# Theoretical Investigation of the Hydrogenated Aluminum Cobalt Clusters

##### Journal of Research in Nanotechnology

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Ling Guo

School of Chemistry and Material Science, Shanxi Normal University, Linfen 041004, China

Volume 2014 (2014), Article ID 850303, Journal of Research in Nanotechnology, 14 pages, DOI: 10.5171/2014.850303

Received date : 29 May 2014; Accepted date : 7 July 2014; Published date : 19 September 2014

**Academic editor:**
Juguang Han

**Cite this Article as:**
Ling Guo (2014), “Theoretical Investigation of the Hydrogenated Aluminum Cobalt Clusters”, Journal of Research in Nanotechnology, Vol. 2014 (2014), Article ID 850303, DOI: 10.5171/2014.850303

Copyright © 2014. Ling Guo. Distributed under Creative Commons CC-BY 3.0

**Abstract**

**Keywords:**
Hydrogenated aluminum cobalt cluster; electronic properties; Density functional theory.

**Introduction**

Among the candidate systems to have been considered, the bimetallic aluminum cobalt clusters

Since the pioneering work of Knight et al. (1984) exhibiting a direct relationship between the pronounced peaks in the mass ion intensities (commonly referred to as magic numbers) of Na clusters and electronic shell closure, considerable theoretical and experimental work has been carried out to search for new magic numbers in compounds as well as charged metal clusters (1997). The electronic shell closure derived from the Jellium model dictates that metal clusters with 2, 8, 20, 40 … electrons are particularly stable as they correspond to complete filling of 1s, 1s1p, 1s1p1d2s, 1s1p1d2s1f2p … groups of orbital, respectively. As Al, Co, and alkali metal atoms exhibit free-electron-like behavior in their respective bulk phases, one would expect the atomic and electronic structure as well as relative stabilities of cobalt-doped aluminum clusters to exhibit the same behavior as those of alkali atom-doped aluminum clusters (1994). Since both clusters contain the same number of valence electron; for example, if clusters are born neutral, Al13Co cluster should exhibit enhanced stability (and, hence, a peak in the mass spectra) over their neighbors, as it would contain 40 valence electrons.

Against this background, the sequential growth of small AlnCo clusters with n=1-17 (Guo 2007, 2008) have been explored recently. And to obtain further insights on the nature of chemisorption of a single H2 molecule on AlnCo clusters, the extensive calculations of chemisorption of H2 and sequential hydrogen loading on the above energetically stable clusters are studied. A detailed picture of chemisorption of H2 on AlnCo (n=1-15) nanoclusters based on an analysis of energies, HOMO-LUMO gap, Stability, fragmentation behavior, and Bonding nature are presented. So, the understanding of the adsorption of H2 molecule on aluminum cobalt clusters could give useful insight on hydrogen interaction with other alloy clusters.

The paper is organized as follows: A brief account of the computational methodology is given in Sec. 2, followed by a detailed presentation and discussion of the first-principles calculations in Sec. 3 on small aluminum cobalt clusters with n=1-15 AlnCo and up to two hydrogen atoms. These will provide an understanding of the nature of interaction of hydrogen with aluminum cobalt clusters and the magic behavior of these clusters. A summary of my findings and conclusions are given in Sec. 4.

**Methodology**

All calculations are performed using the density functional theory (DFT) provided by the Gaussian 03 suite of programs (Frisch 2004). The density functional is treated with the generalized gradient approximation (GGA) corrected-exchange potential of the B3LYP (Becke 1993), and its application has been shown to be effective (Guo 2007, 2008). The double-Î¾ basis set lanl2dz is employed (Hay 1985). Frequency analyses at the optimized structures are carried out at the same theoretical level to clarify if the optimized structures are true minima or transition states on the potential energy surfaces of specific clusters. All of the obtained, most stable clusters are characterized as energy minima without imaginary frequencies. The geometries are fully optimized. The structures of small AlnCo (n=1-15) clusters are reported in my previous paper (Guo 2007, 2008).

Low energy structures may be missed if the starting configurations of the search are not set appropriately. In order to avoid this, ab initio simulations starting with several initial two-dimensional and three-dimensional structures are performed for each AlnCo adsorbate cluster. For simulating the adsorption process, different orientations of the molecules with respect to the AlnCo cluster are considered for optimization, and the H2 molecules and the AlnCo cluster are allowed to relax freely. To avoid computational bias, the cluster and H2 chemisorptions geometries are fully optimized without imposing symmetry constraints until the maximum force is less than 4.5×10-4 eV/Šand the maximum displacement is less than 1.8×10-3 Å.

The Binding energies (BE) of AlnCo and AlnCoHm are calculated based on eqs (1) and (2).

