Evolution of Small Zr Clusters and Dissociative Chemisorption of H2

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J. Phys. Chem. C 2008, 112, 17828–17834

Evolution of Small Zr Clusters and Dissociative Chemisorption of H2 on Zr Clusters Xue-feng Sheng, Gao-feng Zhao,* and Li-li Zhi Institute of Theoretical Physics, School of Physics and Electronics, Henan UniVersity, Kaifeng 475004, People’s Republic of China ReceiVed: August 14, 2008; ReVised Manuscript ReceiVed: September 6, 2008

Here, we have systematically studied the growth behavior of small zirconium clusters of up to 15 atoms and the adsorption of a H2 molecule on the minimum energy clusters using the density functional theory (DFT) within the generalized gradient approximation (GGA). From the Zr4 cluster, the low-energy clusters grow three dimensionally and prefer to form compact structures. The fragmentation energy and the second-order difference of binding energy plots indicate that the magic numbers of the calculated the Zrn clusters are 7, 13, and 15, corresponding to the high symmetrical pentagonal bipyramidal and icositetrahedronal structures, respectively, which accords well with the experimental mass spectra results. To our knowledge, this is the first time that a systematic study of chemisorption of molecular hydrogen on small Zrn clusters (n ) 2-15) is performed. It turns out that H2 prefers a dissociative chemisorption, and the favorite adsorption sites for H2 reacting with the Zrn clusters are the bridge sites except for Zr4, Zr7, Zr11, and Zr12, on which the favorite adsorption sites are the top sites. The chemisorption energies of Zr4 and Zr13 clusters are found to be the highest and the second highest. I. Introduction Small atomic clusters containing two to a few hundred atoms often have properties between those of bulk systems and the constituent atoms, and then exhibit novel electronic, magnetic, optical, and chemical behaviors, which is due to the large surface to volume ratio and the enhanced quantum mechanical size effect.1-3 In the last two decades, a number of experimental and theoretical studies have been performed on atomic and molecular clusters of transition metals, mainly because of their potential applications as building blocks for functional nanostructure materials, electronic devices, and nanocatalysts.4,5 Hydrogen adsorption on metal surfaces and clusters is a widely studied subject, which provides the opportunity to gain a basic understanding of the complicated nature of many interesting problems, such as hydrogen embitterment of metals, catalytic processes, and hydrogen storage. Hydrogen adsorption on such nanosystems, for example, on clusters, gives an atomic perspective of the process.6-8 Zirconium atom, a typical 4d transition metal, has an electronic configuration of 4d25s2. The zirconium hydride with high hydrogen content (H/Zr > 1.5) is potentially one of the most ideal moderators for nuclear reactors because of its high neutron scattering cross-section, low neutron absorption crosssection, and negative temperature coefficient of reactivity.9,10 In addition, the Zr-based AB2 Laves phase alloys are one family of alloys with high hydrogen storage capacity.11 The resonant two-photo ionization spectroscopy of Zr2 dimer was investigated experimentally by laser ablation and jet-cooled molecular beam.12 Extensive theoretical studies on Zr3,13 Zr4,14 and Zr515 clusters have revealed that electron correlation effects are so significant that the relative ordering of different electronic states varies as a function of the level of theory. Turgut et al.16 have investigated the structural stability and energetics of zirconium microclusters Zrn (n ) 3-13) using molecular dynamics simulations and density functional calculations. They mainly * Corresponding author. E-mail: [email protected].

