Molybdenum Oxides versus Molybdenum Sulfides: Geometric and

ARTICLE pubs.acs.org/JPCA

Molybdenum Oxides versus Molybdenum Sulfides: Geometric and Electronic Structures of Mo3Xy (X = O, S and y = 6, 9) Clusters Nicholas J. Mayhall, Edwin L. Becher III, Arefin Chowdhury, and Krishnan Raghavachari* Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States

bS Supporting Information ABSTRACT: We have conducted a comparative computational investigation of the molecular structure and water adsorption properties of molybdenum oxide and sulfide clusters using density functional theory methods. We have found that while Mo3O6- and Mo3S6- assume very similar ring-type isomers, Mo3O9- and Mo3S9- clusters are very different with Mo3O9- having a ring-type structure and Mo3S9- having a more open, linear-type geometry. The more rigid — (Mo-SMo) bond angle is the primary geometric property responsible for producing such different lowest energy isomers. By computing molecular complexation energies, it is observed that water is found to adsorb more strongly to Mo3O6- than to Mo3S6-, due to a stronger oxide-water hydrogen bond, although dispersion effects reduce this difference when molybdenum centers contribute to the binding. Investigating the energetics of dissociative water addition to Mo3X6- clusters, we find that, while the oxide cluster shows kinetic site-selectivity (bridging position vs terminal position), the sulfide cluster exhibits thermodynamic site-selectivity.

’ INTRODUCTION Molybdenum sulfide has long been used as an efficient hydrodesulfurization and hydrogenation catalyst.1 More recently, there has also been an emerging interest in MoS2 as a photocatalyst for the efficient production of H2. Li and co-workers have recently reported great enhancements in H2 evolution on CdS following the loading of a small amount (0.2 wt %) of MoS2 cocatalyst in the presence of sacrificial reagents.2,3 However, very little work has been done thus far to understand the interactions between water and molybdenum sulfide clusters at the molecular level. In the past few years, many studies have been undertaken to investigate Group VI metal oxides using small molecular clusters by both experimental and theoretical means.4-21 Focusing on water reactivity, we have recently investigated the interactions of small tungsten oxides and water to understand the associated reaction mechanisms.22-25 From those investigations, we have observed that initial water adsorption and subsequent proton mobility are the critical components that characterize the chemistry between small tungsten oxide anion clusters and water. Prior to computing chemical interaction energies, the geometric as well as the electronic structures of the reactants must first be understood. While there has been a significant amount of research in determining the structure of molybdenum and tungsten sulfides on the nanoscale,26-32 the factors that determine the structures and stabilities of small molybdenum sulfide clusters are still not clearly understood. For example, though several published reports on the computation of the structures of anionic and neutral Mo3S9 clusters are available, they show significant differences among each other in r 2011 American Chemical Society

their findings regarding the lowest energy isomers.33-37 While most of the isomers identified in these studies are based on a central Mo3 cyclic unit, they vary in the number and location of terminal sulfide, bridging sulfide, and S2 units. As a knowledge of the low-lying geometric isomers is a prerequisite for chemical consideration, more work is warranted to reach definitive results on these important catalytic systems. In this paper, we initiate studies aimed at understanding the chemistry and structure of molybdenum sulfide clusters via comparison to the more well studied molybdenum oxide clusters. We compare the geometric structures of the Mo3O(6,9) and Mo3S(6,9) clusters. These clusters are of particular interest due to the stoichiometries of the bulk oxide (O/Mo = 3) and sulfide (S/ Mo = 2) materials. In addition to the calculation of the lowest energy isomers, we investigate the process of water adsorption and dissociation onto Mo3X6 clusters.

