The Evolution of Geometric and Electronic Structures for the Hydrogen

Department of Physics, Ningbo University, Ningbo, Zhejiang 315211, and Department of Physics, Fudan University, Shanghai 200433, People's Republic of ...
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J. Phys. Chem. C 2009, 113, 15507–15513

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The Evolution of Geometric and Electronic Structures for the Hydrogen Storage on Small Tin (n ) 2-7) Clusters Ming-Hui Shang,† Shi-Hao Wei,*,†,‡ and Yue-Jin Zhu*,† Department of Physics, Ningbo UniVersity, Ningbo, Zhejiang 315211, and Department of Physics, Fudan UniVersity, Shanghai 200433, People’s Republic of China ReceiVed: February 23, 2009; ReVised Manuscript ReceiVed: June 18, 2009

We perform first principles density functional theory calculations to investigate the geometric and electronic structures of Tin-mH2 (n ) 2-7, and m ) 1-22). By optimizing geometric structures, we obtain the saturated configurations for hydrogen storage on small Tin (n ) 2-7) clusters. Interestingly, we find that with an increase in the size of the Tin cluster, the effective space for each titanium atom to adsorb hydrogen molecules decreases, as does the maximum amount of hydrogen molecules adsorbed on each titanium atom. When the size of the Tin cluster goes beyond n ) 5, the maximum number of hydrogen molecules adsorbed on each Ti atom keeps a constant of 3. For Ti7-mH2 clusters, the average Mulliken charges increase at first and decrease afterward, the binding energy EHb per atom of H increases when the hydrogen molecule number m changes from 1 to 3, and then, it shows a slow decrease with m increasing from 3 to 21. Furthermore, we suggest/ propose that the hybridization of atomic orbitals in different atoms could be used to estimate the type of the bonds between the different atoms in clusters. As the Tin-mH2 clusters get bigger, due to the charge density redistribution, the interaction between titanium atoms becomes weaker and the bond length of Ti-Ti increases gradually. Meanwhile, the H-H bonds are elongated or even broken. The geometry of the host cluster is distorted from D5h into C3V when 21 H2 molecules are chemisorbed. I. Introduction Hydrogen is the most abundant element on the earth, but less than 1% presents as molecular hydrogen gas H2.1 The overwhelming majority of hydrogen (H) is combined with oxygen (O) and stored as H2O. Besides in the form of H2O, there is still some H bound to liquid or gaseous hydrocarbons. It is wellknown that H2 and O2 can be generated by decomposing water, and the final product of hydrogen burning is H2O. So, this kind of energy can be recycled and is environmentally friendly. Another advantage of using H2 as an energy source is the large chemical energy per mass of hydrogen (142 M J kg-1), which is at least three times larger than that of any other chemical fuels; for example, the value for liquid hydrocarbons is 47 M J kg-1. However, to date, how to store hydrogen is still a serious problem. In past decades, a large amount of work has been performed on developing more effective and safe approaches to storing hydrogen. In recent years, nanostructural materials have attracted more and more attention because of their high gravimetric and volumetric density in hydrogen storage, and storing H2 in nanostructural materials is also a very safe and time-saving way.2-4 A theoretical study based on density functional theory (DFT) showed that the cluster Al4H6, an analogue of borene, may be a promising energetic material if it could be prepared in the bulk phase.5 As a possible structure of boron isomers, with a very high symmetry analogous to C60 fullerene, B80 was studied by Szwack et al., and they predicted that it has a higher stability than boron double rings and could be used as the building blocks of boron nanotubes.6 Subsequently, Prasad et al. found that the fullerene-based icosahedral* To whom correspondence should be addressed. E-mail: (S.-H.W.) [email protected]; (Y.-J.Z.) [email protected]. † Ningbo University. ‡ Fudan University.