obtained the geometries of zirconium microclusters and found that zirconium microclusters preferred to form three-dimensional compact structure, but it is exactly as they said, the MD results obtained were qualitative. Wang et al.17 have studied the growth behaviors, electronic properties, and magnetic properties of the small-sized Zrn (n ) 2-8) clusters at UB3LYP level employing Lanl2DZ basis sets. Theoretical results show that the small clusters (n ) 2, 5, and 7) are more stable. The Zr7 is the most stable nonmagnetic cluster with a D5h pentagonal bipyramidal structure. Recently, Zhao et al.18 have studied the ground-state structures and stability of the Zrn (n ) 2-16) clusters using DFT within the GGA using the Perdew-Wang exchangecorrelation functional (PW91) as implemented in the DMOL3 package. They obtained the icosahedronal structure with the high symmetry (Ih) as the ground-state structure of Zr13. Takashi et al.19 have investigated adsorption of H2, 2H2, O2, and CO on ZrB2 (0001) using high-resolution electron energy loss spectroscopy. In hydrogen and oxygen adsorption, a strong loss peak appeared in the specular spectra, showing the dissociative adsorption on the 3-fold hollow site. Despite the rapid growth in the research concerning TM clusters, studies on zirconium clusters are limited because the Zr clusters always possess complicated electronic structures caused by the 4d5s electrons. For the Zr clusters, the energies between different spin multiplicities states are so close that determining the ground-state structures is always a complicated progress, even a challenging work. Furthermore, to our best knowledge, there have been no reports on chemisorption of H2 on the zirconium clusters. Stimulated by the above discussion, in this Article, we first present systematic theoretical studies on the geometrical and electronic properties of the Zrn (n ) 2-15) clusters, including growth patterns, relative stabilities, the energy gaps between the highest occupied orbital (HOMO) and the lowest unoccupied orbital (LUMO), the small cluster electron affinity, and ionization energy. We then studied the chemical reactivity of the small zirconium clusters toward chemisorption of H2. We hope that this study can help people

10.1021/jp8072602 CCC: $40.75  2008 American Chemical Society Published on Web 10/22/2008

Evolution of Small Zr Clusters

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understand the small zirconium clusters better and find appropriate hydrogen storage materials. The rest of this Article is organized as follows. In section II, we describe the details of the computational methodology. In section III, we give a presentation and discussion of the results. Finally, a summary of our findings and conclusions is given in section IV. II. Computational Details Our calculations were performed using DFT within the GGA using the Perdew-Wang exchange-correlation functional (PW91)20 as implemented in the DMOL3 package.21 This method can perform accurate and efficient self-consistent calculations using a rapidly convergent three-dimensional numerical integration scheme. DFT techniques account for exchangecorrelation in many electron systems by the GGA, and they are suitable for studying transition metal clusters.22 The double numerical basis set including d-polarization function (DND)21 was utilized to describe the valence electrons with the core electrons described with effective core potential. All Zr clusters and chemisorption geometries were fully optimized without symmetry constraints and using spin unrestricted. When we carry out the calculation using spin unrestricted, this will cause the spin contamination, which can affect the accuracy of the calculation. Yet DFT techniques consider exchange-correlation in many electron systems by the GGA, so the spin contamination is possible negligible. For each specific cluster size, an exhaustive search for minimum energy structures for both the cluster and its chemisorption structure was conducted and usually ended up with numerous stable isomers. The Direct Inversion in an Iterative Subspace (DIIS) approach was used to speed up SCF convergence. We also applied thermal smearing to the orbital occupation to speed it up. The value of smearing is 0.005 hartree. For the accurate calculations, we have chosen an octupole 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 5.3 Å was used. An energy convergence tolerance is 10-5 hartree. The maximum force and the maximum displacement were less than 0.002 eV/Å and 0.005 Å, respectively. To check the reliability of the methods and basis sets used in this Article, test calculations were carried out on the Zr2 and ZrO dimers. The bond length (2.32 Å) and the fragmentation energy (3.186 eV) of the Zr2 dimer are in nice accordance with the experimental values of 2.24 Å23 and 3.052 ( 0.001 eV;24 meanwhile, the bond length and vibrational frequency of the ZrO dimer are 1.776 Å and 928.49 cm-1, in good agreement with the previous theoretical results of 1.757 Å and 983.43 cm-1,17 and the experimental values of 1.712 Å and 975 cm-1.25-27 Furthermore, the calculated vertical ionization potential of Zr atom is 6.505 eV, in good agreement with the experimental value of 6.634 eV.28,29 Therefore, the calculation method employed is reliable and accurate enough. III. Results and Discussion A. The Properties of Zrn (n ) 2-15) Clusters. In cluster physics, one of the most fundamental problems is to determine the ground-state geometry. Accordingly, we first study the ground-state structures of the Zrn (n ) 2-15) clusters. Because there were few studies on the small zirconium clusters, we mainly refer to the previous studies on Ru, Rh, Ir, and Ti clusters.30-33 The calculated lowest-energy zirconium structures are shown in Figure 1. As can be seen easily from Figure 1, within the small size range, up to n ) 6, the ground-state

