Article pubs.acs.org/JPCC
Theoretical Comparative Study of Oxygen Adsorption on Neutral and Anionic Agn and Aun Clusters (n = 2−25) Meng-Sheng Liao, John D. Watts, and Ming-Ju Huang* Department of Chemistry, Jackson State University, Jackson, Mississippi 39217, United States S Supporting Information *
ABSTRACT: Using density functional theory, we performed a theoretical comparative study of oxygen adsorption on neutral and anionic Agn and Aun clusters in a large size range of n = 2−25. Ionization potentials (IPs) and electron affinities (EAs) of the pure clusters and the Mnq−O2 binding energies Ebind(Mnq−O2) in the (MnO2)q complexes (M = Ag, Au; q = 0, −1) were determined. Three density functionals, namely, BP86, revPBE, and B3LYP, were used in the calculations, among which the BP86 functional gave the best results for IPs and EAs, while B3LYP gave the best results for Ebind(Mnq−O2). A number of differences between the silver and gold clusters and their reactivities toward O2 adsorption are accounted for by the calculations. One interesting result is that the calculated Aun−−O2 binding energies are in good, quantitative agreement with the measured relative reactivities of the Aun− cluster anions toward O2 adsorption. distinct features: (1) a clear Ag15O2− peak was shown in the mass spectra of the reacted species; (2) Ag13− appeared to be a magic-number cluster. On the other hand, experimental characterization of the Ag/Al2O3 catalyst suggested that neutral silver clusters Agn could be active species for O2 adsorption and dissociation,28 also in contrast to gold; neutral Aun clusters were thought to be inert toward O2 uptake.1,2 Much theoretical work has been devoted to the interaction of O2 with gold clusters (e.g., refs12−19, 21−24). But most of these previous theoretical studies are limited to rather small n (n ≤ 11). Mills et al.12,15 employed density functional theory (DFT) to examine the adsorption of O2 on neutral and anionic gold clusters Aun/Aun− with n = 2−7. They predicted that all neutral Aun clusters and odd-n Aun− cluster anions could adsorb O2, which is inconsistent with the experimental results.4 The previous calculations by Mills et al.12,15 used the PW91 functional, which has been shown to overestimate the adsorption energy.16 Wells et al.13 performed a DFT study of the adsorption of O2 on anionic gold clusters Aun− with n = 9− 11, where the hybrid B3LYP functional was used in the calculations, but only three relatively large gold clusters were considered. Ding et al.16 performed a similar DFT/B3LYP study of O2 adsorption on neutral, anionic, and cationic gold clusters Aun/Aun−/Aun+ with n = 1−6. Compared to PW91, the B3LYP results for the adsorption energy are improved significantly and give the same adsorption behavior of O2 on Au cluster anions and cations as the experimental measurements. Yoon et al.14 performed a DFT study of O2 adsorption
1. INTRODUCTION The interaction of silver and gold clusters with O2 has been an active field of experimental1−11 and theoretical12−27 research because this interaction is important for understanding the remarkable catalytic effects discovered for the metal nanoparticles. Cox et al.1,2 were the first to report experimental work for O2 adsorbed on a series of gold clusters Aunq with n = 3−20 and q = +1, 0, and −1. They found a strong dependence of reactivity on both cluster size (n) and charge state (q); for Aun−, only even-numbered (even-n) clusters reacted with oxygen. Salisbury et al.4 described a series of experiments on the adsorption of O2 on gold cluster anions Aun− with n = 2− 22; they showed that only certain clusters (n = 2, 4, 6, 8, 10, 12, 14, 18, 20) exhibit measurable adsorption, and no reaction was detected for any odd-numbered cluster, nor for n = 16. A more detailed experimental study of O2 on Aun− with n = 1−7 was performed by Huang et al.,8 who provided further insight into O2 interactions with small gold clusters. More recently, Pal et al.9 carried out a combined experimental and theoretical study of O2 on some even-n gold cluster anions, so as to unravel the mechanisms of O2 activation by size-selected gold clusters. Here