’ COMPUTATIONAL METHODS All geometry optimizations and frequency calculations were performed using the B3LYP hybrid density functional method38,39 using the Stuttgart-Dresden (SDD) relativistic pseudopotentials to replace the 28 core electrons on molybdenum and an augmented version of the associated double-ζ basis set to treat molybdenum’s 14 remaining electrons.40 To properly describe anionic wave Received: September 1, 2010 Revised: January 18, 2011 Published: March 03, 2011 2291

dx.doi.org/10.1021/jp108344k | J. Phys. Chem. A 2011, 115, 2291–2296

The Journal of Physical Chemistry A

ARTICLE

Figure 2. Lowest energy isomers for Mo3O9 (left) and Mo3S9 (right). Bond lengths and bond angles given in Å and degrees, respectively. Relative free energies at 298 K in eV.

Figure 1. Lowest energy isomers for Mo3O9 (left) and Mo3S9 (right). Bond lengths and bond angles given in Å and degrees, respectively. Relative free energies at 298 K in eV.

functions, diffuse s-, p-, and d-functions were added to the molybdenum centers using an exponent ratio of 0.3 to maintain eventempered basis set behavior,41 and the augmented triple-ζ aug-ccpVTZ basis sets were used for oxygen, sulfur, and hydrogen atoms.42 Finally, two f-type functions (ζf = 0.338, 1.223) and one g-type function (ζg = 0.744) were added to the molybdenum basis set, as recommended by Martin and Sundermann.43 Counterpoise corrections were included to estimate the basis set superposition errors (BSSE) associated with calculating the complexation energies.44,45 To estimate the possible errors in B3LYP, the geometries and energies of complexation were also obtained using the B97 functional46,47 (via the B972 keyword in Gaussian48) and the B97-D functional of Grimme.49 All relevant structures are included in the Supporting Information. All calculations were performed using the development version of the Gaussian suite of electronic structure programs.48

’ RESULTS Molecular Geometries. The lowest energy isomers for the Mo3X6 and Mo3X9 clusters are shown in Figures 1 and 2, respectively. The molecular symmetries and electronic states are given for each isomer along with their relative energies and key geometric parameters. Mo3X6 . From Figure 1, the similarities between the most stable oxide and sulfide clusters are readily seen. Both assume configurations consisting of a triangular Mo3 core with each Mo center supporting a terminal ModX bond and two bridging Mo-X bonds. The lowest energy isomer for each cluster exhibits C3v symmetry with a 2A1 electronic state. This “ring” geometry scheme is particularly stable for y = 6; the second lowest energy structure also has a ring configuration making it an excited spin state (quartet) for both systems, lying 0.3 and 0.5 eV higher in

energy for Mo3O6 and Mo3S6 , respectively. Given the large difference between the metal-oxide and metal-sulfide bond lengths, it is interesting that, for both of the Mo3X6 ground doublet states, the metal-metal bonds are nearly equidistant at 2.58 Å. Interestingly, the Mo-Mo distance is shorter than the corresponding distance in molybdenum metal (2.725 Å), suggesting that direct metal-metal bonding may contribute to the stability of these systems. Mo3X9 . While the lowest energy isomers for the oxide and sulfide y = 6 clusters were found to be very similar, the corresponding oxide and sulfide y = 9 clusters assume completely different geometric configurations. In Figure 2, the most stable isomers are shown for the Mo3O9 and Mo3S9 clusters (ring oxide and open sulfide, bottom) along with the complementary isomer for both systems (open oxide and ring sulfide, top). The lowest energy isomer for Mo3O9 is a C2v ring structure with two Mo = O bonds and two Mo-O bonds on each Mo center and no metal-metal bonding (the Mo-Mo distance is 3.45 Å, substantially longer than in molybdenum metal). All metal centers are roughly tetrahedrally coordinated. The lowest energy isomer for Mo3S9 , however, has an open “linear” structure with only two tetrahedral Mo centers and one central near-square-pyramidal, penta-coordinate Mo center. Here, both of the tetrahedral Mo centers have two ModS and two Mo-S bonds each, while the penta-coordinate Mo has one ModS and four Mo-S bonds. It is quite interesting to see such different structures become favored for the sulfide clusters. In previous work on anionic and neutral Mo3S9, other interesting geometries such as those containing η2-S2 units have also been reported.36,37 We have found those structures to be significantly higher in energy than the linear structure reported in this paper (particularly, for the anion), and hence, these isomers are not shown in this work. We do note, however, that the penta-coordinate -MoS5- bonding motif seen in our ground state structure has been observed experimentally in both molecules50-52 and solids.33 To understand why the Mo3S9 cluster assumes such a different geometry than the Mo3O9 cluster, we break down the atomization energies into three components: bonding, electron affinity (EA), and geometry effects, such as ring strain.

