metalloid Al and Ga Clusters. A Challenge for Chemical Efforts in Nanosciences. Dalton Trans. 2008, 4344−4362. (22) 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.; et al. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (23) 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.; et al. Gaussian 09, Revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. (24) Gaston, N.; Parker, A. J. On the Bonding of Ga2, Structures of Gan Clusters and the Relation to the Bulk Structure of Gallium. Chem. Phys. Lett. 2011, 501, 375−378. (25) Guo, L. Computational Investigation of GanAl (n = 1−15) Clusters by the Density Functional Theory. Comput. Mater. Sci. 2009, 45, 951−958. (26) Yi, J.-Y. Stability, Structural Transformation and Reactivity of Ga13 Clusters. Phys. Rev. B 2000, 61, 7277−7279. (27) Song, B.; Cao, P.-I. Evolution of the Geometrical and Electronic Structures of Gan (n = 2−26) Clusters: A Density Functional Theory Study. J. Chem. Phys. 2005, 123, 144312−1−144312−8.

Analysis of the orbitals of the hydrides reveals that that there is interaction between H 1s and a range of hybrid cluster orbitals. The strength of the H-cluster bond is largely determined by the interaction between the H 1s orbital and one or more orbitals from the Jellium-like 1d or 2s bands of orbitals. However, orbital analysis also reveals that the interactions with the open-shell frontier orbitals are important in explaining the observed regioselectivities for H atom adsorption on these clusters. Consequently, in the Ga12Al and Ga13 clusters, reactivity is generally high at or adjacent to the covalently bonded Ga2 subunits, because the singly occupied HOMO is concentrated in these regions. Increases in reactivity at the axial positions are observed for Ga12Si and Ga12Ge, because the HOMO of these clusters is doubly occupied and, therefore, the LUMO is the key orbital directing interactions with H atom. Finally, in the open-shell Ga12P and Ga12As, the axial aligned orbital becomes a singly occupied HOMO and reactivity is further aligned along the cluster axis. Additionally, electronrich clusters preferentially engage in very localized bonding with hydrogen, whereas electron deficient clusters exhibit a greater number of isomers with delocalized bonding to hydrogen. These trends suggest that there is potential to tune the reactivity of gallium clusters to promote specific types of interaction not only with atomic adsorbents but with a range of small molecules and ligands. The icosahedral-based clusters Ga12B and Ga12C behave in a very similar manner to their aluminum counterparts, with clear differences in reactivity based on total-valence electron configuration and similar regioselectivities for H adsorption. Hydrogen adsorption at some sites on these clusters leads to significant distortions of the Ga12X framework. However, a single H atom does not appear to provide a sufficient perturbation of the bonding in the decahedral-based clusters, to bring about a transformation to icosahedral or cuboctahedral symmetry, as observed in more saturated systems.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +(61 8) 9360 2681. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges generous allocations of computing time from the Australian National Computational Infrastructure (NCI) facility.

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REFERENCES

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