we have performed a theoretical comparative study of oxygen adsorption on neutral and anionic Agn and Aun clusters with n = 2−25. Our work is stimulated by a recent experimental study of Luo et al.11 on the reactivity of silver cluster anions Agn− with O2 (n = 2−20); it was shown that odd-numbered (odd-n) silver cluster anions Agn− could also react with molecular oxygen to yield AgnO2− oxide products, though they exhibited lower (or reduced) reactivity than those with an even number of atoms. This is in contrast to the corresponding oddn Aun− cluster anions, which were shown to be inert to O2 adsorption.4 The experimental results11 also showed two other © 2014 American Chemical Society
Received: February 17, 2014 Revised: August 26, 2014 Published: August 29, 2014 21911
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on the Aun/Aun−/Aun+ clusters with n = 2−8. The functional used by these authors14 was PBE, which tends to overbind, similar to PW91. Using a revised PBE functional, namely RPBE, Molina and Hammer 17 performed a DFT study of O2 adsorption on the Aun/Aun− clusters with n = 1−11; RPBE proved to be an improvement over PBE in calculating the adsorption energies. However, the neutral Aun clusters with odd-n were predicted to bind O2, still inconsistent with experiment (that neutral Aun clusters do not bind O2, with even or odd numbers of gold atoms).17 Fernández et al.22,23 performed a DFT/PBE study of O2 adsorption on neutral Aun (n = 5−10) and anionic Aun− and Agn− (n = 1−7) clusters. More recently, Yoon et al.24 reported a DFT/PBE study of O2 adsorption on some relatively large anionic Aun− clusters with n = 15−24. In summary, most of the previous DFT calculations of O2 adsorption on gold clusters used a generalized gradient approximation (GGA) functional (PW91 or PBE); they are able to account for the dramatic even−odd oscillation in the reactivities of these clusters toward O2, but fail to explain some other O2 adsorption behaviors on the gold clusters as mentioned above because the GGA functional overestimates the adsorption energies. The calculations13 with the hybrid B3LYP functional appear to give O2 adsorption properties that match the experimental results quite satisfactorily. Very recent theoretical studies of the interaction of O2 with gold clusters focused on some special topics.18,19,21 Lyalin and Taketsugu21 investigated molecular and dissociative adsorption of O2 on odd-size Aun clusters for n = 1, 3, 5, 7, 9 with a coadsorbed C2H4. Jena et al.18 investigated the O2 activation on doping a gold cluster with an H atom, Au7H. Gao and Zeng19 studied water-promoted O2 dissociation on small-sized anionic Aun− clusters with n = 1−6. Theoretical studies of O2 on silver clusters are relatively rare.20,23,25−27 Fernández et al.23 studied the trends in the binding energies of O2 on Agn− anions for n = 3−9 within a DFT/PBE scheme. Klacar et al.25 used the same theoretical method to examine the reactivity of neutral Agn clusters containing 1−9 atoms with O 2. In addition to their experimental work, Luo et al.11 also performed DFT/PBE calculations on the AgnO2− systems with n = 1−17. As pointed out above, the PBE functional tends to lead to overbinding. Earlier DFT studies include a study of AgnO2− using a hybrid functional (B3PW91) that was limited to a small n (n ≤ 5).26 and a study of AgnO2 and AgnO2± (n ≤ 7).27 Silver clusters often show physical and chemical properties different from the corresponding gold clusters. For example, the Agn clusters exhibit planar structures for n = 3−6 and threedimensional (3-D) structures for n > 6.29 However, the Aun clusters are planar up to n = 12.29,30 It is therefore of interest to examine the differences in the properties of Agnq−O2 and Aunq−O2. The present paper comprises a systematic and comparative DFT study of O2 adsorption on neutral and anionic Agn and Aun clusters in a large size range (n = 2−25). Three density functionals, that is, BP86, revPBE, and B3LYP, will be employed in the calculations. We want to investigate whether the experimental observations of the various O2 adsorption behaviors can be accounted for by the calculations.