B12 analogue (such as B98, B99, B100, and B102) were more stable than the fullerenelike boron clusters B80.7 Kim and co-workers studied the light element-doped fullerenes and revealed a nondissociative chemisorption mechanism for B- and Be-doped fullerenes.8 Yoon et al. identified Ca as the most desirable coating metal element for functionalizing carbon fullerenes into high-capacity hydrogen storage media by using first principles calculation.9 Very recently, Lee and co-workers carried out first principles calculation on Ti-decorated nanomaterials based on polymers and found that Ti-decorated cispolyacetylene has the highest usable gravimetric and volumetric density of hydrogen among all nanostructures.10,11 Zhao and co-workers proposed a new route for storing hydrogen by binding transition metal atoms to fullernes and predicted that Ti can significantly increase the hydrogen storage material recycling.12 Nearly at the same time, Yildirm and Ciraci reported that a single Ti atom coated on a SWNT could bind up to four hydrogen molecules.13 In the experiments, Liang et al. doped the MgH2 with Ti, V, Fe, Ni, and Mn and found that the hydrogen charging and discharging speed of the adsorbent were improved significantly, especially when Ti or V was doped in MgH2.14 Anton found that Ti2+, Ti3+, and Ti4+, which were doped into NaAlH4 as a catalytic addition through ball milling, could significantly enhance dehydrogenation rates.15 Wang and co-workers’ study revealed that SWNTs, MWNTs, AC, C60, and G all can exhibit significant, sustaining, and synergistic biocatalytic effects on the dehydrogenation and hydrogenation kinetics of Ti-doped NaAlH4. Among them, the SWNT is the best biocatalyst, while the G is the worst one, and in the absence of Ti, all five carbons are inactive as biocatalysts.16 Above all, as a catalyst or an impurity, Ti can improve the performance of hydrogen storage materials. However, to date, the role of Ti as a catalyst or an impurity is still not well understood. The experimental results had indicated that the small

10.1021/jp901642y CCC: $40.75  2009 American Chemical Society Published on Web 08/07/2009

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TABLE 1: Equilibrium Bond Length r0 (in a.u.) for Ti2 present r0 a

3.701 b

theory 3.721a

ETi b (n) ) E(n)/n

(1)

∆E2(n) ) 2E(n) - E(n + 1) - E(n - 1)

(2)

experiment 3.660c

3.677b

c

See ref 22. See ref 29. See ref 20.

Figure 1. Most stable structures of Tin (n ) 2-7) clusters.

size of the Ti clusters plays an important role in increasing the reaction rate of some of the hydrogen storage materials such as complex metal hydrides.17,18 The clusters of Tin have been studied experimentally19 and theoretically.20-22 The Tin-H2 (n ) 2-15), Ti4-mH2, Ti7-mH2, and Ti13-mH2 have been studied by Kumar and co-workers recently.23-25 However, there were a few theoretical studies on the evolution and the H2 saturation of small Ti clusters that adsorbed an amount of hydrogen molecules. In addition, Kumar et al. did not point out how many hydrogen molecules were adsorbed by each titanium atom in Tin-mH2 clusters. Therefore, in this paper, we plan to investigate the interaction between Tin and H2 systematically to have a better understanding of the catalytic mechanism. II. Calculation Details Geometric optimization and electronic property calculations were performed by using the DMol3 package, which is based on DFT.26 The geometric structures of Tin and Tin-mH2 clusters were optimized. Without the symmetry restriction, the generalized gradient approximation (GGA)27 was used with the functional parametrization proposed by Lee et al.28 The present calculations explicitly considered all electrons in the system, (i.e., core electrons were included), with the wave function expanded in the double numeric polarized (DNP) basis set. Optimization was considered to be successful when the adjustments for gradient and displacement are both less than 10-3 Å and that for the total energy and electron density is below 5 × 10-5 hartree. To validate the results of our calculations, the bond length of Ti-Ti for titanium dimer in the present calculation is listed in Table 1 together with previous theoretical and experimental results. For a given cluster size, lots of possible geometries were investigated, to obtain the lowest energy configurations of Tin and Tin-mH2. III. Results and Discussion A. Geometries of Tin (n ) 2-7). Before adsorbing H2, the most stable and metastable structures of the pure Tin clusters were obtained by minimizing the energy. In Figure 1, only the most stable structures are shown, and the results are in good agreement with recent theoretical results.22,23 It is easy to find that general trend of the growth of the structures for these small size clusters: Generally, the structure with the lowest energy of Tin can be obtained by adding one atom to the most stable structure of Tin-1. This evolution was named as the “n + 1” rule by Wei et al.20 To investigate the relative stability of Tin, the binding energy per atom EbTi(n) and the second-order difference of the binding energy ∆E2(n) of each structure are both calculated and shown in Figure 2. The EbTi(n) and ∆ E2(n) are defined by eqs 1 and 2, respectively