Figure 1. The calculated lowest-energy structure of Zrn clusters.

structure of the Zrn+1 cluster can be derived from that of the Zrn cluster by adding one face-capped Zr atom, except for Zr3, which is formed by adding one edge-capped atom on Zr2, and the obtained ground-state structures for Zr3, Zr4, Zr5, and Zr6 are the isosceles triangle, the tetrahedral geometry, the trigonal bipyramidal structure, and the face-capped trigonal bipyramidal structure, respectively. The calculated ground-state structure of the Zr3 cluster is the same as the result obtained by Wang et al.17 and Dai et al.,13 but out of accord with the experimental result,34 in which the ground-state structure was the equilateral triangle. We have optimized two stable Zr4 structures, the tetrahedral geometry and the two-dimensional structure (not shown in Figure 1); the binding energy of the tetrahedral geometry is 0.4497 eV lower than that of the two-dimensional structure. Note that the theoretical result reveals that the most stable Zr4 isomer becomes three-dimensional in geometry. For the Zr5 cluster, because of the Jahn-Teller effect, the D3h symmetry of Zr5 is lowered to be the C1 symmetry. In the case of the Zr6 cluster, we find that the ground-state structure is the face-capped trigonal bipyramid, not the octahedral structure that was obtained by Turgut et al.16 The total energy of the octahedral isomer is 4.789 eV higher than that of the face-capped trigonal bipyramidal structure. This result is in agreement with the result obtained by Wang et al.17 Generally, the high symmetrical polyhedrons such as the octahedron Oh and pentagonal bipyramidal D5h are expected to be the ground state of many TM clusters, and the calculated results show that the pentagonal bipyramidal D5h structure is the lowest-energy geometry for the Zr7 cluster. However, the octahedral Zr6 with Oh symmetry is an energetically unfavorable structure for the ground state. Furthermore, the growth pattern of the small clusters is abruptly terminated at n ) 7, at which the cluster forms the pentagonal bipyramidal structure not via adding a new Zr atom on the face-capped trigonal bipyramid

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TABLE 1: Symmetries (sym), Multiplicity (M), Atomic Averaged Binding Energy [Eb], Fragmentation Energies [D(n,n - 1)], Second-Order Difference of Binding Energies [∆2En], and HOMO-LUMO Gaps (all in eV) for the Most Stable Zrn (n ) 2-15) Clusters cluster

M

sym

gap

Eb

∆2E

VIPn

VEAn

D(n,n - 1)

Zr2 Zr3 Zr4 Zr5 Zr6 Zr7 Zr8 Zr9 Zr10 Zr11 Zr12 Zr13 Zr14 Zr15

3 3 5 1 1 1 1 1 1 1 1 1 1 1

D∞h C2V Td C1 C1 D5h C2 C1 C1 C1 C1 Ih C1 D6d

0.515 0.278 0.530 0.252 0.302 0.560 0.343 0.094 0.263 0.222 0.333 1.304 0.533 0.426

1.5929 2.2571 2.8982 3.3318 3.5274 3.8217 3.8656 3.9786 4.0620 4.0900 4.1343 4.3353 4.3381 4.5004

-0.3994 -1.2308 -0.2437 0.5587 -1.0814 1.4177 -0.7098 0.0668 0.4487 -0.2553 -2.3841 2.8916 -2.6578 1.7918

5.666 5.2096 4.7754 4.9222 4.7283 4.6159 4.5811 4.5238 4.5173 4.4485 4.4707 4.5126 4.4646 4.5797

0.2163 0.5174 0.5905 0.8323 0.8027 0.8045 1.0275 1.0967 1.2002 1.2327 1.3796 1.4243 1.4098 1.5719

