Evolution of Small Ti Clusters and the Dissociative Chemisorption of

P. Tarakeshwar, T. J. Dhilip Kumar, N. Balakrishnan. Hydrogen multicenter bonds and reversible hydrogen storage. The Journal of Chemical Physics 2009,...
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7494

J. Phys. Chem. C 2007, 111, 7494-7500

Evolution of Small Ti Clusters and the Dissociative Chemisorption of H2 on Ti T. J. Dhilip Kumar,* Philippe F. Weck, and N. Balakrishnan Department of Chemistry, UniVersity of NeVada Las Vegas, 4505 Maryland Parkway, Las Vegas, NeVada 89154 ReceiVed: December 20, 2006; In Final Form: March 27, 2007

The sequential growth of small titanium clusters with up to 15 atoms and the dissociative chemisorption of H2 on the minimum energy clusters have been studied within density functional theory under the generalized gradient approximation. It has been found that the low-energy clusters grow three dimensionally from Ti4 and follow a pentagonal growth pattern. The clusters Ti7 and Ti13 show a higher stability than other clusters with a configuration of pentagonal bipyramid and icosahedron structures, respectively. The second difference of binding energy plot indicates that these two clusters are highly stable; this agrees with the experimental collision-induced dissociation studies and previous theoretical calculations. For the first time, a systematic study of chemical reactivity of small Tin clusters, with n ) 2-15, toward dissociative chemisorption of H2 is performed. It is found that the chemisorption occurs preferentially at the two adjacent edges of any Ti atom. The chemisorption energy as a function of the cluster size shows considerable structural changes in the Tin clusters due to H2 dissociation and adsorption, and the chemisorption energy of Ti13 cluster is found to be the highest.

I. Introduction In the last two decades, a number of experimental and theoretical studies have been performed on atomic and molecular clusters of transition metals, largely due to potential applications as building blocks for functional nanostructure materials, electronic devices, and nanocatalysts.1-5 From the fundamental point of view, these clusters provide a unique opportunity to understand the evolution of cluster electronic structure from that of atoms in the bulk6 and also to study the physicochemical properties as a function of the cluster size. Among transition metals, chemical reactivity of titanium clusters is much less studied and understood. Because the free Ti atom possesses a large number of vacant valence d orbitals, the electronic structure and the reactivity of small titanium clusters would be different from other transition metal clusters. Early experiments7-10 performed on Ti2 clusters revealed that the binding energy varies from 2.1 to 1.05 eV, which was considered as the lowest limit by Haslett et al.8 In 1980, experimentally measured Raman spectrum of Ti2 isolated in an Ar matrix yielded a vibrational frequency of 407.9 cm-1.11 Experimentally, Ti clusters have been studied extensively by Lian et al.12 using the collision-induced dissociation (CID) method. CID cross sections of Ti+ n with Xe were measured as a function of the cluster ion kinetic energy. The experiments also allowed determination of bond energies, dissociation mechanisms, and likely geometric structures for Ti+ n (n ) 2-22) clusters. The electronic structure of Ti clusters has been probed by size-selected anion photoelectron spectroscopy by Wu et al.13 who observed that the 3d band emerges at the eightatom cluster beyond which the d band broadens and evolves toward that of the bulk. Burkart et al.14 reported the chemisorption of atomic hydrogen on negatively charged Tin clusters using mass and photoelectron spectroscopy. The data support preferential adsorption of molecular H2 with cluster size * To whom correspondence should be addressed. E-mail: dhilip. [email protected].