where E(n) is the binding energy of the Tin cluster with n atoms. In Figure 2, there is a large peak at Ti7 for ∆E2(n), indicating the extraordinary stability of Ti7. It is indicated that Ti7 is the so-called magic number cluster. This results in good agreement with the experimental results of Sakurai et al.,30 in which the numbers 7, 13, 15, and 19 were defined as magic numbers for Tin clusters due to their extraordinary stability. B. Interaction between H2 and Tin. First, on the basis of the results of the pure Tin clusters in section A, hydrogen molecules were added one at a time to the Tin clusters. To find the ground-state geometry of the Tin-mH2 clusters, the ground state structures, the metastable structures, and the third stablest structures of the pure Tin clusters were all included in the calculation. Then, their structures were optimized with SCF calculation. In view of the fact that the hydrogen energy is always used as a hydrogen molecule, in present work, the hydrogen molecules rather than hydrogen atoms were added to Tin clusters from various directions and distances to examine the preferential relative location of the H atom or H2 on Tin. The binding energy EbTin-mH2 for pure Tin clusters adsorbing m numbers of hydrogen molecules is defined by the following equation: n-mH2 ETi ) Eb(Tin - mH2) - Eb(Tin) - mEb(H2) b

(3) where the Eb(Tin-mH2) is the binding energy of the Tin-mH2 cluster, the Eb(Tin) is the binding energy of the pure Tin cluster, and the Eb(H2) is the binding energy of the hydrogen molecule. We also calculated the binding energy EbH per atom of H for Tin-mH2 cluster:

EHb

n-mH2 ETi b ) 2m

(4)

The energy gap Egap between highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) and the binding energy EbH per atom of H for natural Tin-1H2 clusters are all presented in Table 2, where the characters “G” and “M” denote the ground state and metastable state, respec-

Figure 2. Binding energy ETi b per atom and the second difference of total energy ∆E2 for the most stable structure of the Tin (n ) 2-7) clusters.

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TABLE 2: Binding Energy Eb(Tin-1H2), the Energy Gap Egap between HOMO and LUMO Orbitals and the Binding Energy EbH Per Atom of H for Tin-1H2 Clustersa cluster Ti2-1H2 Ti3-1H2 Ti4-1H2 Ti5-1H2 Ti6-1H2 Ti7-1H2

G M G M G M G M G M G M

Eb(Tin-1H2)

EHb

10.294 10.166 14.341 14.133 19.039 18.599 23.452 23.432 28.031 27.913 33.335 33.158

0.617 0.553 1.107 1.003 1.164 0.944 0.850 0.841 0.917 0.858 0.789 0.701

a The values are all in eV, and the characters “G” and “M” denote the ground state and metastable state, respectively.

tively. From Table 2, it can be seen that all of the EbH values are larger than 0.600 eV. From Ti2-1H2 to Ti4-1H2, the EbH increases with an increasing number of titanium atoms n, and for the Ti4-1H2 cluster, the EHb is larger than 1.100 eV. Beyond Ti4-1H2, the EbH decreases fluctuately with an increase in the number of titanium atoms n, and for Ti7-1H2, the EbH is about 0.789 eV. It is well-known that the hydrogen molecule can be easily adsorbed or dissociated from the host matter when the EbH is about 0.15-0.20 eV on board vehicles.12 So, we could conclude that every structure of the Tin-1H2 cluster is so stable that the H atom can hardly dissociate and form the hydrogen molecules under the ambient conditions. Because the strong Ti-H bonds lead to a large chemisorption energy, hydrogen molecules can be easily adsorbed. The ground state configurations of Tin-1H2 (n ) 2-7) are presented in Figure 3. During the process of chemisorption of one hydrogen molecule onto Tin clusters, the H-H bond was interrupted, and then, the hydrogen molecule was adsorbed to Tin clusters dissociatively, and the original configuration of the host cluster was unaltered. As an example, let us focus on Figure 3b. When the first hydrogen molecule was added on the Ti3 cluster, in the original Ti3-1H2 cluster configuration, the line through the two H atoms of hydrogen molecules is parallel to the line linking the two Ti atoms further away from the hydrogen molecule. During the adsorption by the Ti3 cluster, the two hydrogen atoms of the hydrogen molecule were both attracted by the host cluster symmetrically. Subsequently, the H-H bond was interrupted, and the two hydrogen atoms both nearly lay on the top of the bridge sites, respectively. If two H atoms were added to Ti3 cluster one by one, the most stable configuration would be the one in which the line linking the two H atoms threads the face center of the isosceles triangular. This configuration is much more compact and symmetrical. However, for the hydrogen molecule case, it was too difficult to overcome the potential barrier between these two configurations under the ambient conditions. So, the configuration shown in Figure 3b is the most stable structure for the hydrogen molecule case under ambient conditions. Then, we can conclude that when hydrogen molecules are adsorbed on host clusters or matter, more attention should be payed to hydrogen molecules, not hydrogen atoms. For Ti4-1H2, the ground state structure as shown in Figure 3c is very similar to that of Ti3-1H2. The two H atoms are also nearly located at the top of the bridge sites, respectively. The difference between these two structures is that the line linking the two hydrogen atoms is out of the triangular plane of Ti4-1H2, while it is in the triangular plane of Ti3-1H2. When