Frozen-core techniques31 were used here to reduce the computational cost. For both metals, a relatively small core definition was used, that is, [Ar]3d10 for Ag and [Kr]4d104f14 for Au; the valence set on the metal included subvalence (n − 1)s and (n − 1)p shells. For O, 2s and 2p were considered as valence shells and [He] was treated as core and kept frozen. The molecular orbitals were expanded in atom-centered STO (Slater-type orbital) basis sets. To obtain accurate results, triple-ζ basis sets plus one polarization function were used for the valence shells of all metal and nonmetal elements. Three density functionals were employed. They are BP86 (Becke’s 1988 gradient correction for exchange33 plus Perdew’s 1986 gradient correction for correlation34), revPBE (revised Perdew−Burke−Ernzerhof functional proposed in 1998 by Zhang and Yang35), and B3LYP. BP86 is shown to give the best metal−metal (M−M) bond lengths and M−M binding energies (Supporting Information, Table S1). The revPBE is a revised PBE functional and is expected to give better results than the original PBE. The latter was used in previous calculations11,20,25 and yielded too large metal−ligand binding energies. The hybrid B3LYP functional was shown to provide reliable O2 adsorption energies consistent with the experiments.16 Relativistic corrections for the valence electrons were calculated by the so-called scalar relativistic zero-order regular approximation (ZORA).36 It is known that relativistic effects are large for gold,37 and they must be taken account in the calculations on the Aun clusters. For the open-shell states, the calculations were spin-unrestricted.
3. RESULTS AND DISCUSSION We first present our calculations on the pure metal clusters since their structures and properties are the basis for understanding their chemical reactivity toward various molecules. Numerous papers have been published on silver and gold clusters in the literature (e.g., refs 38−49); they provide significant information about the geometric structures of a series of pure metal clusters. In the case of large clusters, the lowest-energy geometry cannot be easily determined, since consideration of all structures with a technique like simulated annealing requires too much computer time. As we have so many clusters here, it is impractical for us to do a thorough search for the lowest-energy structures. Our structures of the various metal clusters are taken mainly from the literature38−40 but have been reoptimized in our calculations with the BP86 functional. A thorough search for global minimum structures was carried out by Fournier (Ag3−12),37 Zorriasatein et al. (Au13−19),39 and Wang et al. (Ag3−6).40 For some clusters, references41−49 that used different computational methods may give somewhat different structures. Therefore, a number of cluster isomers have also been considered in our calculations (see Supporting Information, Figures S1− S4). In addition to structures, we have calculated the following properties for each cluster: binding energies per atom (Ebind/atom), ionization potentials (IP, which is vertical), electron affinities (EA, which is adiabatic). Ebind, IP, and EA are defined as −E bind = E(M n) − n × E(M) IP = E(M +n ) − E(M n)
EA = E(M n) − E(M−n )
2. COMPUTATIONAL METHOD All calculations were carried out using the Amsterdam Density Functional (ADF) program packageversion 2013.01.31,32
Here E(Mn), E(M), E(Mn+), and E(Mn−) are the total energies of the indicated species. The IP is calculated as the difference 21912
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Figure 1. Optimized ground-state structures of the neutral Agn clusters from BP86 calculations. Two structures are shown for certain clusters. The number in parentheses in the left superscript of the cluster formula is the multiplicity of the cluster. The three numbers in parentheses on the right of the cluster formula Agnb are, respectively, the BP86, revPBE, and B3LYP energies (in eV) of this isomer relative to the ground-state structure Agna. The other numbers on the cluster structure are the optimized Ag−Ag bond lengths (in Å).
