SilverâWater Clusters: A Computation of Agn(H2O)m for n = 1â6; m

Article pubs.acs.org/JPCC

Silver−Water Clusters: A Computation of Agn(H2O)m for n = 1−6; m = 1−8 Roger C. Baetzold* 4026 West 32nd Street, Erie, Pennsylvania 16506, United States S Supporting Information *

ABSTRACT: Calculations of the equilibrium structure and properties of silver−water neutral, cation, and anion clusters Agn(H2O)m, n = 1−6; m = 1−8 are reported. Density functional theory using the PBE1PBE functional is applied to determine stationary points on the energy surface. Several basis sets were compared in this study of cluster thermodynamic properties in the gas and aqueous phases. Clusters of each charge state show Ag−O coordination and a significant number of H bonded water molecules forming a second sphere. This is apparent for neutral clusters that have Ag−O and Ag−H coordination and a chain of H bonded water molecules. Cation clusters have Ag−O coordination in the first sphere with the next water ligands attached by H bonds. The anion structures involve Ag−H coordination, and at sizes of four silver atoms and above the Ag−O coordination mode is also observed. The hydration free energies at room temperature and energy were computed and are consistent with aggregation to larger particles in gas and aqueous phases. The free energy of solvation of charged silver clusters decreases with size in contrast to several neutral clusters. The calculated value for Ag+ solvation free energy and bond strengths compared well with experiment. Possible reactions in aqueous phase involving nucleation, silver ion adsorption, or electron acceptance from reducing agents were evaluated, and trends were found to be consistent with experiment. A reaction pathway under mild reducing conditions for nucleation and growth of small silver clusters in the aqueous phase involving catalysis by neutral particles is proposed based on calculated thermodynamic properties.

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INTRODUCTION Silver clusters can be found in the gas or liquid phases or supported on solid surfaces in contact with aqueous solution where they act as active components in a variety of diverse processes. One area of current interest involves the roles of neutral and charged silver nanoparticles in mechanisms of bactericides, degradation of organic pollutants, and other environmental issues.1−4 In nucleation studies, the role of these silver particles in aqueous media and their redox properties have been of much interest.5−11 The particles are very similar to silver particles that have been long studied in chemical photography.12 One important process is physical development wherein silver ions in the aqueous phase containing suitable reducing agents and catalyst can be converted to silver and deposited under suitable conditions. One catalyst for this reaction is a silver cluster of four or more atoms.13−15 This phenomenon of size-dependent catalysis has long been known and seems to be related to the many recent observations of size-dependent metal cluster catalysis in various reactions.16 A reaction similar to physical development has been reported in aqueous solutions of silver ions in the presence of hydroquinone reducing agent.17,18 In the presence of a seed particles, chemically produced by a strong reducing agent, the deposition of silver on the seed can be observed, although no reaction occurs in the absence of seed under the conditions of the experiment. This phenomenon is explained in terms of the difficulty of reducing silver ions to aqueous silver atom clusters in the absence of the seed particles. © 2017 American Chemical Society

Several reactions are common to the processes described above in aqueous solution. These include the release of silver ions from nanoparticles in contact with aqueous solution, the oxidation of silver particles through the action of dissolved oxygen, aggregation of silver species, and their redox behavior. It seems that knowledge of silver clusters hydrated with water ligands could be important in better understanding these processes. Silver nanoparticles in aqueous solution have been studied by pulse radiolysis.19−22 Particles identified include Ag2+, Ag4+2, or Ag9+ which were formed in aqueous solution with an excess of silver ions, but when studies were conducted with no excess silver ions, the neutral clusters Ag2, Ag4, and Ag8 formed. Lifetimes of the order of hours were reported for such neutral clusters. The ionization potential and redox potential of such clusters produced by pulse radiolysis increased with size and were considered important in determining a critical size for reduction of silver ions in a photographic context.23−25 Gas-phase studies using photoelectron imaging of neutral and anion Ag with one or two water ligands have been reported and the corresponding structures computed with density functional theory (DFT).26 One water ligand interacts through hydrogen with Ag anion or through oxygen with neutral Ag. The calculated incremental binding enthalpies were 9.4 and 9.9 Received: February 20, 2017 Revised: April 6, 2017 Published: May 3, 2017 11811