it comes to Ti5-1H2, one hydrogen atom for H2 is on the top of bridge, while the other is on the top of the face. For Ti6-1H2 and Ti7-1H2, the dissociated H atoms were located on the top of the face as shown in Figure 3e,f, respectively. From Figure 3, we can see that when the size of Tin cluster is relatively small, the hydrogen atoms prefer the bridge site of the titanium clusters; there is a transition at the Ti5 cluster where one hydrogen atom is on top of the bridge and the other hydrogen atom is on top of the face; when the host cluster size is larger than n ) 5, all of the hydrogen atoms prefer staying on top of the face. In all cases, all of H-H bonds were broken, and the two H atoms adsorbed on the host cluster Tin. C. Geometric and Electronic Structures of Ti7-mH2. In this section, the evolution of geometric and electronic structures corresponding to Ti7-mH2 (m ) 1-22) clusters is discussed. To find out the ground state geometries of the Ti7-mH2 clusters, the hydrogen molecules H2 were symmetrically added to the most stable, metastable structure and the third stablest structure of Ti7 cluster from various directions. The most stable and the metastable structures for those clusters are all shown in Figure 4. The binding energy Eb(Ti7-mH2), the energy gap Egap between HOMO and LUMO orbitals, and the binding energy EbH per atom of H and the average Mulliken charges (AMC) per atom of H for Ti7-mH2 clusters are shown in Table 3. For Ti7-mH2 clusters, due to the AMC increases first and decreases afterward as shown in Figure 5, the binding energy EHb per atom of H first increases when the hydrogen molecule number m increases from 1 to 3 and then decreases slowly when the hydrogen molecule number m increases further from 3 to 21. The average bond length of Ti-Ti in the most stable structure for Ti7 cluster is 2.607 Å. The most stable structure of Ti7-3H2 cluster is shown in Figure 4 (Ti7-3H2-G); the average bond length of Ti-Ti in the host cluster Ti7 has increased to 2.642 Å. When five hydrogen molecules were chemisorbed on the Ti7 cluster, the average bond length of Ti-Ti in the host cluster Ti7 is 2.610 Å. After seven H2 had been chemisorbed, the bond length in Ti7-7H2-G increases to 2.724 Å. The bond lengths are 2.762 and 2.780 Å, corresponding to 15 and 17 hydrogen molecules being chemisorbed, respectively. In general, the bond length of Ti-Ti increases with the number of hydrogen molecules chemisorbed, while the geometric structure of the host cluster distorts more severely. This is in accordance with the results by Kumar et al.25 It is important to note that recently Kobayashi et al.31 have experimentally observed that the lattice constants of the palladium nanoparticle increase under high hydrogen pressure, and this discovery provides a strong corroboration for our finding. Recently, Tarakeshwar et al.24 had pointed out that the structure was saturated when 15 hydrogen molecules were adsorbed onto the Ti7 cluster (with D5h symmetry). We also notice that Yildirm et al.13 had pointed out a single Ti atom adsorbed on hexagonal phase of SWNT can bind up to four molecular hydrogens. It seems to imply that Ti7 should adsorb more than 15 hydrogen molecules, so we recalculated their structure. We find that the structure of the Ti7-30H cluster proposed by Tarakeshwar et al.24 is not the most stable one of the Ti7-30H in our calculation, and the ground state structure of this size obtained in this work is shown in Figure 4(Ti7-15H2-G). On the basis of pentagonal bipyramid structure (with D5h symmetry), as shown in Figure 4, as many as 17 hydrogen molecules could be chemisorbed. When there are more than about 21 hydrogen molecules adsorbed on the Ti7 cluster, the geometric structure of the host cluster (Ti7) is distorted significantly, and the symmetry of the bare Ti7 cluster resembles

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Figure 3. Most stable structures of Tin-H2 (n ) 2-7). Hydrogen atoms are in green, while titanium atoms are in blue.

Figure 4. Most stable and metastable structures of Ti7-mH2 (m ) 1-22). Green and red balls are for H atoms, while Ti atoms are all in blue.