with BP86. The experimental M−M binding energies (1.66 eV for Ag2 and 2.29 eV for Au2) are very well reproduced by the calculations with BP86 (1.67 and 2.15 eV). The revPBE and B3LYP functionals underestimate the M−M binding energies significantly. The calculated M−M binding energies vary in the order BP86 > revPBE > B3LYP. Concerning MnO2−, the only experimental values are the Mn−−O2 binding energies,7,8 and they are shown to be in generally good agreement with the calculations through B3LYP. There is no systematic trend in the calculated Mn−−O2 binding energies from BP86 to revPBE to B3LYP. While revPBE gives excellent binding energies for Ag5O2− and Au6O2−, it greatly overestimates the binding energies for AuO2− and Au3O2−, which were not detected in experiment,7 consistent with the
between the energies of a cationic and a neutral cluster, both evaluated at the optimized structure of the neutral. EA is defined as the energy of the origin transition between the ground state of the anion and the ground state of the neutral. IPs and EAs for Ag n and Au n have been measured experimentally as a function of cluster size.50−52 As a first step in this work, we performed a test of the three functionals on some systems (Ag2, Au2, Au2−, Ag2−5O2−, Au1−6O2−), where experimental data are available. The results are presented in Supporting Information (Table S1). The BP86 calculated M−M bond lengths are 2.576, 2.540, and 2.665 Å for Ag2, Au2, and Au2−, respectively. They are larger than the experimental values (2.48, 2.47, and 2.58 Å) by 0.07−0.10 Å. The revPBE and B3LYP calculated bond lengths are comparable, but are 0.02−0.05 Å larger than those obtained 21913
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Figure 2. Optimized ground-state structures of the anionic Agn− clusters from BP86 calculations. See legend of Figure 1
B3LYP results. The Mn−−O2 binding energies predicted by BP86 are usually too high as compared to experiment. 3.1. Structures of Silver Clusters Agn and Agn−. The optimized ground-state structures of the neutral and anionic silver clusters are displayed in Figures 1 and 2, respectively, together with some bond lengths obtained for each cluster. For certain clusters, a closely or higher-lying isomer is shown together with the calculated relative energies of this isomer with respect to the ground-state structure. A number of other higher-lying isomers are presented in Supporting Information (Figures S1 and S2). The same is true for the gold clusters. According to the DFT calculation, the ground-state structure of neutral Ag3 corresponds to two isomers: linear and isosceles triangle, which are nearly degenerate. The DFT calculations by others46 gave similar results. Experiments gave evidence that
neutral Ag3 is a Jahn−Teller distorted isosceles triangle.53 A recent high-quality CCSD(T) calculation on Ag3 by some of us54 indicates that the 2B2 state is the global minimum and about 0.15 eV lower than the linear ground state 2Σu. The stability of the linear structure for Ag3 is somewhat overestimated by the DFT calculations here. The structures of Ag4−7 are fairly well-established; they are rhombus for Ag4, trapezoid for Ag5, equilateral regular triangle for Ag6, and pentagonal bipyramid for Ag7. While the Agn clusters with n ≤ 6 exhibit a quasi-planar structure, those with n > 6 display 3-D ones. For Ag10, Ag12, and Ag15, two isomers are close in energy. The energy difference between the two isomers is very small and does not allow prediction of structure. It is shown that many isomers may coexist at relatively large cluster sizes.9,38 21914
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Figure 3. Optimized ground-state structures of the neutral Aun clusters from BP86 calculations. See legend of Figure 1
The negative charge on Ag3 changes the structure of the cluster. Ag3− is clearly linear; its triangular structure has a much higher energy than the linear one. For Ag4−, the rhombic and Yshaped structures are now close in energy. For the larger clusters, the charge on the cluster does not change the groundstate structure. However, it is shown that the energy difference between the 3-D and planar structures is significantly reduced with n = 7, 8, indicating that the cluster anions have a tendency to form a planar structure. According to the M−M bond lengths given for each cluster, the anionic clusters expand somewhat as compared to the neutral clusters. 3.2. Structures of Gold Clusters Aun and Aun−. The optimized ground-state structures of the neutral and anionic gold clusters are displayed in Figures 3 and 4, respectively (see
