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Density Functional Study of Neutral and Charged Silver Clusters Agn with n = 2−22. Evolution of Properties and Structure Michael L. McKee*,† and Alexander Samokhvalov*,‡ †

Department of Chemistry and Biochemistry, 179 Chemistry Building, Auburn University, Auburn, Alabama 36849, United States Department of Chemistry, 315 Penn Street, Rutgers University, Camden, New Jersey 08102, United States

‡

S Supporting Information *

ABSTRACT: Geometries and electronic properties of neutral Agn, cationic Agn+, and anionic Agn− silver clusters with n = 2−22 were investigated by density functional theory (DFT) with M06 functional. For neutral clusters, transition from planar to “empty cage” structure occurs at n = 7, “empty cage” to “cage with one Ag atom” at n = 18, and to “cage with two Ag atoms” at n = 22. For lowestenergy Agn clusters, Ag8 and Ag18 show lowest polarizability due to closed-shell valence electron configurations 1S2/1P6 and 1S2/1P6/1D10. High stability of Ag8 is manifested in small dissociation energies of Ag9 to Ag8 plus Ag1 and Ag10 cluster to Ag8 plus Ag2. Cluster Ag20 with configuration 1S2/1P6/1D10/2S2 is stable due to low dissociation energy of Ag21 to Ag1 and Ag22 to Ag2. Cationic clusters with even n namely Ag10+ (9 valence electrons), Ag16+ (15 valence electrons), and Ag22+ (21 valence electrons) dissociate to Ag1 and closed-shell Ag9+ (1S2/1P6), Ag15+ (1S2/1D10/2S2) and Ag21+ (1S2/1P6/1D10/2S2). For odd n, Ag11+ and Ag17+ dissociate to Ag2 and closed-shell Ag9+ and Ag15+. For anionic clusters Agn−, cohesion energy Ecoh and binding energy (BE) show maxima at n = 7 and n = 17 due to stable Ag7− and Ag17− clusters. Small Agn− clusters (n = 4−11) with even n (except n = 8) have lower dissociation energy for loss of Ag1 while those with odd n have lower dissociation energy for loss of Ag2. For n = 12−22, all clusters have lower dissociation energy for loss of Ag1.

1. INTRODUCTION Small to medium size silver clusters Agn where n ≈ 2−20, feature quite interesting optical,1 electronic,2 and magnetic3 properties, and they find applications in photonics,4 catalysis,5 biomedical technology.6 Small silver clusters have been a topic of much interest in recent decade, because their chemical and physical properties change significantly when cluster size increases. Understanding changes in geometry of small silver clusters versus their size may lead to design of new nanodevices, more efficient nanostructured catalysts, fluorescent markers, and so forth. The properties of silver clusters have been understood less than the properties of gold clusters of the same size.7 Quantum chemical computations of silver clusters are of interest, because they can reveal new stable structures that are yet to be obtained by experiment. For neutral silver clusters, many quantum chemical computations have been reported. Tiago et al.8 computed electronic and optical excitations in small neutral Agn clusters with n = 1−8 by density functional theory (DFT) in comparison to many-body theories within an ab initio pseudopotential framework. Harb et al.1 reported a joint computational (time-dependent density functional theory, TDDFT) and experimental study of absorption spectra of neutral medium-size Agn clusters with n = 4−22. Recently, Duanmu et al.9 studied all possible isomers for small clusters with n = 5−7 using 42 exchange−correlation functionals to assess geometries (e.g., internuclear distances), structures (e.g., planar versus © 2017 American Chemical Society

nonplanar), and energies. The M06 was concluded to be one of the best functionals for computation of properties of cationic and anionic silver clusters.9 Chen et al.10 used DFT followed by high level coupled cluster CCSD(T) calculations to optimize geometry of Agn clusters with n < 100. Yang et al.11 optimized structures of neutral Agn clusters with n = 13−160 using a modified dynamic lattice searching (DLS) method. Cationic silver clusters Agn+ have been frequently studied by experiment, and they are of major interest in photonics, biomedicine, and catalysis. Small cationic Agn+ clusters are easily obtained in aqueous solutions including those at ambient conditions,12−14 which is in stark contrast with neutral small Agn clusters that require cryo-matrix of inert gas to remain stable.15,16 In heterogeneous catalysis, silver clusters supported on metal oxides are of significant interest in ethylene epoxidation.17 As relevant to catalysis, computational studies were utilized to study interactions of cationic silver clusters with small molecules such as hydrogen,18 carbon monoxide,19 chlorine,20 oxygen,21 and so forth. Duanmu et al.9 studied small clusters Ag2+ through Ag7+ by DFT/M06 and CCSD(T). Gamboa et al.22 reported computations of geometry and electronic properties of small neutral Agn versus cationic Agn+ and anionic Agn− clusters with n = 3−15 using generalized Received: April 25, 2017 Revised: June 5, 2017 Published: June 6, 2017 5018

DOI: 10.1021/acs.jpca.7b03905 J. Phys. Chem. A 2017, 121, 5018−5028

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The Journal of Physical Chemistry A

Figure 1. Structures of lowest-energy neutral clusters Ag2 through Ag19.