n ) 4, while dissociative hydrogen chemisorption occurs beyond that forming clusters with an electronic structure similar to that of bulk TiH2. Time-of-flight mass spectroscopy studies by Sakurai et al.15 showed that Tin clusters with n ) 7, 13, and 15 correspond to magic numbers with unusual stability. As early as 1976, theoretical calculations have been performed by Anderson16 to characterize the atomic structures of Ti clusters by utilizing molecular orbital theory and have found that Ti clusters have tightly packed structures up to n ) 6, (i.e., equilateral triangle for Ti3, rhombus for Ti4, trigonal bipyramid for Ti5, and octahedron for Ti6). In 1981, Cremaschi and Whitten17 studied the chemisorption of H2 on Ti (0001) surface using ab initio configuration interaction theory and concluded that the dissociation of H2 occurs at a distance significantly above the surface and the bonding between the two is mainly due to 4s electrons of Ti to hydrogen. The interaction between Ti-H in small metal clusters and hydrogen atom absorption by hcp titanium is studied using an embedding theory to describe the electronic bonding.18,19 In a subsequent study, Cremaschi and Whitten20 found that reaction of H with a clean Ti(0001) surface or with a Ti adatom on the surface is highly exothermic (3.6-4.7 eV). Bauschlicher et al.21 used the multireference configuration-interaction method (MRCI) to study the lowlying states of Ti2 and pointed out the difficulties in assigning the ground state due to many low-lying states and the correlation effect of inner-shell 3s and 3p orbitals on the binding energies of the structures. Wei et al.22 obtained atomic structures and properties of titanium clusters up to n ) 10 using density functional theory (DFT) with the local spin density approximation and concluded that the inner-shell electrons play a crucial role in the binding of small Ti clusters. Zhao et al. studied23 the structural and electronic properties of Tin clusters up to n ) 14 by plane wave ultrasoft pseudopotential method with the generalized gradient approximation (GGA). They observed pentagonal growth patterns, and the electron density of state showed similarity with the bulk due to the delocalization of 3d orbitals. The structural stability of icosahedral Ti13,

10.1021/jp068782r CCC: $37.00 © 2007 American Chemical Society Published on Web 05/01/2007

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Figure 1. The calculated cluster structures with their binding energies per atom for n ) 2 to 15. 24 Ti+ 13, and Ti13 clusters has been studied by Wang et al. using the DMOL cluster method based on DFT using GGA. They found that these clusters favor a D3d structure due to JahnTeller effect. Castro et al.25 performed a systematic study of the electronic and structural properties of small Tin (n ) 3-8, 13) clusters and their anions and found that the small Ti clusters possess multiple isomers and spin states with very close energies. Recently, Wang et al.26 studied the electronic structures of icosahedral, hexagonal close-packed, and face-centered cubic (fcc) close-packed Tin clusters (n ) 13, 19, 43, and 55) using a real-space first-principles cluster method with GGA for exchange-correlation potential. The calculations show that the clusters favored icosahedral structure except for n ) 43, in agreement with the collision-induced dissociation12 and sizeselected anion photoelectron spectroscopy experiments.25 Villanueva et al.27 presented a detailed structural analysis of small Tin clusters from n ) 2-15 through density functional calculations using GGA employing the Lee-Yang-Parr (LYP) functional parametrization.28 Their results further confirmed the exceptional stability of Ti7 and Ti13 clusters observed in

experimental studies. While much research effort has been devoted to study the physical properties of Ti clusters over the past few years, fewer studies have been devoted to the understanding of chemical reactivity of these clusters. Only bare Ti clusters have been studied both theoretically and experimentally.29,30 Ti-decorated nanomaterials have been found to be potential high-capacity hydrogen storage media due to unique Ti-H2 interactions.31-33 H2 chemisorption on Ti has been studied both experimentally and theoretically on various bulk surfaces.17,20,34,35 When Ti is added as a dopant, it plays an important role in the crucial first step to trap hydrogen within a particular class of hydrogen storage materials.36-39 The hydrogenation and dehydrogenation measurements indicate that the small size of the Ti clusters added in catalytic amount increases the reaction rate of some of the hydrogen storage materials such as complex metal hydrides.40,41 Hence, the examination of electronic and structural properties would yield useful information on the chemical reactivity of Ti clusters. Here, we report a systematic study of the structure evolution of small titanium clusters, and

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Figure 2. Comparison of calculated binding energies per atom of Tin and Ti+ n pentagonal growth clusters and the experimental bond dissociation energies of Ti+ n with n. The experimental bond dissociation energies were measured by collision-induced dissociation studies.12

Figure 3. Adiabatic and structure-relaxed IPs of Tin clusters plotted as a function of n.

for the first time the chemical reactivity of small Ti clusters toward dissociative chemisorption of H2 up to n ) 15. We hope that this study will advance our fundamental understanding of dissociative adsorption of hydrogen in Ti nanoclusters and suggest new routes to find better hydrogen storage and catalytic materials for fuel cell applications. The paper is organized as follows: The details of the computational methodology are given in Section II, followed by a presentation and discussion of the results in Section III. A summary of our findings and conclusions are given in Section IV. II. Computational Details The calculations were performed using DFT within the GGA with the Perdew-Wang exchange-correlation functional42 (PW91) as implemented in the DMOL3 package.43 This method can perform accurate and efficient self-consistent calculations using a rapidly convergent three-dimensional numerical integration scheme. DFT techniques account for exchange-correlation in

Kumar et al.