2292

dx.doi.org/10.1021/jp108344k |J. Phys. Chem. A 2011, 115, 2291–2296

The Journal of Physical Chemistry A

ARTICLE

Table 2. Atomization Energy Decomposition into Bonding a and Electron Affinity of the Ring and Linear Mo3X9 Clusters Ebonding X=

Figure 3. Structures used to estimate the ModX and Mo-X bond strengths for X = O and S.

Table 1. Estimation of MdX and M-X bond strengths (0 K) in eV for X = O,S X=O

X=S

ΔX

ModX

5.93

4.15

1.78

Mo-X

4.14

3.02

1.12

E(π)

1.79

1.13

0.66

This is shown below: Eatomization ¼ Ebonding þ EEA þ Egeometry To find Ebonding, we have computed estimations of the ModX and Mo-X bond strengths for X = O and S. This has been done by calculating the binding energies of two different clusters (MoX3 and Mo2X6), which have different numbers of double and single bonds. The structures are represented in Figure 3. As MoX3 has 3 double bonds, and Mo2X6 has 4 double bonds and 4 single bonds, the bond strengths can be estimated as EðModXÞ ¼ EðMo-XÞ ¼

ΔE1 3

ΔE2 - EðModXÞ 4

where ΔE1 : MoX3 f Mo þ 3X ΔE2 : Mo2 X6 f 2Mo þ 6X The double and single bond strengths for both X = O and X = S are given in Table 1. We note that, while we have used B3LYP to estimate the bond strengths, our estimations for molybdenum oxygen bonds are close to the complete basis set CCSD(T) results obtained by Dixon and co-workers, with values of 5.96 eV (137.4 kcal/mol) and 4.21 eV (97.0 kcal/mol) for Mo-O bonds, respectively.20 Values for EEA are simply obtained by the difference in zeropoint corrected energies of the anion and neutral structures each at their respective optimized geometries. Egeometry includes all other effects that contribute to the atomization energy. For the Mo3X9 clusters, the ring structures each have 6 single and 6 double bonds. The linear structures, however, have 5 double bonds and 8 single bonds. Because a π-bond is significantly weaker than a σ-bond, both Mo3O9 and Mo3S9 would favor a linear structure over a ring structure based solely on bond energies. As shown in Table 2, the values for Ebonding favor the linear structure by 2.4 and 1.9 eV for the oxide and sulfide, respectively. It is quite interesting that, despite the fact that the oxide ring structure is more stable, the oxide cluster has a stronger linear structure bonding stabilization than the sulfide structure. In addition to the bonding, for both oxide and sulfide the EEA stabilizes the linear structure over the ring structure. This is not surprising because a linear arrangement allows the charges to be distributed over a greater distance, resulting in lower

O

S

EEA O

S

ring 60.4 43.0 3.4 3.7 linear 62.8 44.9 4.4 5.1 Δ 2.4 1.9 1.0 1.4 a

Ebonding þ EEA

Eatomization

O

S

O

S

63.8 67.2 3.4

46.7 50.0 3.3

65.6 65.4 -0.2

47.6 48.3 0.7

Egeometry O

S

1.8 þ0.9 -1.8 -1.7 -3.6 -2.6

Relative energies at 0 K in eV.