energy (VDE), excitation energies Te for transition from ground to the first excited state, bond lengths re, and vertical ionization potentials (IPv) of anionic Ag2− versus neutral Ag2 clusters and used the DFT with S2LYP functional24 to calculate geometries of larger Ag11− and Ag12− clusters. Liao et al.25

gradient approximation (GGA) functional by Perdew, Burke, and Ernzerhof (PBE). Computations of anionic silver clusters Agn− are more seldom than those of neutral clusters. Matulis et al.23 tested the set of the DFT functionals to calculate vertical detachment 5019


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Figure 2. Structures of lowest-energy neutral clusters Ag20 through Ag22.

and heat capacity computed at the M06/SDD(Ag) level of theory. Table S2 shows Cartesian coordinates for Agn clusters with n = 2−22 (neutral, cation, and anion) optimized at the M06/SDD(Ag) level. Small neutral silver clusters with n < 12 were extensively studied by the DFT calculations, for example,1,8,23 including the M06 functional.9 Our main interest is to study the larger clusters with n = 12−22. Structures of all computed neutral clusters for Ag12 through Ag22 are in the Supplementary Figures S1−S10; in our search of lowest-energy structures, we considered all of lowest-energy geometries of neutral silver clusters reported in ref 10. Figure 1 shows computed lowest-energy structures for neutral Ag2 through Ag19 clusters. As n increases, one can see a progression in the lowest-energy structures from planar to “empty cage” (transition from Ag6 to Ag7). This finding is consistent with reported22 change in geometry of the lowestenergy neutral smaller Agn clusters with n = 1−15, where threedimensional cage structure becomes of lower energy than its isomeric planar structure at n = 7, as determined by the firstprinciples molecular orbital (MO) approach with the exchange correlation included within a generalized gradient DFT formalism.31 In Figure 1, when n further increases for Agn clusters, there are progressions from empty cage structure to the structure with one Ag atom in cage (at Ag18). Figure 2 shows lowest-energy structures of the largest clusters Ag20 through Ag22. Within the size range n = 18−22, the transition occurs from “cage with one Ag atom” to “cage with two Ag atoms” (for Ag22 cluster). To our knowledge, structural transitions of lowest-energy cluster from empty cage to “one atom in cage” and further to “two atoms in cage” have not been systematically investigated. To draw correlations “structure/electronic properties” for neutral silver clusters, attention was paid to highly symmetric structures with zero, one or two silver atoms located entirely inside the cage; these “internal” silver atoms are fully coordinated with other silver atoms. Table 1 shows correlations between the energy difference (kcal/mol) for neutral Agn clusters of different symmetry. The energy of isomeric Agn clusters with the given number of Ag atoms inside the cage is shown versus computed total energy of lowest-energy cluster Agn. When several clusters existed for the given n and the given geometry, for example, cage with one Ag atom, the lowest energy structure was chosen. Notations of structures are the same as in Table S1 and in Supplementary

calculated geometries, ionization potentials (IPs) and electron affinities (EAs) of anionic Agn− versus neutral Agn clusters with n = 2−25 using DFT with functionals BP86, revPBE (revised Perdew−Burke−Ernzerhof functional), and B3LYP. Duanmu et al.9 compared an accuracy of M06 functional and CCSD(T) versus experimental data for small clusters Ag2− through Ag7−. It would be of interest to find the DFT functional that allows reliable calculations of geometry and electronic properties of both neutral and charged silver clusters of variable size. The M06 functional has been parametrized for transition metals and nonmetals and tested successfully against multiple databases including thermochemistry, kinetics, noncovalent interactions, transition metal bonding, and so forth.26 As pertinent to nanoclusters, the M06 functional has been validated to predict the planar-to-3D transition in anionic gold clusters.27 To our knowledge, the M06 functional has not been used to calculate geometry and electronic properties of medium-size neutral or charged silver clusters with n > 12. Recently, we successfully used the M06-2X functional with DFT to calculate energy and geometry of adsorption sites28 in metal−organic frameworks (MOF). Herein, we describe the systematic DFT computations with M06 functional to determine optimized geometry, IP, EA, cohesion energy (Ecoh), binding energy (BE) of Ag atom, and dissociation energy for loss of Ag1 monomer or Ag2 dimer for neutral Agn, cationic Agn+ and anionic Agn− clusters with n = 1−22.

2. COMPUTATIONAL DETAILS All structures were optimized at the M06 level26 with the Stuttgart small core scalar relativistic effective core potential29 (SDD) with the ECP28MWB basis set for Ag (contracted to 6s5p1d). Vibrational frequencies were computed to determine the nature of the stationary points and to make zero-point and thermal corrections to 298 K. The Gaussian09 program system30 was used for all geometry optimizations and frequency calculations. 3. RESULTS AND DISCUSSION 3.1. DFT Computations of Geometry of Neutral Silver Clusters Ag1 through Ag22. We have optimized geometry of neutral clusters Agn for n = 1−22 of all possible structures using the M06 functional, as well as cationic clusters Agn+ and anionic clusters Agn− for the same range of n. Table S1 shows notations, charge, symmetry, electronic and spin states, energy, entropy 5020