Figure 4. Comparison of calculated adiabatic and structure-relaxed EAs of Tin clusters with the experimental values25 plotted as a function of n.

Figure 5. Comparison of calculated second difference of highest binding energies of Tin clusters with the GGA/LYP results27 as a function of n.

many electron systems by the GGA, and they are suitable for studying transition metal clusters.44 Recent theoretical studies on small Ti clusters have been performed using this method23,25 although the results of electron affinities and density of states show significant deviations from the experimental measurements. Hence, our calculations involving GGA using PW91 functional will perform reasonably well over other methods. Double numerical basis sets augmented with polarization functions (DNP) were utilized to describe all the electrons of Ti because inner-shell (3s and 3p) effect is a crucial factor in the binding of small Ti clusters.22 The size of the DNP basis sets is comparable to that of the Gaussian 6-31G** basis sets, but the numerical basis set is more accurate than a Gaussian basis set of the same size. With Ti being an early transition metal, the inner orbitals such as 3s and 3p are close to valence states and play an important role in the formation of the cluster and predicting the ground-state properties of Ti clusters. All clusters and the chemisorption geometries were fully optimized without spin restrictions and without imposing symmetry constraints using an energy convergence tolerance of 10-6 hartree. For accurate calculations, we have chosen an octupole

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Figure 7. Dissociative chemisorption energy of H2 on Tin as a function of n.

TABLE 1: Hirshfeld Charges on the Ti Atom and Two H Atoms in the Lowest Total Energy H2 Chemisorbed Clusters

Figure 6. H2 chemisorbed structures and their bond lengths (in Å) and the chemisorption energies ∆ECE (in eV) for the Tin-H2 system for n ) 2 to 15.

scheme for the multipolar expansion of the charge density and Coulomb potential. In the generation of the numerical basis sets, a global orbital cutoff of 4.5 Å was used. The maximum force and the maximum displacement were less than 0.002 eV/Å and 0.005 Å, respectively. III. Results and Discussion A. Electronic Structure of Tin Clusters (n ) 2-15). For a given cluster size, a variety of initial structures were selected followed by energy minimization, yielding numerous stable

cluster size, n

Ti

H1

H2

2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.1184 0.1276 0.1144 0.1484 0.1162 0.1319 0.0485 0.0433 0.1251 0.1478 0.0641 0.0865 0.0449 0.0723

-0.1684 -0.1912 -0.182 -0.1761 -0.1782 -0.1757 -0.1434 -0.144 -0.1463 -0.1832 -0.1430 -0.1418 -0.1387 -0.1359

-0.1684 -0.1912 -0.1816 -0.1762 -0.1783 -0.1757 -0.1434 -0.144 -0.1755 -0.1832 -0.1428 -0.1416 -0.1387 -0.1313

isomers. The cluster structural search scheme used in our calculations is to add a new atom on the preceding cluster with the highest binding energy at various possible binding sites and then to identify the energetically most stable site via geometry optimization. The computational complexity increases quite rapidly as the cluster size increases. To speed up the structural search, the geometry optimization was conducted by searching the structures for all the possible potential minima and using only the clusters with the highest binding energies. In this way, we systematically built structures of the n + 1 clusters from these minimum or nearly minimum energy structures. The principle behind building these structures was that the most stable new n + 1 clusters were built upon the most stable or nearly most stable n-preceding clusters. In Figure 1, the various isomers of optimized titanium clusters are shown along with some characteristic cluster binding energies per atom. As can be seen from Figure 1, the electronic energies of various isomers for each cluster is very close. For Ti3, the triangular structure was more stable than the linear structure (not shown) by 0.4138 eV. For Ti4, the binding energy of the tetrahedral geometry was higher than the two-dimensional planar structure by 0.1278 eV. We have optimized two isomers for n ) 5, for which the three-dimensional trigonal bipyramid structure was found to be more stable than the nearest energy two-dimensional planar structure by 0.3565 eV. Four isomers for Ti6 cluster were optimized of which three are of nearly degenerate energies with the octahedral structure being more stable than the other three (only octahedral and next stable isomer are shown). In the case of Ti7 cluster, we obtained a pentagonal bipyramid structure as the ground state, and it was energetically lower than the face-capped octahedron by 0.1620 eV. We obtained four low-energy structures for Ti8. An additional atom capped on