electrostatic repulsion energy. It is also seen that for both isomers EEA is larger for Mo3S9 than for Mo3O9 , again consistent with simple expectations (e.g., atomic electron affinity of S vs O, 2.08 vs 1.46 eV).53 Once the bonding and electron affinities are accounted for (Ebonding þ EEA), the remainder of the adsorption energy in Table 2 is ascribed to the geometric effects. We see that there are significant geometric effects present in both the ring and the linear structures. Both the oxide and the sulfide clusters incur rather large energy penalties upon formation of a linear structure, -1.8 and -1.7 eV, respectively. While this may be partly ascribed to the simplicity of our decomposition scheme, the fact that they are very similar suggests that it is not a significant factor that contributes to the difference between the oxides and the sulfides. Formation of a ring structure, however, lowers the energy of both clusters, with the oxide being stabilized twice as much as the sulfide cluster. This difference in ring structure stabilization is ultimately responsible for the different lowest energy isomers reported in Figure 2. To understand why the ring structure is stabilized so much more for Mo3O9 than for Mo3S9 , we focus attention on the bond angles on the Mo centers in Figure 2. The key difference is that the bond angles around oxygen (Mo-O-Mo) are quite floppy and can have a large range of values without incurring significant energy penalties, while the bond angles around sulfur (Mo-SMo) can occur only in a narrow range. For Mo3O9 , the floppy — (Mo-O-Mo) bond angle extends to values as large as 148, as seen in the ring structure. This permits reasonable values without much distortion for the tetrahedral Mo centers (notice the — (O-Mo-O) angle of 103). The hybridization on the bridging sulfurs, however, prohibits such large bond angles (the — (Mo-S-Mo) angle does not exceed 100). Consequently, the metal centers in the Mo3S9 ring structure are forced to distort from tetrahedral to assume — (S-Mo-S) angles of around 120, and the molecule twists in order to alleviate some of the ring strain. The oxide and sulfide linear structures, do not differ significantly (except for the expected lower bond angles around sulfur), a similarity reflected in the geometries as seen in Figure 2 and the values of Egeometry for the linear structures as seen in Table 2. Therefore, we find that while the larger σ-bond/π-bond ratio results in the linear structures being favored over the ring structures based on bond energy estimates, the most important factor in determining the lowest energy isomer, however, is ultimately ring strain due to differences in the — (X-Mo-X) and — (Mo-X-Mo) angles. Water Adsorption. In recent work, we have found H2 elimination to be a rather facile result of reactions between unsaturated gasphase tungsten-oxide clusters and water.22-25 With the emerging interest in the use of MoS2-based catalysts in the photocatalytic production of H2 from water, it is our aim to initiate studies into the manner in which the cluster-water interactions are dependent on 23 the identity of X in Mo3Xy clusters. Our recent work suggests that 2293

dx.doi.org/10.1021/jp108344k |J. Phys. Chem. A 2011, 115, 2291–2296

The Journal of Physical Chemistry A

ARTICLE

Figure 4. Molecular electrostatic potential shown for isovalue = -0.11.