3.1858 3.5853 4.8215 5.0652 4.5064 5.5879 4.1724 4.8826 4.8156 4.3669 4.6222 7.0064 4.1147 6.7725

of the Zr6 cluster. We have optimized four isomers for the Zr8 cluster; the Zr2 dimer bicapped octahedronal structure is the most stable. The ground-state structure of the Zr8 cluster is different from that of the Ti8 cluster, the face-capped pentagonal bipyramidal structure.35 When the size of the Zrn clusters is up to 9, we obtain the Zr2 dimer bicapped pentagonal bipyramidal structure as the ground state of the Zr9 cluster. As the clusters grow from n ) 9 to n ) 14, the most stable structures of these clusters are formed by adding a face-capped Zr atom on the pentagonal bipyramidal structure. A new addition always occurs at a site where interactions with more atoms are available to form the close-packed structure. It is worth being pointed out that the ground-state structures of the small-sized clusters with n ) 3-7 have a regular symmetry. However, the larger clusters for the sizes n ) 8-12 have no regular symmetry. For the Zr13 cluster, we found the icosahedronal structure with the high symmetry (Ih) as the ground-state structure. For 3d and 4d transition metal clusters, Pd13, Rh13, Ru13, and Fe13, theoretical studies have reported that the high spin solution of icosahedral symmetry is the ground-state structures.36 With respect to the Zr15 cluster, the icositetrahedronal structure with high symmetry (D6d) is found as its ground-state structure. Note that the multiplicities of the lowest-energy Zrn clusters (listed in Table 1) are 1 except for Zr2, Zr3, Zr4, corresponding to 3, 3, 5. This result is the same as the result obtained by Zhao et al.18 In general, the small Zrn clusters tend to form the close-packed structures. This is mainly due to the delocalization of 4d electrons. Furthermore, the existence of only two electrons in 4d orbitals of Zr atom easily comes into being empty antibonding orbitals, which facilitates the close-packed structure. We now discuss size-dependent physical properties of Zr clusters. The atomic averaged binding energy [Eb], the fragmentation energies [D(n,n - 1)], and the second-order difference of binding energies [∆2En] are calculated for the lowest-energy structures of the Zrn clusters using the following formulas:

increases rapidly as the clusters grow from n ) 2 to n ) 7, and then increases slowly with the cluster size increases. Thus, the clusters can continue to gain energy during the growth processes. In cluster physics, the fragmentation energies and the secondorder difference of binding energies are sensitive quantities that reflect the relative stability of the calculated clusters. Figures 3 and 4 show the size dependence of the fragmentation energies and the second-order difference of binding energies. Local peaks are found at n ) 7, 13, 15 in both curves, corresponding to the high symmetrical pentagonal bipyramid, icosahedronal, and icositetrahedronal structures, respectively, showing these clusters are more stable than their neighboring clusters. According to Figures 3 and 4, it shows apparently that the magic numbers of our investigated small zirconium clusters are 7, 13, and 15, which accords well with the experimental mass spectra results.37 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. So we calculated the vertical ionization potential (VIP) and vertical electron affinity (VEA) according to:

VIPn ) E(Zr+ n ) - E(Zrn) VEAn ) E(Zrn) - E(Zrn) where E(Zrn+) and E(Zrn-) represent the total energies of ionic clusters at the neutral optimized geometry. As can be seen from Figure 5, the calculated ionization potential (VIP) decreases rapidly until n ) 4 as the clusters grow, and then remain

Eb(Zrn) ) [E(Zrn) - nE(Zr)]/n D(n, n - 1) ) E(Zrn-1) + E(Zr) - E(Zrn) ∆2En ) E(Zrn+1) + E(Zrn-1) - 2E(Zrn) where E(Zrn), E(Zr), E(Zrn+1), and E(Zrn-1) represent the total energies of the ground-state of Zrn, Zr, Zrn+1, and Zrn-1 clusters, respectively. The calculated atomic averaged binding energy, fragmentation energies, and the second difference of binding energies are plotted in Figures 2-4. As can be seen from Figure 2, the atomic averaged binding energy of the Zrn clusters

Figure 2. Size dependence of average binding energies [Eb(n)] of the lowest-energy Zrn clusters.

Evolution of Small Zr Clusters

Figure 3. Size dependence of the fragmentation energies [D(n,n 1)] of the lowest-energy Zrn clusters.

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Figure 5. Size dependence of VIPs of the lowest-energy Zrn clusters.

