A density functional theory study of adsorption and dissociation of H2 molecule on small PdnAgm (n + m ≤ 4) metal clusters

doi:10.21203/rs.3.rs-1516797/v1

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A density functional theory study of adsorption and dissociation of H2 molecule on small PdnAgm (n + m ≤ 4) metal clusters

https://doi.org/10.21203/rs.3.rs-1516797/v1

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The adsorption and dissociation of hydrogen molecule on small Pd_nAg_m (n + m ≤ 4) clusters is studied employing density functional theory (DFT) calculations. The lowest energy structures of the Pd_nAg_m clusters are initially presented. Based on the obtained structures, various geometries of H₂ adorption and dissociation with these clusters are examined. The cluster size and composition of the Pd_nAg_m clusters are found to control the nature of the adsorption process. The results suggest that molecular adsorption is more favourable on the Pd atom and mixed clusters, while hydrogen dissociation is more favourable on the Pd_n (n = 2–4) clusters. The Pd dimer and trimer are found to be the most reactive clusters for hydrogen adsorption, while single Ag atom is the least reactive one. The natural bond orbital (NBO) population analysis indicates that hydrogen atoms tend to draw electrons from the metal clusters in the dissociative form and donate electrons to the metal clusters in the molecular adsorption form. The density of states (DOS) of the Pd_nAg_m trimers are also presented and discussed.

Bimetallic clusters

Pd-Ag small clusters

DFT

Hydrogen adsorption and dissociation

A metal cluster can be defined as aggregates of a small number to hundreds of atoms. This class of materials possesses high surface to volume ratio compared to their bulk counterparts reflecting distinctive physical and chemical properties [1, 2]. The geometric structure and size of small transition metal clusters play a key role in controlling their behaviour [3]. Consequently, the catalytic properties of small metallic clusters are expected to vary and be sensitive to the cluster size and composition [4]. Adding an impurity atom or alloying can further modify the physical and chemical properties of pure transition metal clusters affecting their catalytic properties [4–6]. Typically, the presence of the second component is expected to change the electronic and geometric properties and enhances the catalytic performance of monometallic catalysts [5–7]. The enhanced activity of bimetallic catalysts could be attributed to ''geometric ensemble effects'' where by active sites on the catalyst surface consist of atoms arranged in specific groupings [7].

The study of interactions between transition metal clusters with atoms or small molecules is fundamental to understand catalytic processes. A primary step to the reaction mechanism is the adsorption behavior of the atoms or small molecules on the metal clusters [6, 8, 9]. Hydrogen possesses the characteristics of being abundant, high energy content material, eco-friendly and renewable that makes it a candidate alternative to fossil fuels and a potential energy source [10, 11]. The interactions and behavior of hydrogen on metal surfaces and clusters are of importance to various applications and technologies such as catalytic processes, metal embrittlement, hydrogen storage and fuel cells [11–15]. In the latter case, for instance, electricity can be generated by harmless electrochemical reactions of hydrogen and oxygen on metal surfaces as catalysts; and the process typically involves the adsorption and diffusion of the constituents. For example, proton conducting fuel cells employ an acidic media and hydrogen gas as a fuel, and consequently hydrogen oxidation occurs at the anode producing electrons and protons which migrate to the cathode and recombine with oxygen resulting in water [11, 14, 16].

The electronic structure of hydrogen atoms and molecules is simple. Therefore, electronic structure methods can be effectively employed to describe their interactions with metal surfaces and provide valuable insights into essential properties of hydrogen-metal systems such as surface reactivity, bond-making and bond-breaking behaviors [17]. In this regard, a number of theoretical studies have been carried out on the interactions between atomic or molecular hydrogen with pure and/or binary metal clusters [5, 6, 8, 9, 13, 14, 18–29]. It has been largely proposed that the nature of the metallic components, geometry and size are crucial in controlling the adsorption and dissociation behaviors of hydrogen on the binary cluster surfaces.

A series of Pd-Ag bimetallic catalysts have experimentally been shown to be efficient for methane combustion [30], oxidation of carbon monoxide [31], partial hydrogenation of acetylene [32], dehydrogenation of formic acid [33, 34] and fuel cell-related reactions [35–37]. Pd-Ag binary alloys have also been acknowledged as efficient and promising materials for hydrogen gas permeation and storing [38–41] as well as sensing [42]. Additionally, various physiochemical properties of Pd-Ag bimetallic cluster system have been estimated by theoretical calculations [3, 43–45]. For instance, a DFT study of small Pd_nAg (n = 1–8) clusters [45] has indicated that the Pd_3 − 8Ag clusters possess three-dimensional configurations and their binding energies are nearly similar to that of the corresponding Pd_n clusters. The study has also found that stability and reactivity of the ground-state clusters are size-dependent, and that a universal charge transfer takes place from Ag atom to Pd atoms within the clusters. It has also been shown for Ag_m-Pd_n (m + n = 5) clusters that structures of bimetallic tetramers and pentamers shift from two to three dimensions with the presence of two Pd atoms in the cluster. Besides, stability analysis of the bimetallic tetramers has revealed that Ag₂Pd₂ is the most stable cluster [3]. Other theoretical studies have focused on the assessment of various chemical processes over Pd-based [46–48], Pd-doped and Ag-doped surfaces [49, 50]. Furthermore, a recent DFT study by Yang et.al. has examined the HCOOH decomposition over pure and Ag-modified Pd nanoclusters [51]. The study suggests that the activity and selectivity of the process can be improved by controlling the size and Ag composition of the nanoclusters.