the energetics and the mode of initial adsorption dictate to a large extent which reaction pathways will be explored. In this section, we compare the formation of H2O 3 3 3 Mo3O6 and H2O 3 3 3 Mo3S6 molecular complexes. To provide a more direct comparison between oxides and sulfides, we focus only on the Mo3X6 clusters in this section because they have similar lowest energy isomers, as shown in Figure 1. The formation of a molecular complex is largely determined by the cluster’s molecular electrostatic potential (ESP). In Figure 4, the ESP for both Mo3O6 and Mo3S6 is shown. The blue surface, corresponding to an ESP isovalue of -0.11, represents regions that are attractive for a positive charge (i.e., water’s hydrogens) and repulsive to a negative charge (i.e., water’s oxygen). While complexes formed through X 3 3 3 H-OH hydrogen bonds are, no doubt, expected to be fairly stable, the ESPs shown in Figure 4 reveal windows of oxygen accessibility to the positive molybdenum center. This accessibility permits a stabilizing interaction between the water’s negative oxygen center and the positively charged Mo center at the expense of having to form a bent X 3 3 3 H-OH hydrogen bond. The shape of the ESPs gives rise to two predominant modes of adsorption resulting in two different complexes, A and B. Complex A involves three points of attraction, two X 3 3 3 HOH hydrogen bonds and one H2O 3 3 3 Mo interaction, while complex B involves only two points of attraction, two X 3 3 3 HOH hydrogen bonds. Each complex is shown in Figure 5 along with the corresponding adsorption difference density (ΔFAd), which is defined as ΔFad ¼ Fcluster þ H2 O - ðFcluster þ FH2 O Þ Positive values (gray) of ΔFAd indicate a region of density accumulation, while negative values indicate a region of density depletion. In Figure 5a,b, complex A ΔFad is shown for Mo3O6 and MoFS6 , respectively. In both figures, the water molecule has an orientation that allows for the three points of attraction, as described above. In Figure 5c,d, complex B ΔFad is shown for Mo3O6 and Mo3S6 , respectively. Here, the water molecule is complexed to the cluster via two hydrogen bonds. In Table 3, the adsorption energies are given for both types of complexes. In the results shown, counterpoise corrections have been included to estimate the BSSE, although this yields a minimal correction for all adsorption energies (no larger than 0.3 kcal/mol), indicating that our basis set is sufficient for these systems. Complex A versus Complex B. From Table 3, it is clear that complex A is the most favored adsorption configuration for both Mo3O6 and Mo3S6 . This can be seen clearly in Figure 5, which shows the greater extent of density accumulation between the

Figure 5. Adsorption density, ΔFad. Gray indicates regions of density accumulation (isovalue = þ0.002). Green indicates regions of density depletion (isovalue = -0.002). B3LYP densities used.

Table 3. Adsorption Energies (kcal/mol) for Two Modes of Complexationa complex A Mo3X6

þ H2O

B3LYP

B97

complex B B3LYP

B97

X=O

-12.9

-11.7 (-10.4)

-8.0

-7.7 (-9.5)

X=S

-9.3

-8.5 (-10.1)

-4.9

-4.7 (-6.6)

Energies are zero-point and counterpoise corrected: E = ESCF þ EZPE þ EBSSE. Values in parentheses have been obtained with empirical dispersion.49. a

water and cluster in complex A relative to complex B. While the ΔFad for complex B is primarily localized on the oxygen or sulfur groups, the ΔFad for complex A is quite delocalized throughout the metal system, indicating that the complex A-type adsorption processes will be much more sensitive to cluster geometry and spin state. In order to consider the effect of using different density functionals on this energy difference, we have also evaluated the adsorption energies using the B97 functional as well as with B97D where dispersion effects are included through an empirical correction.49 It is interesting to note that the empirical dispersion effects reduce the difference in adsorption energies between complex A and complex B, particularly for the oxide. Mo3O6 versus Mo3S6 . From the relatively large amount of density accumulation between the water and Mo3O6 clusters in Figure 5, it is clear that water adsorbs more strongly to the metal oxides than the metal sulfide clusters. Following inspection of the molecular electrostatic potentials in Figure 4, the preference of water binding to Mo3O6 over Mo3S6 (via complex A) is perhaps cluster appears to have a larger a bit surprising as the Mo3S6 “window” of accessibility, which would facilitate the stabilizing oxygen-Mo interaction (H2O 3 3 3 Mo). It is interesting to note, however, the inclusion of dispersion effects via the B97-D functional49 preferentially stabilizes the Mo3S6 complex A over complex A, yielding essentially equivalent binding the Mo3O6 energies (see parenthetical values in Table 3). Water Dissociation. To compare the relative affinity toward water addition of the Mo3O6 and Mo3S6 clusters shown in 2294

dx.doi.org/10.1021/jp108344k |J. Phys. Chem. A 2011, 115, 2291–2296

The Journal of Physical Chemistry A

Figure 6. Reaction profile for A þ B f C. Here, A is H2O, B is the bare Mo3X6 cluster, and C is the dihydroxide product cluster formed by one of the two pathways shown in the inset. For both oxide (red profiles) and sulfide (black profiles) clusters, the path 1 reaction is illustrated with a solid line, and the path 2 reaction is illustrated with a dashed line. Units of kcal/mol are used on the y-axis.