C3V. When the number m of the hydrogen molecule adsorbed on Ti7 cluster reaches 22, the symmetry of the bare Ti7 cluster could be viewed as C3V symmetry, and there is a hydrogen molecule 3.86 Å away from Ti7 cluster as shown in Figure 4 (Ti7-22H2-G). To understand the above simulation results, we also calculate the density of state (DOS) and the partial density of state (PDOS) for the Ti7-mH2 clusters, which are shown in Figures 6 and 7, respectively. From Figure 6, it can be seen that the DOS of Ti7-21H2-G (red line) nearly completely overlaps with that of Ti7-22H2-G (black line) except near the peak located at the -6.563 eV energy level. From the PDOS for Tin-mH2 clusters as shown in Figure 7, it is easy to find that the overwhelming majority of this peak located at -6.563 eV energy level as shown in Figure 7l is predominately contributed by the 1s electron of the two hydrogen atoms, which are labeled as H(50) and H(51), respectively. The bond length between H(50) and H(51) atoms, which are shown as red balls in Figure 4 (Ti7-22H2-G), is about 0.75 Å, and the bond length between

the red balls and the titanium atoms is 3.86 Å. It is well-known that the bond length of the free hydrogen molecule is 0.740 Å. So, it can be concluded that the peak at -6.563 eV energy level can be solely assigned to the last hydrogen molecule [named as H(50) and H(51), respectively] adsorbed on the Ti7-21H2 cluster; that is, there is not any hybridizition between the last hydrogen molecule and the host Ti7 cluster. It means that Ti7-21H2 is a saturated structure for hydrogen molecules adsorbed on the Ti7 cluster and the interaction between the last hydrogen molecule and the titanium atoms in the Ti7-22H2 cluster should be considered to be a van der Waals interaction. This is in close agreement with recent theoretical data,24 where Tarakeshwar et al. have pointed out that the interaction between hydrogen molecules and titanium atoms is considered to be a van der Waals interaction or even weaker interaction when the distance between H atom and titanium cluster is longer than 3.70 Å. Then, we come to the conclusion that Ti7-21H2 is the saturated structure for hydrogen molecules adsorbed on the Ti7 cluster and propose that the hybridization of atomic orbitals in

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TABLE 3: Binding Energy Eb(Ti7-mH2), the Energy Gap Egap between HOMO and LUMO Orbitals, the Binding Energy EbH Per Atom of H, and the AMC Per Atom of H for Ti7-mH2 Clustersa cluster Ti7-1H2 Ti7-2H2 Ti7-3H2 Ti7-4H2 Ti7-5H2 Ti7-6H2 Ti7-7H2 Ti7-15H2 Ti7-17H2 Ti7-21H2 Ti7-22H2

G M G M G M G M G M G M G M G M G M G M G M

Eb(Ti7-mH2)

EHb

33.335 33.158 39.753 39.614 46.257 46.179 52.686 51.670 58.782 58.028 64.866 64.789 70.559 70.455 109.469 105.619 119.369 117.391 137.892 137.888 142.463 142.462

0.789 0.701 0.860 0.825 0.898 0.885 0.892 0.780 0.880 0.804 0.860 0.854 0.819 0.811 0.464 0.336 0.432 0.374 0.357 0.357 0.371 0.371

AMC 0.187 0.192 0.198 0.195 0.182 0.161 0.128 0.026 0.020 0.002 0.002

a The values are all in eV, and the characters “G” and “M” denote the ground state and metastable state, respectively. The EHb decreases as the number m increases.

Figure 5. Binding energy EHb per atom of H and the AMC per atom of H for Ti7-mH2 clusters.

Figure 6. DOS of Ti7-mH2 (m ) 1-22). The Fermi energy EF is shifted to zero.

different atoms could be used to estimate the type of the bonds between the different atoms in clusters. The electronic structure of ground state for natural titanium atom is [Ar] 4s23d24p0, and the 4p orbital is unoccupied. From

Figure 7. Evolution of 3d PDOS of Ti7-mH2 (m ) 1-22). All of the PDOS are 3-fold magnified except that in part a. Only the spin-up of DOS (part of PDOS) is shown here, and the number in brackets only denotes the serial number of the atom in the cluster. The Fermi energy EF is shifted to zero.