A particular attention has also been directed towards studying the interactions of small molecules with Pd-Ag binary clusters. Zhao et.al. have indicated that a preferential binding of both CO [52] and NO [53] molecules takes place on Pd sites when both elements co-exist in the cluster. The authors have also found that the binding energy in both cases increases with increasing Pd content in the cluster. A study of Ag_nPdH (n ≤ 5) clusters [21] has shown that hydrogen atom binds to Ag-Pd bridge site when (n = 1–4) and to top site in the case of Ag₅Pd.

It has also been verified that hydrogen molecule adsorbs more favorably and dissociates more easily at Pd atom than Ag atom on the PdAg dimer [19, 23]. The dissociation behavior of hydrogen molecule on Ag₅ and Pd₅ clusters has been compared by Bartczak and Stawowska to that on Ag₄Pd and AgPd₅ clusters [8]. The authors have suggested that the molecule dissociates on Pd₅ cluster, while no dissociation occurs on Ag₅ cluster. The study has also concluded that mixing Ag with pure Pd catalyst reduces its ability for hydrogen dissociation, while mixing Pd with pure Ag enhances its ability for the dissociation process. Moreover, Zhang and Yang [29] have shown that, among Pd_nAg_(8−n) alloy clusters, Pd₅Ag₃ and Pd₂Ag₆ provide promising candidates for hydrogen dissociation and storage processes respectively. A variety of other DFT studies have focused on the evaluation of the catalytic performance of Pd-Ag clusters for hydrogenation of acetylene [54, 55] and CO oxidation [56]. These studies broadly suggest that mixing the two elements enhances the adsorption properties of the reactant molecules on the bimetallic clusters leading to a better performance in comparison with the mono-component clusters.

This work aims to systematically address the adsorption and dissociation behavior of hydrogen molecule on Pd_nAg_m (n + m ≤ 4) clusters within the frame work of density functional theory (DFT) at the B3P86/Lanl2DZ level of theory. Initially, the lowest energy structures of Pd_nAg_m clusters are presented. Then, a number of structural and electronic properties of most stable structures of Pd_nAg_m-H₂ clusters are presented and discussed.

All the calculations presented in this work are carried out using Gaussian 09 software [57]. GauusView 05 [58] is used for drawing atomic and molecular structures of Pd_nAg_m and Pd_nAg_m-H₂ clusters and results visualization. B3P86 exchange correlation functional and Lanl2DZ basis set are used for Pd and Ag atoms, while the 6-311 + + G(d,p) basis set is used for hydrogen atoms. The B3P86/Lanl2DZ level of theory has recently been shown to be reliable for the assessment of small Pd_nAg (n = 1–8) clusters [45]. The reliability of this method for the study of molecular hydrogen adsorption on Pd_nAg_m clusters has been initially assessed by calculating the binding energies, bond lengths and vibrational frequencies of Pd₂, Ag₂, PdAg, PdH, AgH and H₂ dimers at the B3P86 / Lanl2DZ level of theory alongside the PW91PW91 and B3LYP methods. The PW91PW91 method has been previously employed for the study of CO and NO bindings on small Ag_nPd_m clusters [52, 53] and atomic hydrogen interaction with Ag_nPd clusters [21]. In addition, the B3LYP method has been used for the study of molecular hydrogen interaction with various transition metal homonuclear and heteronuclear dimers [19]. The calculated parameters of the dimers are shown in Table 1 alongside other theoretical data from the literature and the corresponding experimental values; the blank values are not available to the best of the authors' knowledge. In comparison with the other two functionals, the results obtained with B3P86 method are largely closer to the experimental values. Besides, the calculated parameters using the B3P86 functional are consistent with the theoretical findings from other published works [3, 18, 19, 22–24, 59–61]. Hence, the results in the table suggest that the B3P86 is an effective method for the evaluation of hydrogen adsorption on Pd_nAg_m clusters.

The study of the H₂ adsorption and dissociation on Pd_nAg_m (n + m ≤ 4) clusters is accomplished by, first, optimizing various possible geometries of the clusters to identify the lowest energy structures. Then, a variety of possible configurations of the adsorption and dissociation of hydrogen molecule on the most stable configurations of Pd_nAg_m clusters are optimized to identify the lowest energy structures. The most stable geometries of the Pd_nAg_m and Pd_nAg_m-H₂ clusters are determined by performing structural optimization and vibrational frequency calculations for each structure at different spin multiplicities. Natural bond orbital (NBO) analysis is carried out for the Pd_nAg_m-H₂ clusters at the B3P86/Lanl2DZ level of theory to investigate the charge distributions. The DOS analysis is carried out using the GaussSum software [62].

3.1. Geometrical structures of Pd_nAg_m clusters

Initially, the lowest energy structures up to four atoms of pure Pd, Ag and bimetallic Pd_nAg_m clusters are determined by optimizing various possible structures at B3P86/Lanl2DZ level of theory and different spin multiplicities. Figure 1 shows the obtained results arranged in the order of decreasing Pd content in the cluster. The lowest energy structures of pure Pd clusters are obtained with triplet spin state apart from the single atom. On the other hand, the ground states of pure Ag and bimetallic Pd_nAg_m clusters are found to be in the singlet and doublet spin multiplicities respectively. It is clear from the figure that the lowest energy structure of pure and bimetallic trimers is an isosceles triangle, while that of pure Pd and Ag tetramers are distorted tetrahedron and rhombus respectively. The calculations also show that the ground state configurations of both Pd₃Ag and Pd₂Ag₂ clusters are similar to that of Pd₄, while that of PdAg₃ cluster is similar to that of Ag₄ indicating that the elemental content dominates the configuration of the Pd_nAg_m tetramer. Similar structural properties have been previously reported for Ag-Pd clusters [3, 52].