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The Journal of Physical Chemistry A Table 1. Geometry and Total Energy (kcal/mol) of Neutral Agn Clusters versus the Lowest-Energy Agn Isomer for Planar Structure and Cage with Zero, One, or Two Ag Atoms

cluster Ag6 Ag7 Ag12 Ag13 Ag14 Ag15 Ag16 Ag17 Ag18 Ag19 Ag20 Ag21 Ag22

planar structure/ energy Ag6A 0.0 Ag7C 14.0 Ag12L 18.4

empty cage, structure/ energy

cage with one Ag atom inside, structure/energy

cage with two Ag atoms inside, structure/energy

Ag6B 3.6 Ag7A 0.0 Ag12A 0.0 Ag13A Ag14A Ag15A Ag16A Ag17A Ag18B

0.0 0.0 0.0 0.0 0.0 0.7

Ag13H 21.9 Ag14G 22.6 Ag15E 15.4 Ag16D 4.5 Ag17B 2.4 Ag18A 0.0 (lowestenergy cluster with one Ag atom) Ag19A 0.0 Ag20A 0.0 Ag21A 0.0 Ag22E 15.8

Ag16K 43.8

Ag19G 13.8 Ag20D 18.3 Ag21B 2.7 Ag22A 0.0 (lowestenergy cluster with two Ag atoms)

Figures S1−S10. Planar structures are absent among lowestenergy clusters starting at n = 13 and higher. From Ag13 to Ag18, there is a steady increase in stability of cage with one Ag atom relative to empty cage (with zero Ag atoms). When one Ag atom is located inside a cage, such neutral Agn cluster is of lowest energy (shown as zero energy in Table 1) among isomeric Agn clusters for n = 18, 19, 20 and 21. When two Ag atoms are inside a cage, such neutral Agn cluster is of lowest energy at n = 22. Thus, analysis of symmetry of neutral Agn clusters results in the “transition” regions at n = 7, n = 18, and n = 22, where significant changes in electronic properties are anticipated, based on computed lowest energy structures. 3.2. DFT Computations of Electronic Properties of Neutral Silver Clusters Ag1 through Ag22. Electronic properties of silver clusters can be assessed through IP and EA. Figure 3a shows calculated IP for each lowest-energy neutral cluster (Figures 1 and 2) in the range Ag1 through Ag22. Computed IP for Ag1 at 177.1 kcal/mol is in good agreement with experimental value32 at 7.57 eV or 174.6 kcal/mol (1.4% error). Computed IP for linear dimeric cluster Ag2 at 179.6 kcal/mol is also in good agreement with experimental value32 at 7.65 eV or 176.4 kcal/mol (1.8% error). For larger silver clusters, various linear, planar or 3D structures were found by calculations, while experimental data could have been obtained with specimens containing mixture of geometric isomers, so comparisons with published computed data are preferred. In Figure 3a, several trends can be seen for the IP. First, the IP steadily decreases as n increases for very small clusters with n = 2−5. This finding is in agreement with Gamboa et al.22 who used the MO approach with exchange and correlation functionals as a generalized gradient approximation (GGA) within the DFT for small Ag1−Ag15 clusters, and found a decrease of the IP within n = 1−3. Second, for n > 4, oscillations of the IP are observed for Agn clusters with even/ odd number of silver atoms with the maxima for even n, consistently with other reports.8,22,33 An increased value for the

Figure 3. Calculated energies for removal or attachment of electron from lowest-energy neutral clusters Ag1 through Ag22. (a) IP. (b) EA.

IP for neutral Agn clusters with even n is due to filled valence electronic shells forming lower energy singlet state, compared to higher energy state with one unpaired electron in valence shell (for odd n). Third, a “first minimum” in the IP is found at n = 9, and easy ionization of neutral Ag9 cluster results in stable cationic Ag9+ cluster with eight valence electrons. Neutral Ag8 cluster with eight valence electrons is known to be of an enhanced stability due to the so-called magic number34 n = 8, which is related to closed valence shell with 1S2/1P6 electronic configuration. Further at n = 12−17, the IP shows “even/odd” oscillations without general increase or decrease trend, consistently with empty cage structure (Table 1). Finally, the IP decreases within n = 18−22 forming the “second minimum” at n = 21 in Figure 3a. To our knowledge, such decrease in the IP was not reported for silver clusters with n = 18−21, but it is consistent with transition from cage with one Ag atom structure to Agn clusters with cage with 2 Ag atoms (Figures 1 and 2 and Table 1). The second minimum at n = 21 in Figure 3a is consistent with easy ionization of neutral Ag21 cluster to stable cationic Ag21+ cluster with 20 valence electrons. The obtained stable cationic Ag21+ cluster is isoelectronic, by the number of valence electrons, with neutral Ag20 cluster featuring “magic number” n = 20, closed valence subshell with configuration 1S2/1P6/1D10/2S2 and enhanced stability.35 EA (Figure 3b) is reminiscent of a mirror image of the IP as a function of n: when the IP has a maximum, the EA has a minimum, consistently with other reports, for example, study of silver clusters22 with n = 1−14. For empty cage clusters, local maximum of the EA at n = 9 is consistent with first minimum in the IP at n = 9 in Figure 3a. For cage with one Ag atom structures, global maximum of the EA at n = 17 is consistent with high electron affinity of neutral Ag17 cluster that forms stable anionic Ag18− cluster with closed-shell valence electron 5021