Figure 7a, we can see that there is some PDOS of the 4p orbital of Ti atom, and the PDOS far away from the Fermi energy level is from the 4s orbital of Ti atoms. Around Fermi energy level -2.0 to 2.0 eV, the DOS is predominately contributed by the 3d orbital of titanium. The PDOS of 3d, 4s, 4p orbitals overlap each other around the Fermi energy level. So, there must be hybridization between 4s, 3d, and 4p orbitals of Ti atoms in Ti7 (seen Figure 7a). This is in good agreement with the results of Wei et al.20 We notice that the H 1s energy level is lower than the Ti 3d, 4s, 4p energy levels but higher than the Ti 3s, 3p energy levels. So, the H 1s energy level should be inserted in the region between the Ti 3s, 3p energy levels and the Ti 3d, 4s, 4p energy levels when hydrogen molecules are adsorbed on the host Ti7 cluster. From Figure 7b, it is easy to find that when the first hydrogen molecule was adsorbed on the Ti7 cluster the two peaks around -5.0 eV are due to the 1s orbital of H atoms, and there are some PDOS of Ti 3d, 4s there as well. It is interesting to find that the PDOS of Ti 4p appears in two peaks around -5.0 eV, and its intensity is the same as the PDOS of Ti 4s. At the same time, the PDOS of Ti 3d expands to the lower energy level. So, we conclude that there is strong hybridization among the 1s of H atoms and 4s, 3d as well as 4p of Ti atoms. From Figure 7, we can see that as the number of adsorbed hydrogen molecule m increases, more and more energy levels of hydrogen present at the lower energy region around -4.0 to -10.0 eV, and the degenerated energy level decreases as a function of the number m. Meanwhile, the PDOS of Ti 3d expands to even more lower energy level. It is well-known that charging on the cluster or losing more electrons from the host cluster can lead to the redistribution of thechargedensityandsometimesevenstructuraltransformations.32,33 As more H2 are adsorbed onto Ti7 successively, more hybridization occurs among the 1s of H atoms and 4s, 3d as well as 4p

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Figure 8. Most stable and metastable structures of Tin-mH2 (n ) 2-7, and m ) 1-21). Green or red ball are for H atoms, while blue balls are for Ti atoms. Only these longest distances between H2 (red ball) and Tin clusters were displayed.

of Ti atoms. The intensity of the peaks around EF level, which was originally contributed by 3d orbital of Ti atoms, decreases significantly as m increased to 21 (seen Figure 6). It implies that titanium atoms transfer their 3d, 4s electrons to the hydrogen σ* and Ti 4p orbital. Because of the host cluster Ti7 transferring more electrons to the hydrogen molecules, the geometric structure of the host cluster (Ti7) is distorted significantly; at the same time, the interaction between Ti and Ti becomes weaker and weaker, and some of the H-H bonds in the hydrogen molecules are broken, while others are elongated. This is the reason why the average length of the host cluster (Ti7) has been elongated in this work and why the lattice constants of the palladium nanoparticle increase under high hydrogen pressure.31 D. Geometries of Saturated Tin-mH2 (n ) 2-7, and m ) 1-21). On the basis of the criterion of the bond type as shown in section C and the results of the single hydrogen molecule adsorption on the Tin (n ) 2-7) clusters, the structures of Tin cluster adsorbing more than one H2 molecule can be built from Tin-H2 consecutively. Hydrogen molecules, not hydrogen atoms, were added on the most stable structures of the host Tin-(m-1) H2 clusters, and then, the structures of Tin-mH2 were optimized without symmetry restriction. In Figure 8, only the saturated structure of the most stable and metastable Tin-mH2 clusters are shown with the character “G” or “M” denoting the most stable or metastable, respectively. The binding energy Eb(Tin-mH2), the energy gap Egap between the HOMO and LUMO orbitals and the binding energy EbH per atom of H for Tin-mH2 clusters are all presented in Table 4. It is interesting to find that the structure was saturated when the tenth hydrogen molecule was adsorbed on Ti2, and the mass density of hydrogen for Ti2-10 H2 cluster is 17.38 mass %.

TABLE 4: Binding Energy Eb(Tin-mH2), the Energy Gap Egap between HOMO and LUMO Orbitals, and the Binding Energy EbH Per Atom of H for Tin-mH2 Clustersa cluster Ti2-10H2 Ti3-15H2 Ti4-13H2 Ti5-15H2 Ti6-18H2 Ti7-21H2

G M G M G M G M G M G M

Eb(Tin-mH2)

EHb

56.144 55.996 84.557 84.086 82.198 81.828 98.059 97.761 113.710 108.672 137.892 137.888

0.304 0.296 0.272 0.256 0.416 0.401 0.450 0.440 0.279 0.139 0.389 0.389

a The values are all in eV, and the characters “G” and “M” denote the ground state and metastable state, respectively.