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the pentagonal bipyramid structure of Ti7 yields the groundstate structure of Ti8. It was more stable over other three isomers. Similarly, we obtained various isomers of Tin clusters until n ) 15 and all n + 1 structures face-capped with n-structure were found to be lower in energy than the other possible isomers. As the cluster size increases, the pentagonal bipyramid structure was seen as the core structure for Tin clusters for n ) 7-15. The structures of Ti11 and Ti12 appear like incomplete icosahedron. For n ) 13, complete icosahedron structure was obtained as the minimum. In general, the small Ti clusters preferably evolve in pentagonal pyramidal arrangements to attain maximum stability in its closed structure. The tightly packed structures found in Ti clusters were expected due to the delocalization of 3d electrons. Moreover, the existence of only two d electrons in Ti atoms gives rise to empty antibonding d orbitals, facilitating close-packed structures. The cluster binding energy per atom was calculated using the following expression:

∆EBE ) [E(Tin) - nE(Ti)]/n,

(n ) 2,3,....,15)

(3.1)

where E(Tin) represents the electronic energy of Tin cluster and E(Ti) is the electronic energy of the Ti atom. Figure 2 shows the comparison between calculated binding energy per atom of Tin and Ti+ n clusters corresponding to the most stable isomer with the experimental bond dissociation energies of Ti+ n clusters measured by collision-induced dissociation studies.12 In theoretical calculations, the binding energy per atom of the clusters increases rapidly as the cluster size is increased until n ) 7 and then increases monotonically with the cluster size indicating that the clusters become increasingly stabilized. Our results are in close agreement with recently reported values of Villanueva et al.27 obtained using the LYP functional for GGA.28 The experimental binding energies of the cationic cluster vary between 2.5-4.5 eV with maxima for n ) 7 and 13. Upon extrapolation of the data to 1/n f 0, we obtained a value of 4.91 eV for the binding energy per atom for the infinitely large cluster. The extrapolated value is consistent with the experimental cohesive energy12 of 4.88 ( 0.17 eV for bulk Ti. The ionization potential (IP), and electron affinity (EA) of the Tin clusters are evaluated according to

IPn ) E(Ti+ n ) - E(Tin)

(3.2)

EAn ) E(Tin ) - E(Tin)

(3.3)

and

where E(Ti+ n ) and E(Tin ) represent the optimized electronic energies of cationic and anionic Tin clusters, respectively. The experimental ionization potential of Ti atom is 6.82 eV compared to our calculated value of 6.52 eV. Figure 3 displays the calculated adiabatic and structure-relaxed IPs as a function of the cluster size, n. The structure-relaxed IP is found to be lower than the adiabatic IP. In both cases, IP decreases from the maximum as the cluster size increases until n ) 4 and then remains largely constant until n ) 15 with a local maximum for Ti13 as shown in Figure 3. Figure 4 shows the calculated adiabatic and structure-relaxed EAs along with experimental EA as a function of cluster size, n. Our calculated values are smaller than the experimental values.25 The significant difference between the calculated and the experimental EAs observed here is largely due to the noninclusion of diffused functions in the basis set, which is known to be important for negatively charged

Figure 8. Variation of HOMO-LUMO gap with cluster size for (a) Tin and (b) H2 chemisorbed Tin clusters.

species. The EA value increases gradually as the cluster grows with a minimum at n ) 7, as shown in Figure 4, in agreement with the experimental data. The ionization potential and electron affinity are the most important quantities that can be used to signal the onset of metallic characteristics in the metal cluster because both of the parameters converge to their bulk limit (work function of solid) linearly with n-1/3. We have analyzed the stability of clusters by computing the second difference of binding energies according to