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singlet state). In addition to “even/odd oscillations” in Figure 4b, one can see the first minimum of BE at n = 9 and second minimum at n = 21, consistently with minima for Ecoh in Figure 4a. In Figure 4b, global maximum in the BE for Agn clusters is at n = 20 indicating an enhanced stability of neutral Ag20 cluster. Neutral sodium clusters Nan serve as model to predict behavior of neutral Agn clusters, because each Na atom donates one electron to the molecular orbitals (MOs) of the cluster. Binding energy of neutral clusters Nan calculated for n = 10−25 showed global maximum37 at n = 20, in accord with our data for Agn clusters in Figure 4b with global maximum in the BE at n = 20. Static electric dipole polarizability is another major electronic property, which determines the dynamic response of atomic system with bound electrons to external electric or magnetic field. Quantitative analysis of polarizabilities of metallic clusters (in units of cube of Bohr radius a0 per atom) often reveals a strong dependence upon the structure of the cluster.38 Figure 5

configuration 1S2/1P6/1D10. The minimum in the EA at n = 20 is consistent with high stability of neutral Ag20 cluster with closed-shell valence electron configuration 1S2/1P6/1D10/2S2. Numerically, both IP and EA are defined on “per cluster” basis. We wanted to study how the other electronic properties of silver clusters depend upon n in the range n = 2−22, when assessed on “per atom” basis. The cohesion (or cohesive) energy Ecoh is defined as the energy needed to form a cluster from the individual (noninteracting) atoms, and Ecoh is calculated per atom in the cluster. Fournier et al.33 reported that cohesive energy of lowest-energy neutral Agn clusters steadily increased within n = 2−12. Figure 4a shows calculated

Figure 4. Energy of interactions of Ag atoms for lowest-energy neutral clusters Ag2 through Ag22. (a) Ecoh. (b) BE.

Figure 5. Computed polarizability of lowest-energy neutral clusters Ag2 through Ag22.

cohesion energies Ecoh (average binding energy per Ag atom) for lowest-energy neutral clusters Agn within n = 2−22. In Figure 4a, the Ecoh increases in general when n increases as expected, reflecting the larger gain in the energy due to multiple new bonds in the cluster formed by many individual atoms, consistently with published data.3,33 In Figure 4a, the first anomaly or “first maximum” in Ecoh is at n = 8 due to an enhanced stability of Ag8 cluster with valence 1S2 /1P6 configuration. For “cage with one Ag atom” structures, the “second maximum” at n = 20 is due to Ag20 cluster with closed shell 1S2/1P6/1D10/2S2 configuration. Presence of the two maxima in Figure 4a is illustrated with the two minima in Ecoh at n = 9 and n = 21. BE is defined as the energy change when one atom is added to the cluster; it is one of critical properties to assess the degree of stabilization of metal cluster, for example.36 Figure 4b shows calculated BEs of Ag atom for lowest-energy neutral clusters Agn as a function of n. The BE fluctuates for pairs “odd/even n”, consistently with computational study22 of energy needed for removal of silver atom from neutral clusters Ag1 through Ag16. In Figure 4b, the lower BEs of neutral Agn clusters with odd n (compared to even n) are due to lower stability of clusters with odd number of valence electrons (half-filled orbitals) versus clusters with even number of valence electrons (filled orbitals,

shows computed polarizability for lowest-energy neutral Agn clusters within n = 2−22. In general, when each of the two major structures (planar structure with n = 3 through n = 6 and empty cage with n = 7 through n = 18) progressively increases in size with the increase of n, polarizability of the cluster first remains rather high, but then decreases. The two minima in the polarizability in Figure 5 at n = 8 and n = 18 are consistent with valence electron configuration 1S2/1P6 for neutral Ag8 cluster and 1S2/1P6/1D10 for neutral Ag18 cluster. This indicates that both low-polarizability, “rigid” neutral Ag8 and Ag18 clusters feature closed valence electronic shells. The second minimum at n = 18 for neutral Agn clusters in Figure 5 is consistent with computed minimum in polarizability for neutral sodium Na18 clusters.37 Figure 6 shows computed HOMO−LUMO gap energies of lowest-energy neutral clusters Ag1 through Ag22. In general, computed HOMO−LUMO gaps in Figure 6 steadily decrease as n increases with the trend toward a zero optical gap for bulk silver metal, as expected. The fluctuations in HOMO−LUMO gap for Agn clusters with even n (larger gap) and odd n (smaller gap) in Figure 6 are consistent with published DFT calculations22,36 using functionals other than M06. Clusters Agn with even n have all their valence electrons 5022


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Figure 6. HOMO−LUMO gaps of lowest-energy neutral clusters Ag1 through Ag22.

paired which explains the higher stability (as well as lower chemical reactivity in general) and larger bandgaps.36 In Figure 6, for “empty cage” Agn clusters (with n = 7−17) there is a maximum in computed bandgaps at n = 8, consistently with stable Ag8 cluster with closed shell 1S2/1P6 configuration. For larger clusters “one Ag in cage” with n = 18−21, one can see the maximum at n = 20, consistently with magic number35 and electronic configuration 1S2/1P6/1D10/2S2 explaining an enhanced stability and larger bandgap of Ag20 cluster with 20 valence electrons. The lowest-energy neutral Ag18 cluster of one Ag in cage structure (Figure 1) has valence electron configuration 1S2/ 1P6/1D10 and reminds in terms of number of valence electrons the lowest-energy neutral Na18 cluster.37 The lowest-energy neutral Ag18 cluster showed a global minimum in polarizability curve (Figure 5) versus n and hence an enhanced stability. Figure 7 shows the diagram of molecular orbitals (isosurfaces generated by Gaussian program) for lowest-energy neutral Ag18 cluster denoted Ag18A in Table 1 and Table S1. The lowestenergy MO of this neutral Ag18 cluster (which would be 1S orbital) is strongly mixed with other orbitals to be identified; only eight higher-energy filled MOs including the HOMO are shown, as well as the LUMO. Experimentalists studying small nanoparticles are often frustrated to find out that none of the two nanoparticles are of the same size; precise control of the size of small nanoparticle or nanocluster is of importance. Dissociation of neutral silver clusters Agn with selective formation of Agn−1 or Agn−2 clusters would be attractive for synthesis of small clusters with well-controlled number of atoms. Figure 8 shows the dissociation energy necessary to remove one Ag atom (Figure 8a) and two Ag atoms (Figure 8b) from neutral Agn clusters. In Figure 8a, one can see a first minimum at n = 9 for empty cage Agn clusters with n = 7−18, that is, an easy dissociation of Ag9 cluster with removal of one Ag atom, eq 1 Ag 9 + energy → Ag8 + Ag1 (1)