Based on the obtained ground state structures of pure and bimetallic clusters, numerous geometries of molecular hydrogen adsorption and dissociation on these clusters were examined at the same level of theory and two spin multiplicities (singlet and triplet or doublet and quartet) in order to predict the lowest energy structures. Figure 2 reveals the optimized ground state geometries (denoted as a) alongside other low-lying isomers (denoted as b-f) of Pd_nAg_m-H₂ clusters arranged from the highest to lowest Pd content in the cluster and lowest to highest energy structures. Also, the spin multiplicity, adsorption energy, average bond length, M-M bond length, shortest M-H bond length, H-H bond length, sum of NBO net charges of hydrogen atoms and HOMO-LUMO energy gap of the lowest energy structures are presented in Tables 2-5. It can be noted from these tables that the ground state geometries in all cases are obtained with the lowest spin multiplicity, that is singlet or doublet.

3.2. Molecular hydrogen interaction with Pd_nAg_m clusters

On the Pd atom, molecular hydrogen adsorption takes place without dissociation forming the ground state of Pd-H₂ cluster (PdH₂_a). The shortest Pd-H, H-H distances, H-Pd-H angle and H-H vibrational frequency in this cluster are 1.661 Å, 0.881 Å, 30.76° and 2764.39 cm^-1 respectively. Isomer PdH₂-b, in which molecular hydrogen dissociation occurs, is less stable and higher in energy than the ground state by 0.197 eV. This suggest that an energy barrier of the latter value is required for the transformation from the molecular to dissociative adsorption of hydrogen on the Pd atom. Isomer PdH₂_c is much less stable than the lowest energy structure and found to be higher in energy by 2.415 eV. The obtained results for PdH₂_a and PdH₂_b are comparable to previous theoretical findings [22]. On the other extreme, the ground state geometry on the Ag atom (AgH₂_a) involves molecular hydrogen dissociation with Ag-H, H-H distances and H-Ag-H angle of 1.660 Å, 2.840 Å and 117.59° respectively. The linear structure (AgH₂_b) is less stable and found to be higher in energy than AgH₂_a by 0.390 eV. The atomic configuration of Pd is a closed-shell of 4d¹⁰, while that of Ag is 4d¹⁰ 5s¹ which means that it has only one s valence electron [22, 24]. This could be the reason of the better reactivity on Ag atom towards hydrogen dissociation.

The interaction behaviour on homonuclear dimers is contrary to that on single atoms. Apparently, H₂ prefers to dissociate into two hydrogen atoms at the bridge sites of Pd₂ forming the lowest energy structure (Pd₂H₂_a) with Pd-Pd and shortest Pd-H bond lengths of 2.699 Å and 1.661 Å. This geometry has also been proposed by Ni and Zeng [22] as the ground state of Pd₂H₂ cluster with comparable bond lengths to that obtained in this work. Pd₂H₂_b geometry is higher in energy than the ground state by 0.818 eV. In this geometry, hydrogen molecule binds to the bridge site of the Pd₂ dimer with H-H bond distance of 1.036 Å which is longer than the corresponding experimental value 0.746 Å [19] suggesting more tendency of H₂ towards dissociation. Isomer Pd₂H₂_c is less stable structure than the previous two structures and found to have a higher energy than the ground state by 1.501 eV. This structure involves molecular hydrogen adsorption on top of one Pd atom in line with the axis of Pd₂ dimer with Pd-H and H-H bond lengths of 1.681 Å and 0.870 Å which are close to findings in other reports [14, 22, 27]. Similarly, H₂ prefers to molecularly adsorb on top of one Ag atom in line with the axis of Ag₂ dimer forming the ground state structure (Ag₂H₂_a) with Ag-Ag, Ag-H and H-H bond lengths of 2.573 Å, 2.519 Å and 0.751 Å respectively. These results suggest that H₂ tends to weakly bind to Ag₂ dimer and are in harmony with previous observations by Wang et.al [19]. The dissociative form (Ag₂H₂_b), in which one hydrogen atom is placed at the bridge sites, is less stable geometry and found to be higher in energy than the ground state by 1.425 eV.

On the heteronuclear cluster, molecular adsorption appears to be more favourable than the dissociative adsorption with lower energy when the molecule binds to Pd site. The lowest energy structure is obtained with H₂ molecule horizontally placed on the top of Pd atom (PdAgH₂_a) with H-Pd-H angle of 28.77°. When H₂ molecule is placed on top of Pd atom in line with the axis of the PdAg dimer, another stable structure (PdAgH₂_b) is obtained which is higher in energy than the ground state by 0.117 eV. In contrast, placing H₂ molecule on top of Ag atom forms a lesser stable structure (PdAgH₂_c) with energy higher than the ground state by 0.467 eV. The Ag-H bond length in the latter case is much longer than the Pd-H bond length in the former case which also indicates, as in the case of the Ag₂ dimer, that H₂ molecule tends to physically adsorb on the PdAg dimer when attached to the Ag site in the bimetallic cluster. A similar behaviour of hydrogen adsorption on Ag₂ and PdAg clusters has been stated previously [19]. In the dissociative form, hydrogen atoms prefer binding to the bridge sites of the PdAg cluster (PdAgH₂_d) rather than one atom at the bridge site and the other at the Pd or Ag site (PdAgH₂_e and PdAgH₂_f). These structures are found to be higher in energy than the lowest energy structure by 0.389, 0.398 and 0.609 eV respectively.