Supporting Information, Figures S3 and S4 for some higherlying isomers considered here). Neutral Au3 is predicted to be bent, which is somewhat different from the silver case. For Au4, the rhombic and Y-shaped structures are close in energy, also different from Ag4. Another notable feature of the gold clusters is that planar structures are preferred up to n = 12; starting at n = 13, they form 3-D structure. This conclusion was drawn on the basis of a combined experimental (ion mobility measurements) and theoretical (DFT) studies of gold cluster anions Aun−.30 According to our calculations, neutral Aun clusters form a planar structure for n = 5−9, 11, and 12, where the energy differences between the planar and 3-D structures are shown to be significant (0.3−1.0 eV). Au10 appears to be an exception, for which a 3-D structure (Au10c, Supporting Information) has 21915
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Figure 4. Optimized ground-state structures of the anionic Aun− clusters from BP86 calculations. See legend of Figure 1
the lowest energy. Of course, the Au10− anion still clearly prefers a planar structure. As is shown in the above section, the anions prefer a planar structure more strongly than the neutrals; the energy gap between the planar and 3-D structures increases from the neutral to anionic clusters. The anomalous behavior of gold (atom, clusters, compounds) as compared to the analogous silver systems can be explained by relativistic effects,30 which give rise to a strong sd hybridization in gold. Initially, we did test calculations on a planar structure for both Au13 and Au13−. The energies are −0.01 and −0.07 eV, respectively, relative to the bilayer structures shown in the figures. It was suggested that the stability of planar structures might be overestimated somewhat by DFT.30 Thus, we did not include a planar structure here for Au13 or Au13−. Our calculations show that for Au13 or Au13−, the bilayer structure
is close to a planar structure in energy, and the calculated IP and EA for the bilayer Au13 are also very close to those of a planar Au13. Anion photoelectron spectroscopy (PES)41 predicted the transition from planar to 3-D at n = 13 in gold cluster anions. Some other DFT calculations39,41,43 on Aun− yield planar structures as the ground-state structures in the size range of n = 13−15. The question of the planarity of Au clusters, particularly Au130/−, has been discussed in a van der Waals DFT study.55 Au3− is now linear, similar to Ag3−. Experimental evidence has indicated that the ground states of the trimer anions are linear.56 For Au4−, the Y-shaped structure is calculated to be the ground-state structure, in agreement with the mobility measurement,30 which rules out the rhombic structure for the anionic Au4−. Au16− exhibits two closely lying isomers. One of 21916
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them (Au16b−) is a hollow cage, which was predicted and observed in a PES experiment on Au16−.57 A hollow-cage structure was also reported for Au17− and Au18−.57 Au20 is considered as a magic-number gold cluster with a unique tetrahedral shape. 58 Au 16b can be obtained from the tetrahedron, pyramid Au20 with four missing corner atoms after relaxation. Au19 is pyramidal with one missing corner atom from Au20. The M−M bond lengths in Aun are shorter than in Agn, which is attributed to relativistic effects. 3.3. Binding Energies Per Atom, Ionization Potentials, and Electron Affinities. Table 1 presents the calculated