DOI: 10.1021/acs.jpcc.7b01648 J. Phys. Chem. C 2017, 121, 11811−11823

Article

The Journal of Physical Chemistry C

were employed for O and H atoms. The jun-cc-pvTZ basis set and related basis sets were developed and tested44 by removing diffuse functions from H and retaining only s,p,d diffuse functions on atoms such as O. A double-ζ basis set on O and H atoms was also examined with the SDD effective core potential and basis. The 6-31+G(d,p) basis used previously for calculations of 3d transition-metal complexes with water45 was chosen. Comparison of basis set results are discussed in the Supporting Information as well as a comparison to M06L, TPSS, PW91, and B3LYP functionals for the smaller silver− water clusters reported earlier. A full geometry optimization for each cluster and basis set was applied for every possible structure followed by a harmonic frequency analysis to ensure than no imaginary frequencies were present and thereby guaranteeing an energy minimum. A range of different starting configurations was used with the smaller basis sets in order to select the most favorable stable structures, and the calculations with aug-cc-pvTZ basis were limited to the most favored structures. It was found that overall shapes of optimized structures did not change with the various basis sets with only small differences in the coordinates. In particular, the double-ζ basis gave hydration energies within 1−2 kcal/mol of those calculated with the cc-pvTZ basis, and the overall trends in hydration energy were similar. In some cases, convergence with the larger basis sets was not achieved. The Gibbs free energy was calculated using the rigid rotor, ideal gas, and harmonic oscillator approximations with no scaling. The basis set superposition errors (BSSE) between silver cluster and water molecules were corrected using the counterpoise method.46 The polarized continuum model (SMD) method47 contained in the code was used to simulate the presence of aqueous environments. The energy at 0 K was calculated as the sum of electronic and zero point vibrational energy and is useful for relative comparisons apart from thermal and entropy effects. The free energy at 298.15 K and 1 atm pressure was calculated using the vibrational, rotational, and translational partition functions within the ideal gas approximation in the Gaussian 09 program. The structures with the most negative free energy were most stable, and the energy of hydration at 0 K (ΔE0) and free energy (ΔG0) of hydration were calculated by the difference of the comparable quantities for the water molecules and the bare cluster. As is well-known, the calculation of vibrational frequencies within the harmonic model is an approximation. The lowfrequency vibrations are known to deviate most from the anharmonic nature in these vibrations. To partially correct for this problem, we follow previous calculations48−50 which replaced contributions from frequencies less than 100 cm−1 by 100 cm−1 in the calculation of the vibrational partition functions. Different isomers for each cluster were examined and are discussed in the text and the Supporting Information. Data for the most stable isomers is reported, and these structures are employed in the SMD model with the cluster−continuum method to calculate a free energy of solvation for silver clusters. The formula51,52 for the Gibbs free energy of solvation (ΔGsolv*) that was used was

kcal/mol for one and two water molecules interacting with Ag anion. The corresponding values for Ag atom are 0.9 and 5.3 kcal/mol. A recent review has noted gas-phase studies of Ag(H2O)n+ that determine the bond strengths for successive ligand additions.27 Calculations of gas-phase silver clusters have a long history, and only more recent work that is most relevant to this study is noted. A detailed study of small clusters using DFT and coupled cluster methods (CCSD) compared several density functionals and gave good support to the PBE1PBE functional for clusters up to four atoms.28,29 Structures and properties of neutral clusters up to 100 atoms were computed using different methods and show a slow convergence to bulk behavior.30 More recently, a study of silver clusters up to seven atoms with the three charge states has examined geometry and many physical properties of the clusters for a range of functionals comparing results to experimental and CCSD(T) calculations. A ranking of relative accuracy of functionals was made on this basis.31 Many studies of silver cations with water molecules have been carried out.32−38 A dependence of preferred geometry on method of calculation has been observed in some cases. Evidence for stable silver−oxygen collinear and 3-fold coordination has been reported. Four ligand isomers possess stable structures with tetrahedral or collinear coordination. Xray absorption studies of hydrated silver ions gave evidence for five and six water ligands in the first coordination sphere with a significant number of collinear bond angles.37 An implicit solvation model calculation for Ag(H2O)6+ found that collinear coordination gave good agreement with experimental free energies of solvation that are in the range of −102.8 to −107.0 kcal/mol.38 Calculations39 for silver anions with water gave evidence for ligand coordination through H. Previously small clusters of neutral, cation, and anion silver were studied with water ligands in the first coordination sphere.40 A range of low-symmetry geometries was examined to find the most stable structures. The neutral clusters exhibited mixed oxygen and hydrogen coordination to the silver atoms. The cations were characterized by silver oxygen coordination, while the anions showed predominant hydrogen coordination to silver. Many of the neutral clusters were characterized by a strong intermolecular oxygen−hydrogen interaction, henceforth referred to as an H bond. Details of these small clusters may be examined in the figures of that report. In the present work, larger silver−water clusters containing second sphere water ligands are considered. The PBE1PBE functional used in earlier work was principally employed to compute properties in the gas phase within the scope of the rigid rotor/harmonic oscillator/ideal gas approximation, and the aqueous phase was simulated through use of an improved solvation method in the cluster−continuum method. Various approximations including the quality of the basis set, DFT functional, and aspects of the harmonic model were examined to determine thermodynamic properties and apply these results to problems involving silver particles in the aqueous environment.