For H₂ interaction with Pd₃ trimer, the dissociation process is more favoured than the molecular adsorption. The ground state structure is obtained with one hydrogen atom located at the bridge site and the other one at the face of the isosceles triangle (Pd₃H₂_a). The total energy of the next geometrical structures with one hydrogen atom at each face of the triangle (Pd₃H₂_b) and two hydrogen atoms at the bridge sites (Pd₃H₂_c) are found to be in close proximity to that of the ground state with a difference of only 0.008 and 0.07 eV respectively. Similar results have been proposed by Ni and Zeng [22]. However, the authors suggest that the structure that involves two hydrogen atoms at the bridge sites is the ground state structure of this system. Isomer Pd₃H₂_d involves molecular hydrogen adsorption on the top of one Pd atom with much higher energy than the ground state by 1.404 eV. The lowest energy structure on Ag₃ cluster is obtained by molecular adsorption on the top of a silver atom with Ag-H and H-H bond lengths of 2.218 and 0.761 Å (Ag₃H₂_a). The molecular dissociation into two hydrogen atoms at the bridge sites (Ag₃H₂_b) is less favoured structure and found to be higher in energy than the ground state by 0.226 eV.

The elemental content of the bimetallic trimer controls its behaviour towards hydrogen adsorption. The calculations suggest that H₂ molecule prefers to dissociate on Pd₂Ag trimer, while the molecular adsorption is more favoured on PdAg₂ trimer. Apparently, the adsorption behaviour on the Pd₂Ag and PdAg₂ is similar to that on pure Pd₃ and Ag₃ trimers suggesting that doping pure clusters with only one atom from the other constituent does not change their tendency towards adsorbing hydrogen molecule. The lowest energy structure on the Pd₂Ag trimer (Pd₂AgH₂_a) is obtained by placing the two hydrogen atoms at the bridge sites of Pd-Pd. The next isomers (Pd₂AgH₂_b, Pd₂AgH₂_c, Pd₂AgH₂_d and Pd₂AgH₂_e) are found to be in order higher in energy than the ground state by 0.140, 0.163, 0.175 and 0.455 eV. On the PdAg₂ trimer, the ground state is obtained by molecular adsorption at Pd site with Pd-H, H-H bond lengths and H-Pd-H angle of 1.730 Å, 0.840 Å and 28.09° respectively. Calculations have also shown that (PdAg₂H₂_b, PdAg₂H₂_c, PdAg₂H₂_d, PdAg₂H₂_e and PdAg₂H₂_f) configurations are less stable than the ground state.

In a similar manner to the behaviour on dimers and trimers, hydrogen molecule favours dissociation on the Pd tetramers. The ground state configuration (Pd₄H₂_a) is obtained by placing one hydrogen atom at two triangle faces of the Pd₄ tetrahedron structure. This structure is more stable than that with two hydrogen atoms placed at the bridge sites (Pd₄H₂_b) with energy difference of 0.035 eV. Molecular hydrogen adsorption (Pd₄H₂_c) is also obtained with 0.820 eV energy difference apart from the ground state. The calculations also suggest, only for this configuration, that the triplet spin multiplicity is lower in energy than the singlet spin state by 0.664 eV. On the Ag tetramers, molecular hydrogen dissociation is more preferred with one hydrogen atom at the two-fold bridge sites of the rhombus structure (Ag₄H₂_a) and shortest Ag-H bond length of 1.816 Å. This is in line with previous observations of atomic hydrogen interaction with Ag₄ cluster [9, 24]. The next isomer (Ag₄H₂_b) involves molecular hydrogen adsorption with total energy higher than that of the ground state by 0.291 eV. Structure (Ag₄H₂_c) is obtained with the triplet spin state and its energy is higher than (Ag₄H₂_a) by 1.626 eV.

The adsorption behaviour of hydrogen molecule on the bimetallic Pd_nAg_m tetramers is different from that on the corresponding mono-component tetramers. For Pd₃Ag and Pd₂Ag₂ clusters, the ground states are obtained with molecular adsorption at Pd site in the distorted tetrahedron structure (Pd₃AgH₂_a and Pd₂Ag₂H₂_a). On the PdAg₃ cluster, the ground state is also obtained by molecular adsorption at Pd site in the rhombus structure. This is unlike the behaviour on the corresponding Pd₄ and Ag₄ clusters where molecular dissociation is more preferred (Pd₄H₂_a and Ag₄H₂_a) indicating that doping Pd tetramers with one or two Ag atoms, and doping Ag tetramers with one Pd atom interfere their affinity towards dissociating hydrogen molecule.

Figure 3 illustrates the shortest M-H bond lengths of the ground state geometries of Pd_nAg_m-H₂ clusters. Apparently, the bond lengths in the case of Ag single atom, pure Pd and bimetallic Pd_nAg_m clusters are in close proximity and found to be in the range between 1.650-1.758 Å. The Ag-H bond length is longer in pure Ag clusters with significant peaks appearing at Ag₂H₂ and Ag₃H₂ clusters. It is also noticeable from the results in the Tables 2-5 that Pd-H bond length is mostly shorter than that of Ag-H which suggests a stronger interaction in the case of Pd-H.