dimensional shell model.60 In contrast, M13 is notably less stable than its neighbors M12 and M14. Opposite to this case, the M13− anions are particularly stable, as is evidenced by the large experimental and calculated EAs for M13. Ag13− appeared as a magic-number species in the mass spectra of the reacted species.11 The enhanced stability of M20 is related to the unique, high-symmetry tetrahedral structure of this cluster. Owing to relativistic effects, the Ebind/atom of Aun is significantly larger than that of Agn, and the difference in Ebind/atom between Aun and Agn is enlarged with increasing n. One dominant feature in various calculations and experiments on small coinage metal clusters Mn is the pronounced even−odd oscillation in the IP and EA values with cluster size n. Even-numbered clusters have higher IPs and lower EAs, indicating increased stability, compared to odd-numbered clusters that exhibit lower IPs and higher EAs. This has been explained by an electron pairing effect,61 resulting from the circumstance that each atom in the cluster contributes a single valence electron to the bonding orbitals. Clusters with fully occupied orbitals have an enhanced stability. Looking at Figure 6, our calculated IPs and their trends are generally in good agreement with the available experimental data in the whole size range of the Agn and Aun clusters considered here. There are several notable features in Figure 6: (1) a weak or no even−odd oscillation of IP is found for M12− M13−M14, M16−M17−M18, and M21−M22−M23; (2) M20 has a particularly large IP compared to its neighbors; (3) The IPs show an overall decrease with increasing n. However, certain notable disagreements between the calculation and experiment are found for Ag11, Ag24, and Au9. The experimental IP of Ag11 is shown to be larger than that of Ag10. This unusual trend is not found in our calculations on Agn/Aun and experiments on Aun, which still show an obvious even−odd oscillation of IP from n = 10 to 12. The experimental IPs of Agn show no obvious even−odd oscillation from n = 21 to 25, while the calculated IP chart shows a peak at n = 24, though the calculated IP of Ag24 agrees very well with experiment. We cannot explain these discrepancies between the calculation and experiment. No detailed experimental IPs are available for the Aun clusters larger than n > 23.51 Concerning Au9, the calculated IP for this cluster is notably larger than experiment, in contrast to the IPs calculated for the other clusters (n > 3); the latter are all systematically smaller than the experimental values. For Au9, the planar structure (Au9a) is only a single candidate for the lowest-energy structure. We note that after one electron is removed from Au9, the cation Au9+ possesses a triplet ground state, instead of a singlet, closed-shell one. This is the reason why the calculated IP for Au9 is relatively large. By comparison with experiment, the calculated IPs support a triangular structure for Ag3, a rhombic structure for Ag4, and a planar structure for Au10 because the calculated IPs for these isomers agree better with experiment than those for the other closely lying isomers. It is shown that the calculated IP of M3 depends strongly on the geometry of this cluster. A detailed discussion about the IP of Ag3 has been made in our recent paper.54 From Figure 7, we also see good agreement between the calculated and experimental EAs. This is particularly true for the Aun clusters. The experimental EAs and their trends are almost reproduced by the calculations. An exception is Ag23, for which the experimental EA is smaller than that of Ag22. Again, this unusual trend is not demonstrated in our calculations on Agn/Aun and experiments on Aun, which still show an obvious
Table 1. Calculated Binding Energies (Ebind/atom, eV) Per Atom for the Mn clusters (M = Ag, Au) M = Ag M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25
M = Au
BP86
revPBE
B3LYP
BP86
revPBE
B3LYP
0.83 0.82 1.09 1.19 1.36 1.37 1.46 1.45 1.48 1.50 1.54 1.52 1.62 1.59 1.64 1.65 1.70 1.69 1.73 1.69 1.71 1.71 1.72 1.71
0.76 0.74 0.96 1.05 1.20 1.19 1.28 1.26 1.29 1.30 1.34 1.32 1.40 1.38 1.41 1.43 1.47 1.47 1.50 1.46 1.48 1.48 1.48 1.47
0.75 0.71 0.93 1.02 1.18 1.14 1.23 1.21 1.23 1.24 1.28 1.25 1.34 1.32 1.35 1.37 1.41 1.40 1.44 1.38 1.39 1.40 1.42 1.41
1.08 1.12 1.42 1.55 1.78 1.72 1.85 1.82 1.86 1.91 1.97 1.95 2.02 2.01 2.04 2.08 2.12 2.13 2.18 2.11 2.11 2.13 2.18 2.17