∆2E ) E(n + 1) + E(n - 1) - 2E(n)

(3.4)

Figure 5 shows the comparison between the present results for the highest binding energy clusters with the recently reported GGA/LYP results of Villanueva et al.27 as a function of the cluster size, n. The present results are in close agreement with the GGA/LYP results except for Ti8 and Ti12 for which the present results predict higher stability. In both the plots, two predominant peaks for n ) 7 and 13 were found, corresponding to the pentagonal bipyramid and icosahedron structures, respectively, which reflect the high stability of these clusters. The theoretical prediction of extremely high stabilities for Ti7 and Ti13 agrees well with the experimental mass spectra results.12,15 B. Chemisorption of H2 on Tin (n ) 2-15) Clusters. The main objective of the present work is to understand the chemical

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Figure 9. DOS plots of (a) Tin and (b) H2 chemisorbed Tin clusters. The Fermi energy is set to zero. A Gaussian broadening of 0.05 eV is used.

reactivity of small Ti clusters toward molecular hydrogen. We performed minimum energy structural search for H2 dissociative chemisorption on the geometry-optimized bare Ti clusters from n ) 2-15 with the lowest and the second lowest energy isomers and with higher binding energy isomers calculated earlier. The chemisorption of H2 on Ti bulk surfaces is found to be dissociative.17 Hence, two H atoms were brought to the clusters from various directions and distances for examination on possible sites for chemisorption. It turns out that the hydrogen atoms always prefer to adsorb at the two adjacent edges of any Ti atom, instead of being far apart. In Figure 6, some of the most energetically favorable H2 dissociative chemisorption sites and the structures studied were shown along with the chemisorption energies and their bond lengths. The hydrogen atoms were highlighted with the dark color, and the first structure of various possible isomers obtained for a cluster of a given size was of the minimum energy. The chemisorption energy, which is the energy to form the Tin-H2 species from Tin and H2, was evaluated from the calculated energies of cluster with H2 adsorbate, the Ti bare cluster, and the H2 molecule using the equation

∆ECE ) E(Tin) + E(H2) - E(Tin - H2)

(3.5)

The calculated chemisorption energies (∆ECE) corresponding to the most energetically favorable chemisorption site are shown

in Figure 7 as a function of the cluster size. As Figure 7 illustrates, ∆ECE increases until n ) 4 initially and then decreases reaching a lowest value of 1.82 eV for n ) 7. ∆ECE increases rapidly with subsequent increase in n, attaining a maximum value of 2.5 eV for n ) 13. It is interesting to note that the H2 chemisorption energy is found to be the lowest for the stable Ti7 cluster but highest for the most stable cluster Ti13. Experimental measurements also indicate that when Ti13 cluster is added as a catalyst, it increases the reaction rate of hydrogenation and dehydrogenation processes in alanates.40 The dissociative chemisorption of H2 on Ti clusters is governed by a charge-transfer process in which the H atoms withdraw electrons from the nearby metal atom. Table 1 shows the calculated Hirshfeld charges on the two H atoms in each minimum energy clusters. The chemisorption apparently results in the formation of metal hydride with H atoms withdrawing charges from the metal atoms. As can be inferred from Table 1, the magnitude of charge transfer is found to be high for smaller clusters and then decreases attaining a constant value as the cluster size is increased. As the energetic stability of the system is governed by the magnitude of energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO),45 we have computed the HOMO-LUMO energy gap for the Tin clusters before and after H2 chemisorption. The result is shown in Figure 8a,b. Generally, the HOMOLUMO gap is found to be larger for Tin clusters than H2 chemisorbed Tin clusters. It is seen that in both cases, the energy gap generally decreases with increase in cluster size except for n ) 4, 7, 13, and 15 for which the energy gap is high. Tetrahedral Ti4 has three-dimensional structure and increased stability compared to its neighbors. The prediction of high values of the HOMO-LUMO gaps for Ti7, Ti13, and Ti15 is consistent with the high stability of close-shell geometries of magic number clusters.46 The high stability of Ti7 and Ti13 clusters is consistent with the previous theoretical calculations22,23 and anion photoelectron spectroscopic studies.25 Our results for the bare clusters are in close agreement with those reported recently by Villanueva et al.27 Again the high stability of Ti13 is retained even after hydrogen adsorption. We have explored the geometric effect on the cluster electronic structure by examining the electronic density of states (DOS). In Figure 9a,b, the calculated density of states of Tin clusters and the most energetically favorable H2-chemisorbed Ti clusters for n ) 2-15 are shown. The DOS of small clusters is molecule-like with discrete peaks, as shown for n ) 2. As the size of the cluster is increased, these molecular levels overlap to give a continuous band due to the delocalization of 3d orbitals as shown in Figure 9. For the bare clusters, the DOS spectra remain essentially unchanged for n > 12 indicating the transition to the bulk limit. For H2 chemisorbed clusters, as can be seen from Figure 9, the total DOS spreads out to a relatively wide energy range due to the delocalization of 3d electrons. The peaks in the conduction band appearing in the DOS spectra for smaller clusters shift to lower energies crossing the Fermi level with remarkable changes in the valley depth as the cluster size is increased to n ) 15. The overlap of the energy levels leads to a continuous energy band, as shown in Figure 9, indicating the evolution from cluster to bulk as the size of the cluster is increased. IV. Summary and Conclusions We have performed extensive studies of structural evolution of small Ti clusters and their physicochemical properties by