The average Pd-Ag bond lengths (R_ABL) of the lowest energy structures of Pd_nAg_m clusters before and after hydrogen adsorption are also shown in Figure 4. It is obvious from the figure that the dissociative adsorption increases the R_ABL of the entire cluster, while, with exception in the case of Pd-Ag cluster, no significant change occurs upon the molecular adsorption indicating that the former type of adsorption weakens the atomic interactions in the cluster. These results are consistent with the suggestion by Zhao et.al that dissociative adsorption of hydrogen greatly changes the geometry of Au_nPd_m cluster [27].

3.3. Adsorption Energies

The adsorption energy (E_ads) of the Pd_nAg_m-H₂ cluster system is calculated using the formula [13, 24, 27]:

E_ads = E_PdnAgm + E_H2 – E_PdnAgm-H2

where E_PdnAgm, E_H2, E_PdnAgm-H2 are the total energies of the Pd_nAg_m, H₂ and hydrogen molecule adsorbed on Pd_nAg_m clusters respectively. A more positive value of E_ads is a sign for a stronger bond [27]. The E_adsfor the ground state geometries of Pd_nAg_m-H₂ clusters are displayed in Figure 5. The results reveal that the E_ads of pure Pd clusters are higher than the corresponding Ag clusters which is also another evidence for a stronger interaction of hydrogen with Pd atoms as compared to Ag atoms. For the bimetallic clusters, the adsorption energies are between that of pure clusters suggesting that doping Ag clusters with Pd atoms enhances their interaction with hydrogen and inversely doping Pd clusters with Ag atoms weakens their interaction with hydrogen. The data in the figure also suggest that Pd dimer and trimer are the most reactive clusters for hydrogen adsorption, while single Ag atom is the least reactive one. Besides, the values in Tables 2-5 show that the E_ads for a given bimetallic cluster and geometry is much greater when the hydrogen atoms are around Pd site. Similar trends have been previously reported for CO and NO interactions with Ag_nPd_m clusters [52, 53]. Based on the adsorption energies presented for the ground states in Tables 2-5, it appears that molecular adsorption is more favourable on the Pd atom and mixed clusters, while the Pd_n (2-4) clusters are more appropriate for hydrogen dissociation.

3.4. Charge Transfer

It has recently been shown for small Pd_nAg clusters that a charge transfer from Ag atom to Pd atoms takes place indicating that Ag atom acts as electron donor and Pd atom acts as an electron acceptor within the clusters [45]. This behaviour can be linked to the fact that Pd is more electronegative than Ag (2.20 and 1.93) resulting in larger electron population and a stronger interaction with the adsorbed molecule at Pd site [52, 53].

The NBO population analysis suggests that the charge distribution within the lowest energy structures of Pd_nAg_m-H₂ clusters depends on the nature of hydrogen adsorption. With exception in the case of single Pd atom, one can observe from the data presented in Tables 2-5 that hydrogen atoms possess negative charge in the dissociative adsorption and positive charge in the molecular adsorption. This indicates that hydrogen atoms tend to draw electrons from the metal clusters in the dissociative form, while they tend to donate electrons to the metal clusters in the molecular adsorption form. The charge transfer tendency within the Pd_nAg_m-H₂clusters is similar to the case of H₂ interaction with Au_nPd_m clusters [27]. Ni and Zeng [22] have also indicated for H₂ adsorption on Pd_n clusters that a charge transfer from Pd atoms to hydrogen takes place in the dissociative form.

3.5. HOMO-LUMO energy gap

The chemical stability and reactivity of nanoclusters can be evaluated by the HOMO-LUMO energy gap (E_gap). A larger value of the E_gap indicates higher chemical stability and lower chemical reactivity [59, 60]. The E_gap of the ground state structures of Pd_nAg_m-H₂ clusters alongside the corresponding values of the Pd_nAg_m clusters are represented in Figure 6. The energy gaps of the adsorbed single atoms and dimers are higher than that of the Pd_nAg_m clusters. For the trimers and tetramers, the gaps decrease monotonically with increasing the Ag content in the cluster before hydrogen adsorption and oscillate after the adsorption process. A maximum E_gap occurs in the case of Ag-H₂ cluster, while the Ag₃-H₂ cluster exhibits the smallest E_gap indicating that it tends to be relatively less stable and more reactive among the examined systems. Besides, the Ag atom has the lowest chemical reactivity which is in harmony with the result in Figure 5 that Ag atom is the least reactive for hydrogen adsorption.

The E_gap of the Pd_nH₂ cluster decreases with increasing the Pd content in the cluster, while no similar tendency can be observed for Pd_n or Ag_m and Ag_m-H₂ clusters. Ni and Zeng [22] have also reported similar findings for Pd_nH₂ and Pd_n clusters.