0.99 1.00 1.26 1.38 1.59 1.53 1.66 1.61 1.63 1.69 1.75 1.73 1.77 1.76 1.78 1.81 1.86 1.87 1.92 1.84 1.84 1.86 1.91 1.90
0.95 0.94 1.20 1.32 1.54 1.47 1.60 1.54 1.55 1.62 1.67 1.64 1.69 1.67 1.69 1.72 1.77 1.78 1.82 1.74 1.74 1.76 1.81 1.80
binding energies per atom (Ebind/atom) for the Agn and Aun clusters. The calculated ionization potentials (IPs) and electron affinities (EAs) are reported in Tables 2 and 3, respectively, together with available experimental data.50−52 To facilitate comparison of the calculated properties among the different clusters and metals, plots of the BP86 calculated Ebind/atom, IP, and EA versus n and M are shown in Figures 5, 6, and 7, respectively. Illustrative comparisons of the calculated properties with different functionals are presented in Supporting Information (Figures S5−S10). Figure 5 clearly illustrates the variation of Ebind/atom versus number of Ag and Au atoms in a cluster. We see that Ebind/ atom increases greatly with increasing number of atoms from n = 3 to 6. Then, Ebind/atom increases slowly with cluster size. The increase in Ebind/atom indicates that the stability rises with the size of the cluster. However, the curve of Ebind/atom is not smooth; it has peaks for n = 6, 8, 14, and 20. For example, Au6 is notably more stable than its neighbors Au5 and Au7. This has been reported in previous theoretical studies of small Au clusters.59 The enhanced stability of the planar metal cluster M6 is consistent with the six-electron magic number of a two21917
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Table 2. Calculated (Vertical) Ionization Potential (IP, eV) for the Mn Clustersa M = Ag M2 M3a M3b M4a M4b M5 M6 M7 M8 M9 M10a M10b M10c M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 a
M = Au
BP86
revPBE
B3LYP
exptlb
BP86
revPBE
B3LYP
exptlc
8.08 7.26 6.42 6.75 6.82 6.44 7.23 6.20 6.81 6.15 6.27 6.38
7.78 6.93 6.10 6.45 6.52 6.12 6.91 5.88 6.50 5.83 5.96 6.07
7.75 6.96 6.08 6.42 6.48 6.11 7.14 5.85 6.51 5.82 5.95 6.05
7.60 6.20
5.43 6.05 5.87 6.09 5.44 5.87 5.85 5.94 5.55 6.06 5.22 5.26 5.28 5.66 5.34
5.39 6.04 5.69 6.07 5.41 5.84 5.81 5.92 5.54 6.29 5.18 5.23 5.24 5.64 5.31
6.30 6.50 6.34 6.73 6.40 6.57 6.45 6.53 6.20 6.45 5.90 6.04 6.03 6.08 6.02
9.25 8.18 6.93 7.76 8.02 7.36 8.03 7.19 7.81 7.26 7.29 7.02 7.19 6.85 7.15 7.00 7.21 6.51 6.96 6.91 6.99 6.43 7.03 6.20 6.36 6.43 6.70 6.27
9.23 8.17 6.60 7.71 7.96 7.33 8.19 7.18 7.94 7.25 7.33 7.01 7.19 6.85 7.20 6.83 7.24 6.50 6.97 6.88 6.99 6.42 7.16 6.15 6.35 6.41 6.71 6.25
9.50 7.50
5.75 6.36 6.18 6.38 5.75 6.19 6.17 6.26 5.87 6.38 5.54 5.58 5.59 5.98 5.65
9.52 8.47 7.22 8.05 8.31 7.66 8.30 7.48 8.07 7.55 7.58 7.30 7.48 7.14 7.44 7.29 7.49 6.80 7.25 7.20 7.28 6.73 7.31 6.49 6.65 6.72 6.99 6.56
6.65 6.35 7.15 6.40 7.10 6.00 6.25
8.60 8.00 8.80 7.80 8.65 7.15 8.20
7.28 8.15 7.70 8.00 7.65 7.80 7.60 7.85 7.70 7.82 7.25 7.30
The calculated IPs are given for two closely lying isomers for M3, M4, and M10 and three for Au10. bReference 50. cReference 51.
even−odd oscillation of EA from n = 22 to 24. There are several striking features in Figure 7: (1) An opposite or no even−odd oscillation of EA is found for Au9−Au10−Au11 and Au15−Au16−Au17, indicating that the even-numbered Au10 and Au16 have unusually large EAs compared to their neighbors. (2) The EA of Ag13 is larger than those of all the other Agn clusters with n ≤ 16. It has been shown11 that Ag13− has the highest HOMO−LUMO gap among the Agn− clusters with 8 ≤ n ≤ 17, which is responsible for its reduced reactivity and enhanced stability. (3) Au20 has a very low EA compared to its neighbors. (4) In contrast to IPs, there is an overall increase in EA with increasing cluster size. The very good agreement of the calculated EAs with experiment may be considered as support for the structures considered for the metal clusters. The IP and EA of Aun are significantly larger than those of Agn. In heavy metals like Au, the 6s orbitals are stabilized greatly by relativistic effects, thereby resulting in large IP and EA for Aun as compared to Agn. The revPBE and B3LYP calculated IPs/EAs are comparable and systematically smaller than those obtained by BP86. 3.4. MnO2 (M = Ag, Au). We first examine the adsorption of O2 on the neutral clusters. The optimized structures of the various lowest-energy MnO2 complexes for M = Ag and Au are displayed in Figures 8 and 9, respectively. O2 makes two kinds of bond with metal clusters: atop (coordination to a single M atom, η1-O2 bond) and bridge (coordination to two M atoms, η2-O2 bond). The two forms of adsorption were considered in our calculations on each cluster. It is shown that atop binding is favored for some clusters, but disfavored for the others,