Figure 1, we turn our attention to the water-dissociating reactions between the cluster and single water molecule. In Figure 6, we show two reaction paths for both Mo3O6 and Mo3S6 in which water is added across either a terminal Mo-X bond or a bridging Mo-X bond. These two reaction paths have been studied for metal oxides in our previous work,23,25 and the transition states of the two paths are described by the inset in Figure 6. Upon inspection of these reaction profiles, it is immediately clear that Mo3O6 is more reactive toward water than Mo3S6 , considering both the barrier heights and the exothermicity for insertion. Further, while the Mo3O6 cluster has a strong kinetic preference for path 1, Mo3S6 appears to be quite insensitive to the position (bridging or terminal) of the acceptor sulfur atom. In addition to the differences in barrier heights, the product (Figure 6 “C”) of the water addition to Mo3O6 is slightly more stable when the Hþ acceptor is a bridging oxygen, whereas for Mo3S6 , the terminal position yields a much stronger proton acceptor than the bridged position. Therefore, we find that the strength of a proton acceptor depends not only on the position, but also on the identity of X (O or S). It is also interesting to note that for the (A 3 3 3 B f C) step, paths 1 and 2 are thermodynamically similar and kinetically dissimilar for Mo3O6 , whereas the opposite is observed for Mo3S6 .

’ CONCLUSIONS In this computational investigation, we have sought an understanding of the chemistry and structure of molybdenum sulfide clusters via comparison to the more well studied molybdenum oxide clusters. We have compared the geometric structures of the Mo3O(6,9) and Mo3S(6,9) clusters. These structures are of particular interest due to the stoichiometries of the bulk oxide (O/Mo = 3:1) and sulfide (S/Mo = 2:1) materials. From this work the following conclusions may be drawn: 1 The lowest energy isomers for the Mo3X6 clusters are very similar despite the inherent differences in the Mo-S and Mo-O bond lengths.

ARTICLE

2 The lowest energy isomers for the Mo3X9 clusters (higher S/Mo ratio than in bulk) are completely different, with the Mo3O9 cluster favoring a cyclic metal framework and the Mo3S9 cluster favoring an open structure. This is a result of differences in the — (Mo-X-Mo) bond angles imposing a greater ring strain in the Mo3S9 ring structure. 3 Water complexation to the Mo3X6 clusters can result in two main adsorption configurations, a more stable complex A with two hydrogen bonds and one H2O 3 3 3 Mo interaction and a less stable complex B with just two hydrogen bonds. 4 Due to the larger atomic charges and greater hydrogen bonding, molybdenum oxide clusters adsorb water more strongly than molybdenum sulfide clusters, although this difference in complex A binding is reduced with the inclusion of dispersion. 5 Dissociative water addition to Mo3X6 clusters is more exothermic and incurs lower barriers when X = O than when X = S. 6 Terminal sulfur atoms in a Mo3S6 cluster are better proton acceptors than bridging sulfur atoms, opposite of the trend observed for the analogous oxide systems. 7 Dissociative water addition is kinetically site-selective for Mo3O9 , but thermodynamically site-selective for Mo3O9 .