3.6. DOS Analysis

To further analyse the electronic properties of hydrogen interaction with Pd_nAg_m clusters, the electronic density of state (DOS) spectra of the trimers as a representative system of the others is shown in Figure 7 as well as the DOS spectrum of hydrogen molecule in the gas phase. A number of remarkable DOS peaks can be observed in the vicinity of the Fermi level in the energy range 5 to -5 eV. It is clear from the figure that the Fermi level for pure Pd₃ and heteronuclear Pd₂Ag clusters is less populated. The interaction with H₂ increases the density of state near Fermi level of these clusters and that changes their electronic structures due to charge transfer from hydrogen atoms to the cluster. Moreover, the net charges of hydrogen atoms as shown in Table 4 for these clusters are - 0.266 e and - 0.300 e, respectively, implying more electrons are gained by the cluster. This can be ascribed to the decreased M-H bond lengths as shown in Figure 3 which facilitates more amount of charge transfer to the cluster. Also, the large density of state near the Fermi level after the interaction with hydrogen is manifested in lowering of the Homo-Lumo gap as shown in Figure 6 for these cluster. On the contrary, the charge transfer is very small in pure Ag₃ and PdAg₂ clusters as can be seen from Table 4. Therefore, the Homo-Lumo gap and DOS at the Fermi level are not changing significantly in these clusters as a result of the interaction with hydrogen atoms. Thus, it is interesting to note that molecular hydrogen adsorption is taking place in the latter two clusters with the R_H-H values 0.761 and 0.837 Å respectively. On the other hand, the dissociative adsorption is taking place in the former two clusters as shown in Table 4. Similar trends of large change in the Homo-lumo gap and electronic structure during the molecular and dissociative adsorption of hydrogen molecule on Au_nPd_m bimetallic clusters has been reported by Zhao et.al. [27]. Furthermore, higher interaction of hydrogen atoms with the metal clusters occurs when the adsorption energies are high [29]. The obtained adsorption energies for the trimers are in the order Pd₃ > Pd₂Ag > PdAg₂ > Ag₃ as shown in Figure 5. Therefore, the electronic structure is more affected in the clusters with large adsorption energies as shown by the density of states for Pd₃-H₂ and Pd₂Ag-H₂ clusters in Figure 7.

DFT calculations have been carried out in this study to systematically investigate the adsorption and dissociation of hydrogen molecule on small Pd_nAg_m (n + m ≤ 4) clusters. The ground state geometries of the Pd_nAg_m clusters are initially determined by optimizing various possible structures. Based on the obtained geometries, the lowest energy structures of Pd_nAg_m-H₂ clusters have been identified by optimizing several possible configurations of molecular hydrogen adsorption and dissociation on the most stable configurations of Pd_nAg_m clusters. The results have revealed that the nature of the adsorption process is controlled by the size and composition of the clusters. Molecular adsorption has been found to be more favourable on the Pd atom and mixed clusters, while hydrogen dissociation is more favourable on the Pd_n (n = 2–4) clusters. The adsorption energy calculations have shown that hydrogen interacts more strongly with Pd atoms than Ag atoms. It has also been found that hydrogen interaction with Ag clusters can be enhanced by doping with Pd atoms, while inversely doping Pd clusters with Ag atoms weakens their interaction with hydrogen. The study has revealed that the Pd dimer and trimer are the most reactive clusters for hydrogen adsorption, while single Ag atom is the least reactive one. The NBO population analysis has shown that electrons transfer from the metal clusters to hydrogen atoms in the dissociative form and from hydrogen atoms to the metal clusters in the molecular adsorption form. The DOS analysis of the trimers has shown that Pd₃ cluster possesses higher d density of state close to the Fermi level compared to the other systems resulting in higher adsorption energy.

Acknowledgments

The authors would like to thank the Deanship of Scientific Research at King Faisal University for funding this work under the project (160061).

Funding

This work was supported by the Deanship of Scientific Research at King Faisal University Grant number (160061).

Competing Interests

The authors have no relevant financial or non-financial interests to disclose

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Faisal Al-Odail, and Javed Mazher. The first draft of the manuscript was written by Faisal Al-Odail, and Javed Mazher and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Table (1): The calculated bond length, r (Å), binding energy, E_b (eV) and vibrational frequency, ω (cm^-1) of Pd₂, Ag₂, Pd-Ag, Pd-H, Ag-H and H₂ dimers with other theoretical data and experimental values.