depending on the structure of the cluster. For some clusters, the atop and bridge bindings may have very similar binding energies and so both forms of adsorption are expected to coexist for those clusters. This has been observed in the cluster beam of AunO2−.9 The structures of some clusters are changed substantially upon adsorption of O2. One example is Au3, which is bent, becomes triangular when it adsorbs O2. Another striking example is Ag7O2, for which the Ag7 part is close to a planar D6h structure. This structure of Ag7O2 was the lowestenergy structure found by both Klacar et al.25 and Zhou et al.27 A structure of Ag4O2 in which the O2 is above the Ag4 in C2v symmetry (as found by Wu et al.20 for Ag4O2+) was studied but found not to be the lowest-energy structure. The calculated Mn−O2 binding energies Ebind(Mn−O2) with the different functionals are collected in Table 4. Ebind(Mn−O2) is defined as −E bind(M n − O2 ) = E(M nO2 ) − [E(M n) + E(O2 )]
Here E(MnO2), E(Mn), and E(O2) are total energies of the indicated species. Zero or negative Mn−O2 binding energy implies that MnO2 is unstable with respect to the separate Mn and O2. It has been pointed out above that B3LYP is the best functional here to evaluate the Mn−O2 binding energies. Thus, in this and following sections, our discussion of the results is based on calculations with B3LYP. A comparison of the B3LYP calculated Agn−O2 and Aun−O2 binding energies is schematically illustrated in Figure 10. The Agn−O2 binding energies exhibit a strong, consistent even−odd oscillation with n = 2−12, where the values for evenn AgnO2 are usually notably smaller than those of the adjacent 21918
dx.doi.org/10.1021/jp501701f | J. Phys. Chem. C 2014, 118, 21911−21927
The Journal of Physical Chemistry C
Article
Table 3. Calculated (Adiabatic) Electron Affinities (EA, eV) for the Mn Clusters M = Ag M2 M3 M4a M4b M5 M6 M7 M8 M9 M10a M10b M11 M12 M13 M14 M15a M15b M16a M16b M17 M18 M19 M20 M21 M22 M23 M24 M25
M = Au
BP86
revPBE
B3LYP
exptla
BP86
revPBE
B3LYP
exptla
1.19 2.46 1.82 1.94 2.20 1.53 2.22 1.66 2.44 2.27 2.28 2.55 2.38 3.14 2.06 2.66 2.63 2.74 3.15 3.09 2.42 2.91 2.07 3.30 2.64 2.85 2.52 2.96
0.93 2.18 1.54 1.67 1.93 1.27 1.95 1.39 2.17 1.97 1.99 2.29 2.07 2.85 1.75 2.40 2.34 2.40 2.82 2.77 2.11 2.60 1.80 2.97 2.31 2.53 2.22 2.69
0.96 2.21 1.55 1.69 1.94 1.22 2.05 1.35 2.17 1.96 1.99 2.36 2.03 3.06 1.75 2.40 2.35 2.48 2.85 2.81 2.04 2.62 1.53 2.98 2.26 2.50 2.07 2.65
1.05 2.60 2.00
2.07 3.64 2.65 2.83 3.16 2.29 3.53 2.97 3.86 3.98 3.14 3.77 3.35 4.07 2.87 3.64 3.91 3.75 4.00 4.07 3.31 3.74 2.75 3.61 3.36 3.88 3.43 3.83
1.82 3.38 2.39 2.57 2.90 2.05 3.26 2.71 3.60 3.72 2.88 3.52 3.09 3.80 2.60 3.39 3.65 3.46 3.68 3.76 3.04 3.45 2.48 3.35 3.08 3.61 3.15 3.56
1.81 3.42 2.38 2.59 2.91 1.96 3.22 2.62 3.65 3.57 2.88 3.54 3.09 4.08 2.56 3.41 3.66 3.52 3.68 3.80 3.00 3.51 2.44 3.31 3.07 3.65 2.95 3.53
2.00 3.70 2.60
2.40 2.25 2.90 2.00 2.50 2.20 2.50 2.25 3.00 2.10 2.50 2.80 3.30 2.50 2.95 2.40 3.00 2.50 2.40 2.20 2.80
3.10 2.10 3.50 2.79 3.80 3.91 3.70 3.10 4.00 3.00 3.60 4.10 4.00 3.30 3.75 2.77 3.95 3.80 4.00 3.70 3.90
a
These are measured vertical detachment energies (VDEs) (ref 52); it is shown that adiabatic detachment energies (ADEs, which correspond to our EAs) are usually very similar to VDEs (ref 41), but the latter are not available for large clusters considered here.
Figure 5. Schematic illustration of the calculated binding energies per atom Ebind/atom for the Agn and Aun clusters. Figure 7. Schematic illustration of the calculated electron affinities (EAs) for the Agn and Aun clusters, together with experimental data.
odd-n AgnO2. For most even-n AgnO2 complexes, the calculated Ebind(Agn−O2) values are either negative or very small (