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional supporting data. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by a DOE Grant No. DE-FG0207ER15889. ’ REFERENCES (1) Chianelli, R. R.; Siadati, M. H.; la Rosa, M. P. D.; Berhault, G.; Wilcoxon, J. P.; Bearden, R.; Abrams, B. L. Catal. Rev. 2006, 48, 1–41. (2) Zong, X.; Yan, H. J.; Wu, G. P.; Ma, G. J.; Wen, F. Y.; Wang, L.; Li, C. J. Am. Chem. Soc. 2008, 130, 7176. (3) Zong, X.; Wu, G. P.; Yan, H. J.; Ma, G. J.; Shi, J. Y.; Wen, F. Y.; Wang, L.; Li, C. J. Phys. Chem. C 2010, 114, 1963–1968. (4) Bondarchuk, O.; Huang, X.; Kim, J.; Kay, B. D.; Wang, L. S.; White, J. M.; Dohnalek, Z. Angew. Chem., Int. Ed. 2006, 45, 4786–4789. (5) Huang, X.; Zhai, H. J.; Li, J.; Wang, L. S. J. Phys. Chem. A 2006, 110, 85–92. (6) Huang, X.; Zhai, H. J.; Waters, T.; Li, J.; Wang, L. S. Angew. Chem., Int. Ed. 2006, 45, 657–660. (7) Zhai, H. J.; Huang, X.; Cui, L. F.; Li, X.; Li, J.; Wang, L. S. J. Phys. Chem. A 2005, 109, 6019–6030. (8) Zhai, H. J.; Huang, X.; Waters, T.; Wang, X. B.; O’Hair, R. A. J.; Wedd, A. G.; Wang, L. S. J. Phys. Chem. A 2005, 109, 10512–10520. (9) Zhai, H. J.; Kiran, B.; Cui, L. F.; Li, X.; Dixon, D. A.; Wang, L. S. J. Am. Chem. Soc. 2004, 126, 16134–16141. (10) Zhai, H. J.; Wang, L. S. J. Chem. Phys. 2006, 125, 164315. (11) Bertram, N.; Kim, Y. D.; Gantefor, G.; Sun, Q.; Jena, P.; Tamuliene, J.; Seifert, G. Chem. Phys. Lett. 2004, 396, 341–345. (12) Sun, Q.; Rao, B. K.; Jena, P.; Stolcic, D.; Gantefor, G.; Kawazoe, Y. Chem. Phys. Lett. 2004, 387, 29–34. 2295