Figure 6. Size dependence of VEAs of the lowest-energy Zrn clusters.

Figure 4. Size dependence of the second-order difference of binding energies [∆2En] of the lowest-energy Zrn and ZrnH2 clusters.

unchanged in general with a local maxima for Zr5 and Zr15. For the Zr5 and Zr15 clusters, all electrons are paired, giving a closed shell electronic structure, so it is difficult to remove an electron from the Zr5 and Zr15 clusters. Figure 6 shows that the VEA values of the Zrn clusters increase as the number of Zr atoms increase except at n ) 6 and 14 with a local minimum. It is interesting to point out that the large-sized clusters usually have smaller VIPs and larger VEAs as compared to the smallsized clusters, implying that it is much more difficult to ionize the smaller clusters than the larger ones but much easier to attach an electron to the larger clusters than to the smaller ones. B. Chemisorption of H2 on the Zrn (n ) 2-15) Clusters. The main motive of our current work is to investigate hydrogen molecule adsorption on the small zirconium clusters. We

performed an exhaustive minimum energy structural search for molecular H2 adsorption on the optimized bare Zrn (n ) 2-15) clusters with the lowest-energy structures. We mainly put molecular H2 on the different top, bridge, and face sites and the hollow site of the ground-state structures of the small Zr clusters with different H2 orientations. The lowest-energy structures of the ZrnH2 clusters are displayed in Figure 7. The multiplicities of the lowest-energy ZrnH2 clusters are also listed in Table 2. The lowest-energy ZrnH2 isomers remain singlet states except for Zr3H2 and Zr4H2. We have calculated the adsorption energies of the ZrnH2 clusters, ∆ECE ) E(Zrn) + E(H2) - E(ZrnH2), where E(Zrn), E(H2), and E(ZrnH2) are the calculated lowest energies of the Zrn clusters, H2 molecule, and ZrnH2 clusters, respectively. We find that H2 prefers a dissociative chemisorption with H-H bond lengths much longer than the calculated value of H2, 0.750 Å. The favorite adsorption sites for H2 reacting with the Zrn clusters are the bridge sites except for Zr4, Zr7, Zr11, and Zr12, on which the favorite adsorption sites are the top sites. When we put H2 molecular on the top of the Zrn clusters, the calculated results show that H2 molecular can be physically adsorbed on the Zrn clusters (not including Zr4, Zr7, Zr11, and Zr12) with the adsorption energies less than 0.3 eV and the H-H length a little longer than the value of H2, 0.750 Å. It is well-known that the chemisorption energies can be used to quantitatively describe the reactivity of H2 on the Zrn clusters. The calculated chemisorption energies (∆ECE) corresponding to the most energetically favorable chemisorption site are shown in Figure 8, which has a strong dependence on the clusters and increases until n ) 4, and then decreases to the lowest value of 1.217 eV at n ) 7. The chemisorption energy then increases in

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Figure 8. Dissociative chemisorption energy of H2 on Zrn as a function of the cluster size.

Figure 7. The calculated lowest-energy chemisorption structure of H2 on the lowest-energy structure of Zrn clusters.

TABLE 2: Adsorption Energies [∆ECE], HOMO-LUMO Gaps, Second-Order Difference of Binding Energies [∆2En] (all in eV), Multiplicity (M), H-H Bond Length [RH-H], and Atomic Averaged Charges on the H Atom for the Most Stable of the ZrnH2 Clusters cluster

M

gap

∆ECE

RH-H (Å)

∆2En

charge (e)

Zr2H2 Zr3H2 Zr4H2 Zr5H2 Zr6H2 Zr7H2 Zr8H2 Zr9H2 Zr10H2 Zr11H2 Zr12H2 Zr13H2 Zr14H2 Zr15H2

1 3 3 1 1 1 1 1 1 1 1 1 1 1

0.745 0.460 0.515 0.562 0.139 0.530 0.366 0.427 0.256 0.074 0.250 0.984 0.470 0.858

1.0870 2.1298 2.2890 1.7558 1.6103 1.2172 1.4561 1.6724 1.6401 1.6637 1.8287 2.2773 1.5234 2.0836