BE (AlnCo)=E(AlnCo)-nE(Al)-E(Co) (1)

BE (AlnCoHm)=E(AlnCoHm)-nE(Al)-E(Co)-mE(H) (2)

where m and n represent the size of the clusters, E(AlnCo), E(AlnCoHm), E(Al), E(Co), and E(H) are energies of AlnCo, AlnCoHm clusters, and Al, Co, H atoms, respectively.

**Results and discussions**

**Hydrogen on AlnCo(n=1-15) **

The optimized geometries for the adsorption of one and two H atoms on small AlnCo(n=1-15) clusters are shown in Fig.1. In Table 1 and 2, the values of the binding energy, the HOMO-LUMO energy gaps, and the mean nearest-neighbor bond lengths of AlnCo(n=1-15) and AlnCoHm (n=1-15; m=1,2) clusters are displayed for all the isomers shown in Fig.1. For the chemisorptions of H2 on the AlnCo cluster, there are three possible adsorption sites: 1-fold on top, 2-fold edge, and 3-fold hollow site. The calculation result shows that the on-top adsorption configuration is energetically most stable.

**Table 1: Binding energies (BE), and HOMO-LUMO gaps of various AlnCo clusters obtained using the B3LYP-DFT method. dAl-Co is the mean nearest-neighbor bond lengths between Al and Co atoms**

The ground-state Al2Co cluster is a spin doublet isosceles triangle with C2v symmetry and a binding energy of 3.52 eV. The ground state corresponding to Al2CoH cluster is a spin triplet with a Al-H bond length of 1.64 Š(Table 2) and an Al-H stretching frequency of 1751 cm-1, and the H atom takes on-top adsorption with the Al atom, which is different from the structure of AlCoH with 2-fold edge model. The BE of H on Al2Co is 6.22 eV. The C2v isomer [Fig. 1(2c)] with two H atoms bridging in two Al atoms is found for the most stable geometry of Al2CoH2 cluster. Other optimized geometries are also considered for this cluster, for example, occupied different places of Al and Co atom (2d) or two H atoms are located on top Al atoms (2e). None of them are more stable than the ground state structure.

**Table 2: Binding energies (BE’s), structures, and HOMO-LUMO gaps of various clusters obtained using the B3LYP-DFT method. dAl-Co, dAl-H, and dCo-H, are the mean nearest-neighbor bond lengths between Al and Co atoms, Al and H atoms, Co and H atoms. Location of H is represented by symbols n, o, b, f, t, h which mean neighboring, opposite, bridge, farthest, top and hollow site, respectively**

The ground-state found for Al4Co is a spin doublet pyramid (C4v) structure [Fig. 1(4a)] with a binding energy of 7.24 eV. The spin multiplicity found for Al4CoH is a spin singlet and its structure, different with small clusters above, prefers a top site of Co atom [Fig. 1(4b)] on it. In the case of two H on Al4Co, two H atoms on the top site of Al atom [Fig. 1(4c)] is the ground state, and the spin multiplicity is quartet. The structure with two H atom taking 3-fold hollow site on two Al and one Co atoms [Fig. 1(4d)] is 0.16 eV higher in energy. Both 4c and 4d geometries are with C2v symmetry.

Al5Co is a spin triplet structure [Fig. 1(5a)] with D3h symmetry. Similar to Al2Co and Al3Co, one H is most favorable on a top site of Al atom [Fig. 1(5b)], and it is with a binding energy of 0.36 eV stronger than that of the bridging between Al and Co atom adsorption [Fig. 1(5c)]. The BE (2.98 eV) of H on Al5Co is also one of the largest among all the clusters studied. Accordingly, Al5CoH should have large abundance. Two H favor top sites of neighbor Al and Al atoms [Fig. 1(5d)]. The BE of this isomer is 6.00 eV which is again quite large and slightly lower than the value for Al3CoH2. This should also make hydrogen dissociate on this cluster unless there is a barrier. Isomers with two H on different top sites of Al and Co atoms [Fig. 1(5e)] and the same Al atom have 0.30 and 0.42 eV higher energies, respectively.

For these small clusters the BE per H is high with n=1 and 5. And the addition of a second H increases nearly the same value of BE for n=2-5. On the other hand, for n=1, the addition of a second H increases the BE significantly. My calculations suggest that H2 is likely to be combining at least on AlCo small cluster and these clusters could disintegrate, such as AlCoH2, or combine with others to form energetically more favorable species.