7500 J. Phys. Chem. C, Vol. 111, No. 20, 2007 using DFT calculations employing Perdew-Wang exchangecorrelation functional with the GGA. We have found that the low-energy clusters grow three dimensionally from Ti4. Closepacked structures were found for Ti clusters that follow a pentagonal growth pattern. The clusters Ti7 and Ti13 with pentagonal bipyramid and icosahedron structures, respectively, show much higher stability than the other clusters. The second difference of binding energy plot indicates that Ti7 and Ti13 clusters are highly stable, in agreement with the experimental collision-induced dissociation studies and previously reported theoretical calculations. To the best of our knowledge, this is the first time extensive studies of the chemical reactivity of small Ti clusters toward dissociative chemisorption of H2 from n ) 2-15 have been performed. We found that the chemisorption occurs preferentially at the two adjacent edges of any Ti atom. Subsequently, the minimum energy structures of Tin-H2 were identified, and the chemisorption energies were evaluated. The chemisorption energy obtained as a function of the cluster size indicates considerable structural change taking place due to H2 adsorption. The H2 chemisorption energy is found to be the highest for Ti13. This is an interesting finding because titanium is shown to have increased catalytic activity in reversible hydrogen storage in complex metal hydrides and the presence of Ti13 has been implicated in some of the experiments.40 The variation of electronic density of states of H2-chemisorbed Ti clusters show the evolution from cluster to bulk structure as the cluster size was increased. We believe that the results presented here provide important mechanistic details of hydrogen dissociation on Ti clusters and on the role of Ti in the design of improved materials for hydrogen storage and catalysis. Acknowledgment. This work was financially supported by Department of Energy (Grant No. DE-FG36-05GO85028). The authors thank Hansong Cheng and Robert Forrey for fruitful discussions. References and Notes (1) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607. (2) Hong, B. H.; Bae, S. C.; Lee, C.-W.; Jeong, S.; Kim, K. S. Science 2001, 294, 348. (3) Ha¨kkinen, H.; Abbet, S.; Sanchez, A.; Heiz, U.; Landman, U. Angew. Chem., Int. Ed. 2003, 42, 1297. (4) (a) Guvelioglu, G. H.; Ma, P.; He, X.; Forrey, R. C.; Cheng, H. Phys. ReV. Lett. 2005, 94, 026103. (b) Phys. ReV. B 2006, 73, 155436. (5) Nie, A.; Wu, J.; Zhou, C.; Yao, S.; Luo, C.; Forrey, R. C.; Cheng, H. Int. J. Quantum Chem. 2007, 107, 219. (6) Physics and Chemistry of Finite Systems: From Clusters to Crystals; Jena, P., Khanna, S. N., Rao, B. K., Eds.; Kluwer Academic Publishers: Boston, 1992; Vols. I, II. (7) Kant, A.; Lin, S.-S. J. Chem. Phys. 1969, 51, 1644. (8) Haslett, T. L.; Moskovits, M.; Weitzman, A. L. J. Mol. Spectrosc. 1989, 135, 259.

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