2.163 2.226 3.383 2.126 3.240 2.059 2.180 2.385 2.287 2.450 2.822 2.542 2.317 2.268

-0.0636 -0.0129 0.0164 0.0064 -0.0307 0.0288 -0.0253 0.0116 0.0145 -0.0487 -0.0299 0.1164 -0.1459

-0.182 0.018 -0.118 0.023 -0.196 0.021 -0.025 -0.106 -0.092 -0.149 -0.056 -0.189 -0.082 -0.114

general as the size of the clusters increases, attaining the local maxima for n ) 4 and 13. The present results show the Zr7 cluster is of high inertness with respect to the H2 chemisorption, while both Zr4 and Zr13 clusters are of high activity with respect

to the H2 chemisorption. Note that Dhilip Kumar et al.33 also calculated that the H2 chemisorption energy was found to be the lowest for the stable Ti7 cluster but highest for the most stable cluster Ti13. Experimental measurements indicate that when Ti13 cluster is added as a catalyst, it increases the reaction rate of hydrogenation and dehydrogenation processes in alanates.38 Whether the Zr13 cluster is added as a catalyst to increase the reaction rate of hydrogenation and dehydrogenation processes is to be studied further theoretically and experimentally. To further study the relative stability of clusters after adsorbing H2 molecule, we have calculated the second-order difference of binding energies for the lowest-energy ZrnH2 clusters (listed in Table 2), ∆2En ) E(Zrn+1H2) + E(Zrn-1H2) - 2E(ZrnH2), where E(Zrn+1H2), E(Zrn-1H2), and E(ZrnH2) are the total energies of the ground state of Zrn+1H2, Zrn-1H2, and ZrnH2 clusters, respectively. The second-order difference of binding energies for the lowest-energy ZrnH2 clusters is plotted in Figure 4b for comparison. The local maxima are found at n ) 4, 7, and 13, indicating these clusters possess higher stability than their neighbors. By comparing the values of ∆2En for the Zrn and ZrnH2 clusters, we find that for the even clusters (not including n ) 10), the values of ∆2En become higher after hydrogen adsorption. In contrast, the values of ∆2En for the odd clusters except for n ) 3 and 11 become smaller. The even clusters enhance their stability, and the odd clusters reduce their stability after hydrogen adsorption. As the energetic stability of the system is controlled by the magnitude of energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO),39 we have computed the HOMO-LUMO energy gaps of the Zrn clusters with that of the corresponding reacted products, the ZrnH2 clusters. As shown in Figure 9, for the bare Zrn clusters, the local peaks are found at n ) 2, 4, 7, and 13; especially, the value of Egap is the highest for the Zr13 cluster, implying that these clusters are more stable and have lower chemical reactivity than their neighboring clusters. The tetrahedral Zr4 has three-dimensional structure and increases its stability as compared to its neighbors. The high values of the HOMO-LUMO gaps for Zr7 and Zr13 again indicate that they are highly stable. The HOMO-LUMO gaps for the most stable Zrn (n ) 2-15) clusters (listed in Table 1) range from 0.09 to 1.40 eV, implying that these clusters are semiconductors. In Figure 9, we also find that, for n ) 5, 9, and 15, after H2 chemisorption, the HOMO-LUMO gaps become bigger, while for n ) 4, 8, 10, and 12, the HOMO-LUMO gaps are close to each other. The local maxima occur at n ) 2, 5, 7, 13, and 15, indicating that these clusters are more stable than their neighbors.

Evolution of Small Zr Clusters

J. Phys. Chem. C, Vol. 112, No. 46, 2008 17833 the icosahedronal structure with the high symmetry (Ih) of the Zr13 cluster. We finally perform Mulliken population analysis for the lowest energy of the ZrnH2 clusters, and the atomic averaged charges of H atom are listed in Table 2. Consistently we find that charges transfer from Zr atoms to H atoms except for Zr3H2, Zr5H2, and Zr7H2 clusters, for which the direction of charge transfer reverses. Furthermore, there is weak charge transfer from H atoms to Zr atoms with respect to the Zr3H2, Zr5H2, and Zr7H2 clusters. The chemisorption results in the formation of metal hydride. IV. Summary and Conclusions

Figure 9. Size dependence of the HOMO-LUMO gaps of Zrn and ZrnH2 clusters.