Figure 7. Diagram of molecular orbitals for lowest-energy Ag18 cluster.

This indicates formation of stable Ag8 cluster with valence electron configuration 1S2/1P6 (closed valence shell), consistently with low polarizability of neutral Ag8 cluster in Figure 5.

Figure 8. Energy of dissociation of lowest-energy neutral clusters Ag4 through Ag22. (a) Loss of Ag1. (b) Loss of Ag2. 5023


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The Journal of Physical Chemistry A Respectively, one can see in Figure 8b the first minimum at n = 10, that is, dissociation of Ag10 cluster with removal of Ag2 by eq 2: Ag10 + energy → Ag8 + Ag 2

(2)

The minimum at n = 10 in Figure 8b indicates an easy formation of stable Ag8 cluster, consistently with Figure 8a. For larger clusters with one Ag in cage with n = 18−21, one can see in Figure 8a the second minimum in the dissociation energy at n = 21, which indicates formation of stable neutral Ag20 cluster upon dissociation of Ag21 cluster. An enhanced stability of Ag20 cluster is also illustrated in Figure 8b, where a small energy is needed for dissociation of neutral Ag22 cluster with formation of Ag2 dimer and stable Ag20 cluster. Mass spectroscopic study of neutral sodium clusters Nan has revealed that clusters with n = 8, 20, 40, 58, and 92 showed an enhanced stability.39 For sodium clusters, magic numbers were explained in terms of a one-electron shell model, when independent delocalized 3s electrons of sodium atoms are bound in a spherically symmetric potential well.39 For stable neutral Ag20 clusters, magic number n = 20 would indicate that 5s electrons of Ag atoms contribute to MOs of the cluster with formation of closed valence subshell yielding electronic configuration 1S2/1P6/1D10/2S2. Interestingly, there is local minimum in Figure 8a for dissociation of Ag15 to stable Ag14 cluster with 14 valence electrons and Ag1 monomer as well as the corresponding local minimum in Figure 8b at n = 16 for dissociation of Ag16 to Ag2 dimer and stable Ag14 cluster. The Ag14 cluster has a closed shell 1S21D102S2 configuration; Reber et al.21 found by DFT computations an unusually low reactivity with molecular oxygen for cationic Ag15+ cluster which is isoelectronic (by the number of valence electrons) with neutral Ag14 cluster. Further, global maximum in dissociation energy in Figure 8b at n = 18 indicates highly stable Ag18 cluster, consistently with its closed shell 1S2/1P6/1D10 configuration. Properties of lowestenergy neutral, cationic and anionic Agn clusters originate from their geometric and electronic structure. In the following sections, we discuss computed electronic properties of cationic Agn+ and anionic Agn− clusters. 3.3. DFT Computations of Cationic Silver Clusters Ag2+ through Ag22+. Computed geometries of lowest-energy cationic clusters from Ag2+ through Ag22+ are in Figures S11 and S12; they are close to those of lowest-energy neutral clusters with cage structures dominating for n ≥ 7. Figure 9a shows computed energy of dissociation of lowest-energy cationic Agn+ clusters to Ag1 monomers and respective Ag(n‑1)+ clusters. In Figure 9a, one can see that loss of Ag1 monomer occurs easier (i.e., with lower energy) for Agn+ clusters with even n, compared to Agn+ with odd n in the whole range n = 4−22. Our data in Figure 9a within n = 4−7 are consistent with Duanmu et al.9 who reported that Ag1 is lost from small cationic Agn+ clusters (n = 2−7) with even n at lower dissociation energy than for odd n. Moreover, our data in Figure 9a indicate that the same “even/odd” trend continues for the larger Agn+ clusters within n = 7−22, where cage structure is of lowest energy. Cationic Agn+ clusters with an odd n have an even number (n − 1) of valence electrons and hence closed valence shells, so that they are more stable than their counterparts with even n. For even n, one can see in Figure 9a the two minima at n = 10 and n = 16 for dissociation energy to Ag1 monomer. For the first minimum at n = 10, cationic Ag10+ cluster is to be

Figure 9. Energy of dissociation of lowest energy cationic clusters Ag4+ through Ag22+. (a) Loss of Ag1. (b) Loss of Ag2.