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METHOD The DFT method was employed within the Gaussian 09 code41 using the PBE1PBE and several other functionals. The fully augmented aug-cc-pvTZ basis functions42 were used for O and H atoms, and the SDD43 basis sets and effective core potential were used for Ag. In addition, to make calculations possible for the largest clusters, the cc-pvTZ and jun-cc-pvTZ basis sets

ΔGsolv * = Esoln + Gnes − Egas

(1)

where Esoln and Egas are the respective electronic energies of the solute in the presence and absence of the solvent field and Gnes is the sum of nonelectrostatic contributions to the Gibbs free energy. 11812


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the equilibrium structures for one silver atom coordinated to 3−7 water ligands. A single ring structure is very apparent for the smaller clusters up to five ligands in Figure 1a−c. The sixth ligand starts a second ring by forming a H bond with the second H of the primary ligand, and in Figure 1d this effect is apparent for Ag(H2O)7, which has two chains emanating from the primary water ligand that terminate in a ligand that interacts with the silver atom through H. Additional water ligands are H bonded to the chain ligands in larger clusters such as Ag(H2O)8 and Ag(H2O)10. The most stable equilibrium structures for neutral diatomic silver clusters coordinated to three, four, six, or eight water ligands are shown in Figure 2. The diatomic cluster with three

The solvation energies of the silver clusters are calculated in the cluster−continuum method in the cluster cycle which considers clusters of water molecules rather than just monomers. This approach uses well-known53−58 thermodynamic cycles to express the solvation energy and corrects for the change of standard state of 1 mol per 24.46 L at 1 atm in the gas phase to 1 M in the liquid with recognition that water ligands are also the solvent. The formula ΔGsolv*(S) = ΔG 0(WnS) + ΔGsolv*(WnS) − ΔGsolv*(Wn) − ΔGss − RT ln([H 2O]/n)

(2)

where Wn is a cluster of n water molecules, ΔGsolv*(S) the free energy of solvation of solute S, and ΔG0(WnS) the gas-phase free energy of hydration of a cluster of solute S with n water molecules; ΔGsolv*(WnS) and ΔGsolv*(Wn) are the free energy of solvation of WnS and a cluster of n water molecules Wn, respectively; the last two terms are standard state corrections where ΔGss has been calculated as 1.89 kcal/mol at room temperature in the previous studies, and the last term adjusts the water cluster concentration from 1 M to 55.34/n M. The ideal gas constant R and temperature T are as usual.

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RESULTS The optimized structures for the most stable silver−water clusters in the gas phase are first determined. The hydration free energy at 298.15 K (ΔG0) and energy at 0 K (ΔE0) were calculated from the difference in corresponding energies of the silver−water cluster and constituent water molecules and silver cluster. The coordinates of these optimized structures and competing isomers are given in the Supporting Information. The procedure was first to screen a range of possible structures with a lesser quality basis set on O and H atoms such as 6311G* or cc-pvTZ and then examine the most promising structures with increasingly better basis sets. The gas-phase structures of neutral silver−water clusters show one primary water ligand coordinating through O to the silver atom and succeeding ligands attached by H bonds in the form of a chain that terminates with one water ligand coordinating to the silver atom through H. Figure 1 shows

Figure 2. Calculated equilibrium structure for neutral diatomic silver cluster coordinated to three (a), four (b), six (c), and eight (d) water ligands.

water ligands in Figure 2a has two ligands bound through O to the silver and the third ligand is H bonded to one of these. This ligand is oriented toward the silver so that one of its H atoms can interact with the silver. The neutral diatomic silver cluster with four ligands in Figure 2b continues this pattern such that two ligands interact through H with silver. The cluster with six ligands in Figure 2c has a three-ligand chain structure with H bonds and silver H interactions. The five-ligand cluster is found by just removing one of the water ligands. The eight-ligand cluster is shown in Figure 2d. A more complicated behavior is found with chains of water molecules building from the smaller models. Triatomic neutral silver clusters containing four, six, and eight water ligands are shown in Figure 3. The four-ligand cluster possesses two Ag−O interactions and two Ag−H interactions, in a double chain structure involving H bonding in Figure 3a. In the six-ligand structure, the two chains become more enlarged, as shown in Figure 3b, and with eight ligands the chains become enlarged further (Figure 3c). The tetratomic neutral silver cluster with six water ligands in Figure 3d shows a continuation of this pattern. The larger neutral silver−water clusters are shown in Figure 4. The Ag4(H2O)8 cluster in Figure 4a has three silver−oxygen interactions which provide attachment points for further water ligands. The five-atom Ag5(H2O)5 cluster in Figure 4b and Ag6(H2O)6 cluster in Figure 4c also have three principal silver− oxygen interactions.