Dimer

Parameter

This Work

Theoretical ^*

Experimental

B3LYP

B3P86

PW91PW91

Pd-Pd

E_b

2.536

0.318

197.5

2.494

0.477

215.4

2.504

0.746

208.4

2.510 (B3PW91)^a , 2.509 (BPW91)^b

0.380 (B3PW91)^a , 0.650 (BPW91)^b

203.6 (B3PW91)^a , 204.5 (B3LYP)^c

2.480 ^a

0.366 ^a , 0.515^a

210±10^a , 210.0 ^c

Ag-Ag

E_b

2.611

0.776

177.2

2.575

0.812

190.0

2.583

0.891

186.8

2.626 (BLYP)^d , 2.598 (PBE)^d

0.825 (BLYP)^d , 0.858 (PBE)^d

172.1 (BLYP)^d , 179.2 (PBE)^d

2.534 ^d

0.825^d

192.4^d

Pd-Ag

E_b

2.612

0.577

177.8

2.581

0.594

186.6

2.584

0.768

185.8

2.598 (PBE0)^e , 2.618 (B3LYP)^e , 2.596 (BPW91)^e

0.553 (PBE0)^e , 0.573 (B3LYP)^e , 0.682 (BPW91)^e

178.6 (PBE0)^e , 174.3 (B3LYP)^e , 185.5 (BPW91)^e

Pd-H

E_b

1.537

1.259

2031.8

1.525

1.298

2092.2

1.529

1.345

2078.3

1.548 (BH&H)^f , 1.555 (RPBE)^g

1.125 (RPBE)^g

2011.6 (BH&H)^f

1.534^{f, g} , 1.529 ^g

1.195 ± 0.13 ^g

2036^f

Ag-H

E_b

1.625

1.139

1706.7

1.613

1.192

1751.6

1.611

1.173

1738.3

1.637 (BH&H)^f , 1.631 (B3LYP) ^h

1.249 (GGA-PW91)^I

1768.5 (BH&H)^f

1.618^f

1759.7^f , 1717^h

H-H

E_b

0.744

2.382

4418.1

0.745

2.422

4417.9

0.750

2.271

4331.5

0.749 (BH&H)^f , 0.744 (B3LYP)^c

2.340 (RPBE)^g

4431.4 (BH&H)^f , 4418.9 (B3LYP)^c

0.741^f , 0.746^c

2.240 ^g

4401.2^f

^*: The density functionals are shown between brackets.

a: [59]

b: [60]

c: [19]

d: [61]

e: [3]

f: [23]

g: [22]

h: [18]

I: [24]

Table 2: The spin multiplicity (M), the total energy difference (∆E), adsorption energy (AE), shortest M-H bond length (R_M-H), H-H bond length (R_H-H), sum of NBO net charges of hydrogen atoms (q_H2) and HOMO-LUMO energy gap (E_gap) of the lowest energy structures of hydrogen adsorption and dissociation on single Pd and Ag atoms.

Cluster	M	∆E (eV)	AE (eV)	R_M-H (Å)	R_H-H(Å)	q_H2 (e)	E_gap (eV)
PdH₂_a	1	0	0.902	1.661	0.881	- 0.064	3.979 (2.618)
PdH₂_b	1	0.197	0.704	1.512	1.637	- 0.056	4.609
PdH₂_c	1	2.415	- 1.513	1.627	-	- 0.509	1.642
AgH₂_a	2	0	- 1.475	1.660	2.840	- 0.379	5.131 (4.817)
AgH₂_b	2	0.390	- 1.866	1.723	-	- 0.179	7.510

Table 3: The spin multiplicity (M), the total energy difference (∆E_t), adsorption energy (AE), shortest M-M bond length (R_M-M), shortest M-H bond length (R_M-H), H-H bond length (R_H-H), sum of NBO net charges of hydrogen atoms (q_H2) and HOMO-LUMO energy gap (E_gap) of the lowest energy structures of hydrogen adsorption and dissociation on Pd_nAg_m dimers.

Cluster	M	∆E_t (eV)	AE (eV)	R_M-M (Å)	R_M-H (Å)	R_H-H(Å)	q_H2 (e)	E_gap (eV)
Pd₂H₂_a	1	0	1.974	2.699	1.661	1.939	- 0.281	3.834
Pd₂H₂_b	1	0.818	1.156	2.657	1.570	1.036	- 0.119	3.210
Pd₂H₂_c	1	1.501	0.473	2.738	1.681	0.870	- 0.053	1.596
PdAgH₂_a	2	0	0.505	2.653	1.708	0.849	0.001	3.332
PdAgH₂_b	2	0.117	0.387	2.664	1.770	0.825	- 0.027	4.111
PdAgH₂_c	2	0.467	0.038	2.567	2.426	0.753	0.016	3.405
PdAgH₂_d	2	0.389	0.116	2.602	1.609 (Pd) 1.873 (Ag)	-	- 0.589	2.128
PdAgH₂_e	2	0.398	0.107	2.723	1.578 (Pd) 1.752 (Ag)	-	- 0.505	3.121
PdAgH₂_f	2	0.609	- 0.105	2.687	1.585 (Pd) 1.627 (Ag)	-	- 0.524	4.226
Ag₂H₂_a	1	0	0.019	2.573	2.519	0.751	0.017	3.292
Ag₂H₂_b	1	1.425	- 1.406	2.528	1.976	-	- 1.087	2.648

Table 4: The spin multiplicity (M), the total energy difference (∆E_t), adsorption energy (AE), average M-M bond lengths (R_ABL), shortest M-M bond length (R_M-M), shortest M-H bond length (R_M-H), H-H bond length (R_H-H), sum of NBO net charges of hydrogen atoms (q_H2) and HOMO-LUMO energy gap (E_gap) of the lowest energy structures of hydrogen adsorption and dissociation on Pd_nAg_m trimers.