converted to stable Ag9+ cluster with eight valence electrons. The predicted enhanced stability of Ag9+ cluster is due to valence electron configuration of 1S2/1P6, consistently with an enhanced stability of neutral Ag8 cluster in Figure 8a (high dissociation energy). An enhanced stability of silver clusters with eight valence electrons has been noted by Kahlal et al.40 who reported stable multiply charged [Ag13]5+ cluster of octahedral geometry and its complexes with iron carbonyls as found by the DFT calculations with BP86 functional. Relevant experimental data were reported by Kruckenberg et al.41 who used collision-induced dissociation (CID) in a Penning trap to study low energy dissociation channels of cationic silver clusters Agn+ with n = 3−20. They found41 dissociation of Ag10+ cluster to Ag1 monomer and Ag9+ cluster but not to Ag2 dimer and Ag8+ cluster, consistently with our data (Figure 9a) predicting an enhanced stability of Ag9+ cluster with eight valence electrons. For the second minimum at n = 16 in Figure 9a, cationic Ag16+ cluster is predicted to be dissociated to Ag1 and stable Ag15+ cluster with 14 valence electrons. Reber et al.21 predicted high stability of Ag15+ cluster by DFT with GGA functional by Perdew, Burke, and Ernzenhof, consistently with our data. Computed dissociation energies of cationic Agn+ clusters with formation of Ag2 dimer and Ag(n−2)+ clusters are shown in Figure 9b. One can see that the minima in dissociation energy correspond to odd values of n: at n = 5 (first minimum), at n = 11 (second minimum), and at n = 17 (third minimum). The first minimum at n = 5 is due to an easy dissociation of Ag5+ cluster with four valence electrons to Ag2 dimer and stable Ag3+ cluster with two valence electrons. An enhanced stability of obtained Ag3+ cluster is consistent with Duanmu et al.9 who used DFT with M06 functional and predicted that when small Ag3+, Ag5+, or Ag7+ clusters dissociate with formation of Ag2 dimer, their dissociation energies are 64.7, 39.7, and 57.0 kcal/ 5024


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The Journal of Physical Chemistry A mol, respectively. Namely, among small cationic Agn+ clusters with odd n for n ≤ 7, dissociation of Ag5+ was predicted to require the lowest energy.9 We also investigated the larger Agn+ clusters with 7 ≤ n ≤ 22. The second minimum in Figure 9b at n = 11 indicates an easy dissociation by eq 3 Ag11+ → Ag 2 + Ag 9+

Table 2. Experimental Data by the Low Energy CID for Loss of Ag1 Monomer and Ag2 Dimer from Agn+ Clusters with Odd n (from Figures 2 and 3 in Refernce 41) versus Our Computed Data

(3)

The obtained Ag9+ cluster is stable because it has the same closed shell configuration of eight valence electrons as stable neutral Ag8 cluster. Finally, the third minimum in Figure 9b at n = 17 indicates an easy dissociation by eq 4 Ag17+ → Ag 2 + Ag15+

n

loss of Ag1 by loss of Ag2 by low energy low energy CID in ref 41 CID in ref 41

our computed data in Figure 10

consistency of our computed data with experiment in ref 41

9

detected

detected

yes

11

not detected

detected

13

detected

detected

15

detected

detected

17

detected

detected

loss of Ag1 and Ag2 preferred loss of Ag2 loss of Ag1 and Ag2 loss of Ag1 and Ag2 preferred loss of Ag2

19

detected

not detected

(4)

The obtained Ag15+ cluster with 14 valence electrons is found stable in Figure 9b, consistently with the above discussion of second minimum in Figure 9a for Ag16+. It would be of interest to compare the preference of dissociation of Agn+ clusters with odd n (which are more stable than the respective clusters with even n judged by loss of Ag1) to Ag1 monomer versus Ag2 dimer. Figure 10 shows computed

preferred loss of Ag1

yes yes yes no for ref 41 yes for ref 21, 42, and 43 yes

experimental data.42 In addition, anionic Ag13− cluster with the same number of valence electrons as stable cationic Ag15+ cluster was also found to be highly stable.43 Such high stability is apparently due to closed shell configuration 1S21D102S2 for neutral Ag14, cationic Ag15+, and anionic Ag13− clusters. 3.4. DFT Computations of Anionic Silver Clusters Ag2− through Ag22−. Computed geometries of lowest-energy anionic clusters from Ag2− through Ag22− are in Figures S12 and S13. They are similar to lowest-energy neutral clusters: linear or planar structures are at n = 2−5, empty cage structures start from n = 6, cage with one Ag atom first appears at n = 18 and cage with two Ag atoms at n = 22. To our knowledge, cohesion energy of anionic silver clusters Agn− was not reported. We calculated Ecoh of anionic silver clusters Agn− from computed cohesion energies of neutral Agn clusters using eq 5 Ecoh(anion) = E coh(neutral) −

EA(neutral) − EA(Ag) n (5)

where Ecoh (anion) is cohesion energy of Agn− anionic cluster, Ecoh (neutral) is cohesion energy of neutral Agn cluster, EA (neutral) is electron affinity of neutral Agn cluster, and EA (Ag) is electron affinity of Ag atom (numerically equal to 30.019 kcal/mol). Figure 11a shows calculated Ecoh of lowest-energy anionic Agn− clusters versus n in the range n = 2−22. In Figure 11a, one can see a decreasing trend of Ecoh within n = 3−6 when n increases, while Ecoh shows an increasing trend within n = 9−22 when n increases. The increase in Ecoh versus n for larger clusters is likely due to electronic properties of empty cage as lowest-energy structure at n > 7, while at n < 7 lowest-energy structures are planar or linear. The maxima of E coh versus n correspond to thermodynamically more stable anionic clusters. For cage structures, the first maximum of Ecoh is at n = 7 for Ag7− cluster with eight valence electrons and 1S2/1P6 closed shell configuration, similarly to stable neutral Ag8 cluster (Figures 5 and 8). For the second maximum in Ecoh at n = 17 in Figure 11a, anionic Ag17− cluster is predicted to be stable, due to the same closed shell configuration with 18 valence electrons as stable neutral Ag18 cluster (see Figures 5 and 8). For charged aluminum clusters, electronic shell closing was found responsible for an enhanced cohesion energy.44 Our data of