Ti3 can chemisorb 15 hydrogen molecules resulting in a hydrogen mass density the same as that for Ti2-10H2. The saturated structure for Ti4-mH2, Ti5-mH2, and Ti6-mH2 contain 13, 15, and 18 hydrogen molecules, respectively, and the hydrogen content is reduced surprisedly. When it come to Ti7, the titanium cluster is saturated after it has chemisorbed 21 hydrogen molecules, six hydrogen molecules more than the previous study (Ti7-30H) by Tarakeshwar et al.,24 and the mass density of hydrogen for Ti7-21H2 cluster is 11.21 mass %, lower than that for Ti2-10H2 and Ti3-15H2. In Figure 8, only these longest distances between H2 and Tin cluster are displayed, where the balls in red denote the hydrogen molecules with the longest distance to the Tin cluster. It is very easy to find that the H-H bond in each hydrogen molecule adsorbed on the host

Structures for Hydrogen Storage on Ti Clusters Tin is elongated or even broken eventually, and the longest bond length between H and Ti atom is about 2.20 Å as shown in Figure 8 (Ti4-13H2-G). Tarakeshwar et al.24 have pointed out that it corresponds to the onset of the physisorption barrier when the hydrogen molecules is 2.4 Å away from the host cluster in the Ti4-1H2 cluster. It is evident that all of the hydrogen molecules are strongly adsorbed on the host Tin clusters in the Tin-mH2 clusters. From Figure 8, we also find that each Ti atom in Tin-mH2 clusters can bind up to about 3-5 H2 molecules. This is in agreement with the conclusion of Yildirm et al.13 If we suppose that the effective space for free titanium atom to adsorb hydrogen molecules is 100%, then it is obvious that the effective space for each titanium atom to adsorb hydrogen molecules on the Tin clusters decreases with the increase of the size of Tin clusters. Because the effective space for each Ti atom to adsorb H2 on the host Tin clusters decreases with the size of Tin cluster (shown as in Figure 8), the maximum amount of H2 adsorbed on each Ti atom decreases with the increase of the size of the cluster as well. For instance, in Ti2 clusters, each Ti atom can adsorb up to five hydrogen molecules, whereas in Ti7, each Ti atom can only adsorb at most three hydrogen molecules. It is found that when the size of Tin cluster goes beyond n ) 5, the maximum amount of hydrogen molecules that can be adsorbed on each Ti atom approaches a constant, which is 3. IV. Conclusion Using the DMol3 cluster method based on DFT under the GGA, we have explored the geometric and electronic structures of Tin-mH2 (n ) 2-7, and m ) 1-22). By optimizing geometry structures, we first obtained the saturated configurations for the hydrogen storage on small Tin (n ) 2-7) clusters in theory. It is interesting to find that, because the effective space for each Ti atom to adsorb hydrogen molecules on the host Tin clusters decreases with the increase of the size of Tin clusters, the maximum amount of hydrogen molecules which can be adsorbed on each Ti atom also decreases with the increase of the size of the cluster. In Ti2 cluster, each Ti atom can adsorb up to five hydrogen molecules, whereas in Ti7 cluster, each Ti atom adsorbs at most three H2. It is found that when n (Tin) goes beyond 5, the maximum amount of H2 adsorbed on each Ti atom approaches a constant of 3. For Tin-H2 clusters, when the size of the host cluster Tin is small, the hydrogen atoms prefer locating on the bridge site of the titanium clusters; when the size of host cluster is larger than n ) 5, all of the hydrogen atoms prefer staying on the top of faces. For Ti7-mH2 clusters, because the AMC increases first and decreases afterward, the binding energy EbH per atom of H first increases when the hydrogen molecule number m increases from 1 to 3 and then decreases slowly when the hydrogen molecule number m increases further from 3 to 21. After hydrogen molecules were adsorbed on Ti7, as a result of the redistribution of the charge density, the interaction between titanium atoms in host clusters becomes weaker and weaker, the H-H bonds are elongated, some are even broken, and the dissociated hydrogen atoms prefer staying at the bridge site of the bond of Ti-Ti or locating on top of the face of the host cluster. Furthermore, for Ti7-mH2, with the increase of the hydrogen molecule number m, there is strong hybridization between the 1s of H atoms and the 4s, 3d, and 4p of Ti atoms, and the PDOS (4s, 3d, and 4p) of Ti atoms have expanded to lower energy levels in these clusters, the