Cluster	M	∆E_t (eV)	AE (eV)	R_ABL (Å)	R_Pd-Pd (Å)	R_Ag-Ag (Å)	R_Pd-Ag (Å)	R_M-H (Å)	R_H-H(Å)	q_H2 (e)	E_gap (eV)
Pd₃H₂_a	1	0	2.010	2.727	2.715	-	-	1.650	-	- 0.266	2.871
Pd₃H₂_b	1	0.008	2.002	2.694	2.692	-	-	1.793	-	- 0.255	3.274
Pd₃H₂_c	1	0.071	1.939	2.723	2.632	-	-	1.616	-	- 0.233	2.765
Pd₃H₂_d	1	1.404	0.606	2.575	2.561	-	-	1.670	0.866	0.078	1.746
Pd₂AgH₂_a	2	0	0.641	2.765	2.675	-	2.807	1.678 (Pd) 2.212 (Ag)	-	- 0.300	2.044
Pd₂AgH₂_b	2	0.140	0.502	2.710	2.756	-	2.655	1.599 (Pd) 1.966 (Ag)	-	- 0.476	2.210
Pd₂AgH₂_c	2	0.163	0.478	2.630	2.550	-	2.628	1.732	0.836	0.043	3.398
Pd₂AgH₂_d	2	0.175	0.466	2.717	2.777	-	2.687	1.620 (Pd) 1.914 (Ag)	-	- 0.607	2.445
Pd₂AgH₂_e	2	0.455	0.186	2.700	2.656	-	2.722	1.650	0.945	- 0.059	2.566
PdAg₂H₂_a	1	0	0.619	2.682	-	2.666	2.668	1.730	0.840	0.009	3.066
PdAg₂H₂_b	1	0.025	0.594	2.683	-	2.667	2.670	1.727	0.837	0.003	2.937
PdAg₂H₂_c	1	0.418	0.201	2.789	-	3.161	2.603	1.687 (Pd) 1.937 (Ag)	-	- 0.602	3.107
PdAg₂H₂_d	1	0.895	- 0.276	2.727	-	2.789	2.640	1.560 (Pd) 1.635 (Ag)	-	- 0.622	2.852
PdAg₂H₂_e	1	0.955	- 0.337	2.740	-	2.603	2.772	1.645 (Pd) 1.828 (Ag)	-	- 0.837	2.163
PdAg₂H₂_f	1	1.035	- 0.416	2.702	-	2.604	2.751	1.544 (Pd) 1.912 (Ag)	-	- 0.732	2.477
Ag₃H₂_a	2	0	0.095	2.759	-	2.656	-	2.218	0.761	0.031	1.651
Ag₃H₂_b	2	0.226	- 0.131	2.773	-	2.732	-	1.786	-	- 0.878	2.661

Table 5: The spin multiplicity (M), the total energy difference (∆E_t), adsorption energy (AE), average M-M bond lengths (R_ABL), shortest M-M bond length (R_M-M), shortest M-H bond length (R_M-H), H-H bond length (R_H-H), sum of NBO net charges of hydrogen atoms (q_H2) and HOMO-LUMO energy gap (E_gap) of the lowest energy structures of hydrogen adsorption and dissociation on Pd_nAg_m tetramers.

Cluster	M	∆E_t (eV)	AE (eV)	R_ABL (Å)	R_Pd-Pd (Å)	R_Ag-Ag (Å)	R_Pd-Ag (Å)	R_M-H (Å)	R_H-H(Å)	q_H2 (e)	E_gap (eV)
Pd₄H₂_a	1	0	1.285	2.771	2.701	-	-	1.691	-	- 0.243	2.569
Pd₄H₂_b	1	0.035	1.250	2.752	2.701	-	-	1.631	-	- 0.174	2.204
Pd₄H₂_c	3	0.820	0.465	2.637	2.558	-	-	1.764	0.823	0.054	3.444
Pd₃AgH₂_a	2	0	0.478	2.677	2.594	-	2.677	1.758	0.827	0.036	3.085
Pd₃AgH₂_b	2	0.056	0.422	2.744	2.748	-	2.708	1.648	-	- 0.357	1.872
Pd₃AgH₂_c	2	0.090	0.387	2.743	2.740	-	2.706	1.594	-	- 0.408	2.242
Pd₃AgH₂_d	2	0.403	0.075	2.662	2.603	-	2.721	2.237	0.758	0.032	3.407
Pd₃AgH₂_e	2	0.739	- 0.261	2.726	2.626	-	2.824	1.632	-	- 0.601	3.240
Pd₂Ag₂H₂_a	1	0	0.620	2.723	2.744	2.785	2.663	1.721	0.841	0.010	2.476
Pd₂Ag₂H₂_b	1	0.472	0.147	2.771	2.746	2.679	2.739	1.561	1.821	- 0.178	2.206
Pd₂Ag₂H₂_c	1	0.548	0.072	2.710	2.711	2.822	2.680	2.248	0.758	0.029	2.393
Pd₂Ag₂H₂_d	1	0.583	0.037	2.764	2.756	2.852	2.691	1.637	-	- 0.515	2.710
Pd₂Ag₂H₂_e	1	0.745	- 0.125	2.762	2.736	2.647	2.797	1.653	-	- 0.661	2.559
PdAg₃H₂_a	2	0	0.565	2.725	-	2.695	2.716	1.738	0.835	0.046	2.643
PdAg₃H₂_b	2	0.200	0.365	2.750	-	2.781	2.691	1.681	-	- 0.530	2.159
PdAg₃H₂_c	2	0.490	0.075	2.705	-	2.742	2.666	2.254	0.759	0.036	2.579
PdAg₃H₂_d	2	0.540	0.025	2.749	-	2.683	2.760	1.651	-	- 0.688	3.652
PdAg₃H₂_e	4	2.876	- 2.310	2.794	-	2.754	2.764	1.641	-	- 0.371	2.708
Ag₄H₂_a	1	0	0.452	2.760	-	2.722	-	1.816	-	- 0.897	3.720
Ag₄H₂_b	1	0.291	0.162	2.740	-	2.631	-	2.101	0.769	0.047	2.303
Ag₄H₂_c	3	1.626	- 1.174	2.865	-	2.745	-	1.754	-	- 0.851	1.898

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Editorial decision: Major revisions
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A density functional theory study of adsorption and dissociation of H2 molecule on small PdnAgm (n + m ≤ 4) metal clusters

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2. Computational Method

3. Results And Discussions

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