Figure 10. Dissociation energy and computed preferential loss of Ag1 monomer or Ag2 dimer for lowest-energy Agn+ clusters with odd n within n = 5−21.

dissociation energy for loss of Ag1 monomer and Ag2 dimer for Agn+ clusters with odd n within n = 5−21. Our computed data in Figure 10 for smaller cationic Agn+ clusters with n = 5 and n = 7 are in accordance with ref 9. In addition, we compared the preference of loss of Ag1 or Ag2 (based on lower dissociation energy) for larger cationic clusters for n = 9−21, see Figure 10 and Table 2. Table 2 shows analysis of experimental data by low energy CID of Agn+ clusters as in ref 41 versus our computed data (Figure 10). One can see in Table 2 that fragmentation of Agn+ clusters with odd n to Ag1 monomer or Ag2 dimer as computed by us using DFT with M06 functional has good consistency with experimental data41 by the low energy CID, except for n = 17. Our computed data indicate a preferential loss of Ag2 dimer from cationic Ag17+ cluster by eq 4 with formation of Ag15+ cluster which is predicted to be stable. In accord with our computations, the Ag15+ cluster was found to be of exceptionally high stability by DFT computations21 that are supported by 5025


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Figure 12. Energy of dissociation of lowest-energy anionic Agn− clusters with formation of Ag1 monomer or Ag2 dimer and smaller anionic clusters.

of lower energy than Ag7B- listed in Table S1 and used in Figure 12. We believe that despite the above disagreement with one experimental data point in ref 45 the DFT with M06 functional is reliable in computations of electronic properties of neutral and charged silver clusters. We have also computed the dissociation energies for larger Agn− clusters with n = 12−22, and found that the above “even/odd” rule does not apply (Figure 12). Namely, for n = 12−22 the dissociation requires lower energy for fragmentation to monomer Ag1 than to dimer Ag2 for each Agn− cluster. While this observation is intuitively expected, experimental data are needed to confirm this finding. It would be of interest to determine the validity of DFT with M06 functional in computations of larger clusters with n > 22; such investigations can be the topic of future work.

Figure 11. Energies of interactions of Ag atoms for lowest-energy anionic clusters Ag2− through Ag22−. (a) Ecoh per atom. (b) BE.

enhanced stability of Agn− clusters with closed shell valence electron configuration at n = 7 and n = 17 (Figure 11a) are consistent with published data for charged aluminum clusters and with our data for stable neutral Agn clusters with magic numbers n = 8 and n = 18. Figure 11b shows calculated BE of lowest-energy anionic Agn− clusters versus n. The same observations are made as for Ecoh in Figure 11a. Namely, the two maxima in Figure 11b for BE of Ag7− and Ag17− clusters are consistent with closed shell electron configurations of stable anionic clusters with 8 and 18 valence electrons, respectively. Figure 12 shows the energy of dissociation of lowest-energy anionic Agn− clusters to Ag1 monomer and smaller Ag(n‑1)− cluster versus dissociation to Ag2 dimer and smaller Ag(n‑2)− cluster. One can see that the following rules apply for n ≤ 11: (a) for even n (n = 4, 6 and 10, except n = 8), the lower dissociation energy is for loss of monomer Ag1 and (b) for odd n (n = 5, 7, 9 and 11), the lower dissociation energy is for loss of dimer Ag2. For small anionic Agn− clusters with n = 2−7, the same observations were made by DFT with M06 functional.9 Preferred loss of Ag1 by small Agn− clusters with even n is rationalized via formation of singlet state in the obtained Ag(n‑1)− cluster. A preferred loss of Ag1 by anionic Agn− clusters with even n within n = 2−7 was found experimentally45 by energy-resolved collision induced dissociation (CID). Preferred fragmentation of small anionic clusters Agn− with odd n (even number of valence electrons) occurs with formation of Ag2 dimer and Ag(n−2)− cluster with even number of valence electrons forming singlet state. In attempt to resolve the exception at n = 8 in Figure 12, we have tried all possible geometries of anionic Ag7− cluster and could not find the one