Figure 10. The HOMO and LUMO orbitals of the Zrn and ZrnH2 clusters (n ) 4, 7, 13).

Furthermore, the Zr13H2 cluster also has the highest value of the HOMO-LUMO gap even after hydrogen adsorption. From the above discussion, we know the Zr4H2, Zr7H2, and Zr13H2 clusters are more stable as compared to other clusters. Furthermore, the H2 chemisorption energy is the lowest for the Zr7 cluster, the highest for the Zr4 cluster. So we further study the three special clusters. We have performed an analysis of the molecular orbitals by examining the electron density of the HOMO and LUMO states. The distribution of electron density of the HOMO and LUMO states is plotted in Figure 10. One can see that the distribution of electron density of the HOMO and LUMO states changes a lot after hydrogen adsorption. For the Zr4H2 and Zr7H2 clusters, both the HOMO and the LUMO states are mainly localized around Zr atoms, while there is some distribution around H atoms. This indicates a degree of hybridization between the d orbitals of Zr and the s orbitals of H, which should be responsible for the high stability for the two clusters. However, with respect to the Zr13H2 cluster, both the HOMO and the LUMO states are almost localized around Zr atoms; there is scarcely any distribution around H atoms. So the high stability for the Zr13H2 cluster may be related to

We have performed extensive studies on the growth behavior of small zirconium clusters and their physicochemical properties by using DFT calculations employing Perdew-Wang exchange correlation functional with the GGA. The low-energy growth pattern of small zirconium clusters is to grow three dimensionally from Zr4. The closepacked structures are found for the small zirconium clusters. The Zr7, Zr13, and Zr15 clusters with the high symmetrical pentagonal bipyramidal, icosahedronal, and icositetrahedronal structures, respectively, show much higher stability than do the other clusters. The calculated D(n,n - 1) and ∆2En of the most stable Zrn clusters, which are sensitive quantities that reflect the relative stability, also indicate that Zr7, Zr13, and Zr15 clusters are highly stable. Furthermore, the value of the HOMO-LUMO gap of the Zr13 cluster is much larger than those of the other clusters. Dissociative chemisorption of hydrogen molecules is common for the small Zrn clusters considered here. We find that the chemisorption occurs on the bridge positions of the bare Zrn clusters except for the Zr4, Zr7, Zr11, and Zr12 clusters, which prefer the top sites. We identify that Zr4 and Zr13 have the highest and the second highest adsorption energy for dissociative chemisorption of H2. From the analysis of the second-order difference of binding energies for the lowest-energy ZrnH2 clusters, we draw a conclusion that the even clusters enhance their stability and the odd clusters lower their stability after hydrogen adsorption. A degree of hybridization between the d orbitals of Zr and the s orbitals of H should be responsible for the high stability for the Zr4H2 cluster. We believe that the present theoretical studies on the chemical reactivity of H2 with small Zr clusters will provide valuable information to design the perfect materials for hydrogen storage and catalysis. Acknowledgment. This work was supported by the National Science Foundation of Henan Province Education Department under Grant No. 2008A140002 and the Henan University National Science Foundation under Grant No. 06YBZR021. References and Notes (1) Berry, R. S., Burden, J., Castleman, A. W., Jr., Eds. Small Particles and Inorganic ClustersZ. Phys. 1993, 26. (2) Harberland, H., Ed. Clusters of Atoms and Molecules. In Theory, Experiment, and Clusters of Atoms; Springer-Verlag: Berlin, 1994. (3) Baletto, F.; Ferrando, R. ReV. Mod. Phys. 2005, 77, 371. (4) Guvelioglu, G. H.; Ma, P.; He, X.; Forrey, R. C.; Cheng, H. 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) Huda, M. N.; Kleinman, L. Phys. ReV. B 2006, 74, 195407. (7) Guvelioglu, G. H.; Ma, P.; He, X.; Forrey, R. C.; Cheng, H. Phys. ReV. Lett. 2005, 94, 026103. (8) German, E. D.; Efremenko, I.; Sheintuch, M. J. Phys. Chem. A 2001, 105, 11312.

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