dx.doi.org/10.1021/jp108344k |J. Phys. Chem. A 2011, 115, 2291–2296

The Journal of Physical Chemistry A (13) Sun, Q.; Rao, B. K.; Jena, P.; Stolcic, D.; Kim, Y. D.; Gantefor, G.; Castleman, A. W. J. Chem. Phys. 2004, 121, 9417–9422. (14) Mayhall, N. J.; Raghavachari, K. J. Phys. Chem. A 2007, 111, 8211–8217. (15) Mayhall, N. J.; Rothgeb, D. W.; Hossain, E.; Raghavachari, K.; Jarrold, C. C. J. Chem. Phys. 2009, 130, 124313–10. (16) Li, S. G.; Dixon, D. A. J. Phys. Chem. A 2006, 110, 6231–6244. (17) Li, S.; Dixon, D. A. J. Phys. Chem. A 2007, 111, 11093–11099. (18) Li, S.; Dixon, D. A. J. Phys. Chem. A 2007, 111, 11908. (19) Zhai, H.-J.; Li, S.; Dixon, D. A.; Wang, L.-S. J. Am. Chem. Soc. 2008, 130, 5167. (20) Li, S.; Hennigan, J. M.; Dixon, D. A.; Peterson, K. A. J. Phys. Chem. A 2009, 113, 7861–7877. (21) Li, S.; Zhai, H.-J.; Wang, L.-S.; Dixon, D. A. J. Phys. Chem. A 2009, 113, 11273. (22) Rothgeb, D.; Hossain, E.; Kuo, A. T.; Troyer, J. L.; Jarrold, C. C.; Mayhall, N. J.; Raghavachari, K. J. Chem. Phys. 2009, 130, 124314. (23) Mayhall, N. J.; Rothgeb, D. W.; Hossain, E.; Jarrold, C. C.; Raghavachari, K. J. Chem. Phys. 2009, 131, 144302. (24) Rothgeb, D. W.; Hossain, E.; Mayhall, N. J.; Raghavachari, K.; Jarrold, C. C. J. Chem. Phys. 2009, 131, 144306. (25) Ramabhadran, R. O.; Mayhall, N. J.; Raghavachari, K. J. Phys. Chem. Lett. 2010, 1, 3066. (26) Tenne, R.; Margulis, L.; Genut, M.; Hodes, G. Nature 1992, 360, 444–446. (27) Margulis, L.; Salitra, G.; Tenne, R.; Talianker, M. Nature 1993, 365, 113–114. (28) Rapoport, L.; Bilik, Y.; Feldman, Y.; Homyonfer, M.; Cohen, S. R.; Tenne, R. Nature 1997, 387, 791–793. (29) Seifert, G.; Terrones, H.; Terrones, M.; Jungnickel, G.; Frauenheim, T. Phys. Rev. Lett. 2000, 85, 146. (30) Bertram, N.; Cordes, J.; Kim, Y.; Gantefor, G.; Gemming, S.; Seifert, G. Chem. Phys. Lett. 2006, 418, 36–39. (31) Enyashin, A. N.; Gemming, S.; Bar-Sadan, M.; Popovitz-Biro, R.; Hong, S. Y.; Prior, Y.; Tenne, R.; Seifert, G. Angew. Chem., Int. Ed. 2007, 46, 623–627. (32) Gemming, S.; Seifert, G.; Bertram, G. N.; Fischer, T.; G€otz, M.; Gantef€or, G. Chem. Phys. Lett. 2009, 474, 127–131. (33) Weber, T.; Muijsers, J. C.; Niemantsverdriet, J. W. J. Phys. Chem. 1995, 99, 9194–9200. (34) Jiao, H. J.; Li, Y. W.; Delmon, B.; Halet, J. F. J. Am. Chem. Soc. 2001, 123, 7334–7339. (35) Wen, X. D.; Zeng, T.; Li, Y. W.; Wang, J. G.; Jiao, H. J. J. Phys. Chem. B 2005, 109, 18491–18499. (36) Murugan, P.; Kumar, V.; Kawazoe, Y.; Ota, N. J. Phys. Chem. A 2007, 111, 2778–2782. (37) Gemming, S.; Seifert, G.; Gotz, M.; Fischer, T.; Gantefor, G. Phys. Status Solidi B 2010, 247, 1069–1076. (38) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (39) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (40) Andrae, D.; Haussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990, 77, 123–141. (41) Jensen, F. Introduction to Computational Chemistry, 2nd ed.; JohnWiley and Sons: Chichester, England; Hoboken, NJ, 2007. (42) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796–6806. (43) Martin, J. M. L.; Sundermann, A. J. Chem. Phys. 2001, 114, 3408–3420. (44) Simon, S.; Duran, M.; Dannenberg, J. J. J. Chem. Phys. 1996, 105, 11024. (45) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (46) Becke, A. D. J. Chem. Phys. 1997, 107, 8554–60. (47) Wilson, P. J.; Bradley, T. J.; Tozer, D. J. J. Chem. Phys. 2001, 115, 9233–42. (48) Frisch, M. J. et al. Gaussian Development Version, Revision H.08; Gaussian, Inc.: Wallingford, CT, 2010. (49) Grimme, S. J. Comput. Chem. 2006, 27, 1787–1799.

ARTICLE

(50) Spivack, B.; Dori, Z. Inorg. Nucl. Chem. Lett. 1975, 11, 501–503. (51) Pan, W. H.; Leonowicz, M. E.; Stiefel, E. I. Inorg. Chem. 1983, 22, 672. (52) Bernholc, J.; Stiefel, E. I. Inorg. Chem. 1985, 24, 1323–1330. (53) Hotop, H.; Lineberger, W. C. J. Phys. Chem. Ref. Data 1985, 14, 731.

2296

dx.doi.org/10.1021/jp108344k |J. Phys. Chem. A 2011, 115, 2291–2296