The lowest-energy isomer of Al6Co is a capped triangular prism structure [Fig. 1(6a)] with C2v symmetry. Adsorption of single hydrogen on a top, edge or hollow site of Al atom or Co atom is considered. The BE (2.71 eV) of H on an edge site of two Al atoms of Al6Co [Fig. 1(6b)] is the smallest among all the clusters. The fragmentation energy (see below) is also small and this gives further support for the instability of Al6CoH. Accordingly, it may not have large abundances, and the structure (6c) with hydrogen on a top site lies 0.08 eV high in energy. For two hydrogen atoms on Al6Co, several configurations are studied. These include two opposite top of Al and Al atoms in the different triangle [Fig. 1(6d)], two neighboring top of Al and Al atoms in the same triangle [Fig. 1(6e)] and different triangle [Fig. 1(6f)]. The calculated BE’s given in Table 2. The most favorable adsorption sites are structure 6d. The two H have a similar configuration as in Al4CoH2. The BE for 2H is 5.32 eV and it shows that interaction between two hydrogen on Al6Co is not more attractive than clusters discussed above. However, this energy is also higher than the dissociation energy of H2 (4.6 0 eV). Accordingly, hydrogen is likely to be dissociated on Al6Co. The distance between two hydrogens on Al6Co in the lowest-energy state is very long as compared to the bond length of 0.75 Šin H2. Therefore, two hydrogens are in a dissociated on Al6Co. The dissociation can happen on a top site of Al6Co. Since there are several such sites, the probability for such a dissociative process is also high.

For Al7Co, the lowest-energy structure is a spin triplet with Cs symmetry [Fig. 1(7a)]. One hydrogen adsorption is favorable on the top of the headpiece Al atom [Fig. 1(7b)]. The BE (2.83 eV) of H on Al7Co is also one of the smallest among all the clusters studied. Isomers with H on the top site of capping Al atom [Fig. 1(7c)] and Co atom [Fig. 1(7d)] are 0.02 and 0.56 eV higher in energies, respectively. The small HOMO-LUMO gap is likely to make further interaction of hydrogen with this cluster energetically not so favorable. In order to confirm this, some calculations are carried out on Al7CoH2. Several initial configurations are considered for two hydrogens. These include H atoms on the top of two neighboring Al and Al atoms in the lower part of the Al7Co cluster [Fig. 1(7e)]. This has the lowest energy. The HOMO-LUMO gap is lower (1.93 eV) and the addition of one more hydrogen to Al7Co leads to a gain of 5.50 eV, an increase of more than 2.67 eV in the BE of H as compared to one hydrogen on Al7Co. The other calculated positions for two hydrogens on Al7Co are one on top of two distant Al atoms [Fig. 1(7f)] or two opposite Al atoms [Fig. 1(7g)]. The energy, the HOMO-LUMO gap, and other structural information are given in Table 2. The energies of the isomers [Fig. 1(7f, 7g)] are close to that of Fig. 1(7e), and their energy differences with 7e are 0.08 and 0.31 eV, respectively.

Al8Co has Cs symmetry [Fig. 1(8a)]. This structure can be very roughly decomposed into two interacting entities: structure Al4Co and Al4 are bridged with two Al-Co and Al-Al bonds. Similar to Al4Co, this cluster would be anticipated not to favor to react with one hydrogen; indeed, the BE of H is 2.57 eV similar to Al4Co of 2.24 eV. One H is favorable on a top site of Al atom in the top part of Al8Co [Fig. 1(8b)], and from now on, all the clusters later have the same geometry. Structure Fig. 1(8c) with H atom on a top site of another Al atom is only 0.06 eV less stable. Therefore, the interaction depends very sensitively on the electronic and atomic structures of clusters. Adsorption of two hydrogen are studied on a few selected sites which included two neighboring faces with H atoms on the different Al atoms [Fig. 1(8d)], the two H atoms on the top sites of neighboring Al and Al atoms in the upper part of Al8Co [Fig. 1(8e)], and two opposite top sites of neighboring Al atoms in the upper part of Al8Co [Fig. 1(8f)]. The 8d isomer has the lowest energy (Table 2). The BE of this isomer is 5.57 eV, which is larger than AlnCo (n=2, 4, 6 and 7) and similar to AlCo and slightly slower than the value for Al3Co and Al5Co.

The lowest energy structures for Al9Co, Al10Co and Al11Co clusters are spin triplet structure with C1 symmetry, spin doublet structure with C2 symmetry, and spin triplet structure with C1 symmetry, respectively. And the binding energies are 16.87, 18.39 and 20.86 eV. The Al9Co may be viewed as an Al atom attached to the most stable form of Al8Co. H adsorption on Al atom [Fig. 1(9b)], a doublet, is the most stable with a binding energy of 2.64eV. The ground state corresponding to Al9CoH2 cluster is a spin singlet with an average Al-As bond length of 2.378 Å, which is the same as Al9CoH. Two H favor top sites of neighbor Al and Al atoms [Fig. 1(9c)]. Just like the Al3Co and Al5Co, Al7Co clusters discussed above. Two H adsorption on distant Al and Al atom [Fig. 1(9d)], a spin singlet is a substable structure with a binding energy of only 0.09 eV less than the ground state.