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CONCLUSIONS For neutral Agn clusters, transition from planar to empty cage structure occurs at n = 7, from empty cage to cage with one Ag atom at n = 18, and to cage with two Ag atoms at n = 22. For the first time, medium-size neutral Agn, cationic Agn+, and anionic Agn− clusters with n = 12−22 were systematically studied by DFT with M06 functional via computed ionization potential, electron affinity, polarizability, binding energy, cohesion energy, and dissociation energy to Ag1 monomer and Ag2 dimer. For medium-size neutral, cationic and anionic silver clusters with n = 12−22, an enhanced stability is found for the number of valence electrons 14, 18, or 20 per cluster. Valence shell configurations of most stable neutral Agn clusters are 1S2/1D10/2S2 for empty cage, 1S2/1P6/1D10 and 1S2/1P6/ 1D10/2S2 for cage with one Ag atom. Preferential dissociation of medium-size (n = 11−22) stable cationic Agn+ clusters with odd n toward Ag2 dimer versus Ag1 monomer is predicted by computations. Specifically, Ag11+ and Ag17+ clusters easily dissociate to Ag2 and stable closed shell clusters Ag9+ and Ag15+, consistently with published experimental data by collisioninduced dissociation (CID). Computed cohesion energy and binding energy of anionic clusters Agn− with n = 2−22 are mutually consistent and consistent with stable clusters with 8 and 18 valence electrons. For small anionic clusters Agn− with n = 4−11, clusters with even n have the lower dissociation energy for loss of Ag1 (except n = 8), while clusters with odd n have 5026


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The Journal of Physical Chemistry A the lower dissociation energy for loss of Ag2. For larger Agn− clusters with n = 12−22, all clusters have the lower dissociation energy for loss of Ag1 monomer.

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Growth in the Absence of Stabilizing Ag+ Ions. J. Phys. Chem. 1993, 97, 4589−4594. (14) Treguer, M.; Rocco, F.; Lelong, G.; Le Nestour, A.; Cardinal, T.; Maali, A.; Lounis, B. Fluorescent Silver Oligomeric Clusters and Colloidal Particles. Solid State Sci. 2005, 7, 812−818. (15) Harbich, W.; Fedrigo, S.; Buttet, J. The Optical Absorption Spectra of Small Silver Clusters (n = 5−11) Embedded in Argon Matrices. Chem. Phys. Lett. 1992, 195, 613−617. (16) Rabin, I.; Schulze, W.; Ertl, G. Absorption Spectra of Small Silver Clusters Agn (n ≥ 3). Chem. Phys. Lett. 1999, 312, 394−398. (17) Chongterdtoonskul, A.; Schwank, J.; Chavadej, S. Ethylene Epoxidation Activity over Ag-Based Catalysts on Different Nanocrystalline Perovskite Titanate Supports. Catal. Lett. 2012, 142, 991− 1002. (18) Zhao, S.; Liu, Z.-P.; Li, Z.-H.; Wang, W.-N.; Fan, K.-N. Density Functional Study of Small Neutral and Charged Silver Cluster Hydrides. J. Phys. Chem. A 2006, 110, 11537−11542. (19) Zhou, J.; Li, Z.-H.; Wang, W.-N.; Fan, K.-N. Density Functional Study of the Interaction of Carbon Monoxide with Small Neutral and Charged Silver Clusters. J. Phys. Chem. A 2006, 110, 7167−7172. (20) Zhao, S.; Li, Z.-H.; Wang, W.-N.; Fan, K.-N. Density Functional Study of the Interaction of Chlorine Atom with Small Neutral and Charged Silver Clusters. J. Chem. Phys. 2005, 122, 144701. (21) Reber, A. C.; Gamboa, G. U.; Khanna, S. N. The Oblate Structure and Unexpected Resistance in Reactivity of Ag15+ with O2. Journal of Physics:Conference Series 2013, 438, 012002. (22) Gamboa, G. U.; Reber, A. C.; Khanna, S. N. Electronic Subshell Splitting Controls the Atomic Structure of Charged and Neutral Silver Clusters. New J. Chem. 2013, 37, 3928−3935. (23) Matulis, V. E.; Ivashkevich, O. A.; Gurin, V. S. DFT Study of Electronic Structure and Geometry of Neutral and Anionic Silver Clusters. J. Mol. Struct.: THEOCHEM 2003, 664−665, 291−308. (24) Matulis, V. E.; Mazheika, A. S.; Ivashkevich, O. A. DFT Study of Electronic Structure and Geometry of Anionic Silver Clusters Agn− (n = 11, 12, 17). J. Mol. Struct.: THEOCHEM 2008, 850, 61−66. (25) Liao, M.-S.; Watts, J. D.; Huang, M.-J. Theoretical Comparative Study of Oxygen Adsorption on Neutral and Anionic Agn and Aun Clusters (n = 2−25). J. Phys. Chem. C 2014, 118, 21911−21927. (26) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (27) Mantina, M.; Valero, R.; Truhlar, D. G. Validation Study of the Ability of Density Functionals to Predict the Planar-to-ThreeDimensional Structural Transition in Anionic Gold Clusters. J. Chem. Phys. 2009, 131, 064706. (28) Dai, J.; McKee, M. L.; Samokhvalov, A. Fluorescence of A100 MOF and Adsorption of Water, Indole, and Naphthalene on A100 by the Spectroscopic, Kinetic, and DFT Studies. J. Phys. Chem. C 2015, 119, 2491−2502. (29) Wedig, U.; Dolg, M.; Stoll, H.; Preuss, H. In Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A. E., Ed.; Reidel Publishing: Dordrecht, 1986; p 79. (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; J. A. Montgomery, J.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.;

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b03905. Figures S1−S14 and Tables S1 and S2 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*Tel: +1-334-844-6985. E-mail: [email protected]. *Tel: +1-856-225-6282. E-mail: [email protected]. ORCID

Alexander Samokhvalov: 0000-0002-7273-7322 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for computer time provided by the Alabama Supercomputer Center. REFERENCES

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