J. Phys. Chem. C, Vol. 113, No. 35, 2009 15513 average bond length of Ti-Ti in the host cluster increases generally, and the geometric structure of the host cluster is distorted from D5h into C3V. Acknowledgment. We thank Dr. Chaohui Tong and Dr. Xiangmei Duan for useful discussions and suggestions. This research is supported by the National Science Foundation of China, Grants NSFC 10804058 and NSFC 10774079, the Science Foundation of Zhejiang, Grant Y607546, the Science Foundation of Ningbo, Grant 2009A610056, and K. C. Wong Magna Foundation in Ningbo University. The computation was performed at Ningbo Center of Supercomputing. References and Notes (1) Schlapbach, L.; Zu¨ttel, A. Nature 2001, 414, 353. (2) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature (London) 1997, 386, 377. (3) Liu, C.; Fan, Y. Y.; Liu, M.; Cong, H. T.; Cheng, H. M.; Dresselhaus, M. S. Science 1999, 286, 1127. (4) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keeffe, M.; Yaghi, O. M. Science 2003, 300, 1127. (5) Li, X.; Grubisic, A.; Stokes, S. T.; Cordes, J.; Gantefo¨r, G. F.; Bowen, K. H.; Kiran, B.; Willis, M.; Jena, P.; Burgert, R.; Schno¨ckel, H. Science 2007, 315, 356. (6) Gonzalez Szwacki, N.; Sadrzadeh, A.; Yakobson, B. I. Phys. ReV. Lett. 2007, 98, 166804. (7) Prasad, D. L. V. K.; Jemmis, E. D. Phys. ReV. Lett. 2008, 100, 165504. (8) Kim, Y.-H.; Zhao, Y.; Williamson, A.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2006, 96, 016102. (9) Yoon, M.; Yang, S.; Hicke, C.; Wang, E.; Geohegan, D.; Zhang, Z. Phys. ReV. Lett. 2008, 100, 206806. (10) Lee, H.; Choi, W. I.; Ihm, J. Phys. ReV. Lett. 2006, 97, 056104. (11) Lee, H.; Nguyen, M. C.; Ihm, J. Solid State Commun. 2008, 146, 431. (12) Zhao, Y.; Kim, Y.-H.; Dillon, A. C.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2005, 94, 155504. (13) Yildirim, T.; Ciraci, S. Phys. ReV. Lett. 2005, 94, 175501. (14) Liang, G.; Huot, J.; Boily, S.; Van Neste, A.; Schulz, R. J. Alloys Compd. 1999, 292, 247. (15) Anton, D. L. J. Alloys Compd. 2003, 400, 356–357. (16) Wang, J.; Ebner, A. D.; Ritter, J. A. J. Phys. Chem. B 2006, 110, 17353. (17) Fichtner, M.; Fuhr, O.; Kircher, O.; Rothe, J. Nanotechnology 2003, 14, 778. (18) Balema, V. P.; Balema, L. Phys. Chem. Chem. Phys. 2005, 7, 1310. (19) Lian, L.; Su, C.-X.; Armentrout, P. B. J. Chem. Phys. 1992, 97, 4084. (20) Wei, S. H.; Zeng, Z.; You, J. Q.; Yan, X. H.; Gong, X. G. J. Chem. Phys. 2000, 113, 24. (21) Zhao, J.; Qiu, Q.; Wang, B.; Wang, J.; Wang, G. Solid State Commun. 2001, 118, 157. (22) Salazar-Villanueva, M.; Herna´ndez Tejeda, P. H.; Pal, U.; RivasSilvas, J. F.; Rodı´guez Mora, J. I.; Ascencio, J. A. J. Phys. Chem. A 2006, 110, 10274. (23) Dhilip Kumar, T. J.; Weck, P. F.; Balakrishnan, N. J. Phys. Chem. C 2007, 111, 7494. (24) Tarakeshwar, P.; Dhilip Kumar, T. J.; Balakrishnan, N. J. Phys. Chem. A 2008, 112, 2846. (25) Dhilip Kumar, T. J.; Tarakeshwar, P.; Balakrishnan, N. J. Chem. Phys. 2008, 128, 194714. (26) Delley, B. J. Chem. Phys. 1990, 92, 508. (27) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (28) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (29) Russon, L. M.; Heidecke, S. A.; Birke, M. K.; Conceicao, J.; Morse, M. D.; Armentrout, P. B. J. Chem. Phys. 1994, 100, 4747. (30) Sakurai, M.; Watanabe, K.; Sumiyama, K.; Suzuki, K. J. Chem. Phys. 1999, 111, 235. (31) Kobayashi, H.; Yamauchi, M.; Kitagawa, H.; Kubota, Y.; Kato, K.; Takata, M. J. Am. Chem. Soc. 2008, 130, 1828. (32) Wei, S.-H.; Huang, L.; Ji, M.; Gong, X. G. Chem. Phys. Lett. 2006, 420, 125. (33) Li, S. F.; Gong, X. G. Phys. ReV. B 2004, 70, 075404.

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