For Al12Co, the Cs symmetrical Al12Co cluster [Fig. 1(12a)] has been computed to be the most stable using B3LYP/lanl2dz method. Adsorption of single hydrogen on the top site of Al atom [Fig. 1(12b)] is considered. The BE (2.88eV) of H on Al12Co is one of the largest among all the clusters studied. However, the HOMO-LUMO gap is small (1.39 eV). The small HOMO-LUMO gap is likely to make further interaction of hydrogen with this cluster energetically so favorable. In order to confirm this, calculations on Al12CoH2 are carried out. Several initial configurations are considered for two hydrogens. These include two H atoms on the top sites of neighboring and opposite Al and Al (Co) atoms in the same hexagon and two H atoms on the top sites of Al and Al (Co) atoms in the neighboring faces. The 1(12d) isomer is 0.62 eV less stable as compared to the 1(12c) isomer that is the most favorable. In order to further check the results obtained from the B3LYP method, BE’s for H on the top sites of Al12Co is calculated using the PW91 method. It is found that the BE’s of hydrogen is 2.69 eV. This result is quite close to the value (2.88 eV) obtained from the B3LYP method.

AlnCo (n=13-15) take the C1, C1 and Cs structures as their ground states, respectively. For AlnCoH (n=13-15), the ground states reveal top H bonding to the Al atoms [Fig. 1(13b), 1(14b) and 1(15b)]. The spin multiplicity found for them are all doublet. Top on the neighboring Al and Co atoms ground-state structures are found for AlnCo (n=13-15) [Fig. 1(13c), 1(14c) and 1(15c)].

**Stability and fragmentation behavior**

In order to check the stability of the lowest-energy isomersï¼Œvibrational frequencies for selected clusters have been calculated using the B3LYP/lanl2dz level of theory. It is found that the lowest-energy isomers of all kinds of clusters discussed above have all real frequencies and are, therefore, stable. Figure 2 shows the plot of the BE of one and two H atoms on AlnCo clusters. As discussed in the previous section, the BE is large for H with n=3, 5, 7, 10, 12, and 15 of AlnCoH atoms. And, for 2H, clusters with n=3, 5, 10, 12, and 14 have higher BE’s. The stability of these complexes is further studied from the fragmentation energies (Table 3). Channels with Aln-1CoHm, Aln-2CoHm, or Aln-1CoHm-1 molecule being one of the fragments have been studied. It is noted that in all these processes, the fragmentation energy is the largest for Al15CoH2 and therefore, it is expected to be among the most stable species. Also the fragmentation energies for Al3CoH, Al8CoH2, Al14CoH, Al14CoH2, and Al15CoH are next largest for all these channels, suggesting them to be other stable clusters. On the other hand the fragmentation energy for Al13CoH2 is 0.74 eV for Aln-1CoHm +Al channel and it is close to the lowest values. The small clusters of Al4CoH also have lower values.

**Table 3: Fragmentation energies of AlnCoHm clusters with the product Aln-pCoHm-q, p=1 and 2, and q=1. All the values mean the parent cluster has a larger binding energy than the sum of the BE of the products**

**Bonding nature**

**Summary**

The result on hydrogen interaction with aluminum cobalt clusters has been presented. Hydrogen undergoes chemisorptions and interacts strongly with aluminum cobalt clusters. The Al-on top sites are the most stable chemisorptions site for one hydrogen adsorption in most AlnCo clusters except for AlnCo (n=1, 4, 6, and 11) cluster. Top on the neighboring Al and Al atoms ground-state structures of AlnCo (n=2, 3, 5, 7, 9, 10, 12, 13, 14, 15) and top on the opposite Al and Al atoms ground-state structures of AlnCo (n=4, 6, 8, 11) are found for two hydrogen adsorption on AlnCo cluster. And there is a slight increase in the mean Al-Co bond lengths after H adsorption on the lowest-energy sites of the most AlCo clusters. In addition, the nearly constant value for Co-H and Al-H bond lengths on different clusters at specific adsorption sites suggests the similar nature of bonding of H in different clusters. In general, the binding energy of H and 2H are both found to decrease with a decrease in the cluster size. And the result shows that large binding energies of the hydrogen atoms and large highest occupied and lowest unoccupied molecular-orbital gaps for Al3CoH, Al15CoH and Al14CoH2 make these species behaving like magic clusters. The stability of these complexes is further suggesting being the stable clusters from the fragmentation energies.

**Figure.1 Relaxed structures of AlnCoHm (n=1-15; m=1, 2). Gray, black and white balls are used for Al, Co and H, respectively**

**Figure2: Binding energies of H (left) and 2H (right) atoms on AlnCo clusters**

**Acknowledgment**

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