Figure 1. Equilibrium structures for one neutral silver atom coordinated to three (a), four (b), five (c), and seven (d) water ligands. 11813


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Table 1. Calculated Interatomic Distances (Å) for Most Stable Silver−Water Clusters Using PBE1PBE Functional

Figure 3. Equilibrium structures for neutral triatomic silver cluster coordinated to four (a), six (b), or eight (c) water ligands and tetratomic neutral silver cluster with six water ligands (d).

cluster

Ag−O

Ag−H

Ag(H2O)3 Ag(H2O)4 Ag(H2O)5 Ag(H2O)6 Ag(H2O)7 Ag2(H2O)3 Ag2(H2O)6 Ag3(H2O)4 Ag3(H2O)6 Ag4(H2O)6 Ag(H2O)6+ Ag2(H2O)3+ Ag2(H2O)8+ Ag3(H2O)6+ Ag4(H2O)6+ Ag(H2O)3− Ag(H2O)6− Ag2(H2O)4− Ag3(H2O)6− Ag4(H2O)4− Ag5(H2O)5−

2.457 2.408 2.386 2.351 2.301 2.409 2.336 2.332 2.286 2.280 2.117 2.409 2.370, 2.463 2.220 2.291, 2.471

2.606, 2.862 2.524, 2.864 2.495, 2.862 2.442, 2.740 2.445,2.753 2.627 2.553 2.647, 2.691 2.693, 2.706 2.670, 2.680

2.549 2.557

2.395 2.802 2.745 2.723 2.724, 2.726 2.676, 2.557

O−H 1.735, 1.733, 1.697, 1.710, 1.743, 1.844 1.698, 1.748, 1.684, 1.839, 1.716, 1.762 1.759 1.635, 1.720 2.122 1.989 1.951 1.814, 1.868, 1.841,

1.786 1.762 1.717 1.799 1.756 1.748 1.758 1.727 1.840 1.717

1.793

1.833 1.883 1.887

collinear Ag−O coordination begins with the first two water ligands, and successive ligands add to build up to the structure in Figure 4d having four H bonded ligands in the second sphere. The diatomic silver cation has the structures shown for three, six, and eight ligands shown in panels a, b, and c, of Figure 5, respectively. The structural evolution is much like that for the monomer leading to four H bonded ligands at

Figure 4. Calculated equilibrium structures for (a) Ag4(H2O)8, (b) Ag5(H2O)5, (c) Ag6(H2O)6, and (d) Ag(H2O)6+.

The bond lengths calculated for typical silver−water clusters are given in Table 1. There is one silver−oxygen distance in each neutral silver atom cluster that decreases in length slightly as the size increases. The corresponding silver hydrogen distances also generally decrease in length as the number of ligands increases. Several intermolecular O interactions with H are given, which for the single silver atom number as one less than the number of ligands up to six and show how H bonds are connecting the ligands. The silver oxygen bond length decreases as the number of silver atoms increases. Cation silver clusters coordinated by water ligands display a number of different structures. The single silver ion coordinated by six water ligands is shown in Figure 4d. The

Figure 5. Equilibrium structures calculated for (a) Ag2(H2O)3+, (b) Ag2(H2O)6+, (c) Ag2(H2O)8+, and (d) Ag3(H2O)6+. 11814


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The Journal of Physical Chemistry C Ag2(H2O)6+. With eight ligands, the structure changes to bonding two water ligands through Ag−O coordination at each silver with four H bonded water ligands. There are two different Ag−O bond lengths at each silver with lengths of 2.370 and 2.463 Å for Ag2(H2O)8+ shown in Figure 5c. The other four ligands are H bonded to the first four ligands, and there are not significant Ag−H interactions from any ligands. The Ag3(H2O)6+ cluster shown in Figure 5d has three ligands attached to silver through Ag−O bonds and three H bonded ligands. Attempts to find more symmetrical geometries relaxed to this and less stable geometries. The larger cation structures are shown in Figure 6. For Ag4(H2O)6+ there are four Ag−O bonds with the shortest bond

Figure 7. Calculated equilibrium structures for (a) Ag(H2O)3−, (b) Ag(H2O)4−, (c) Ag(H2O)5, and (d) Ag(H2O)6−.

Figure 6. Calculated equilibrium structures calculated for (a) Ag4(H2O)6+, (b) Ag3(H2O)8+, (c) Ag4(H2O)8+, and (d) Ag5(H2O)5+.

length to the two silver atoms closest to one another and shown in Figure 6a. The fifth and sixth ligands are H bonded to the first ligands and not in contact with silver. For Ag3(H2O)8+ in Figure 6b, there are three primary Ag−O bonds and successive ligands H bonded to these. Similarly, this effect is noted for Ag4(H2O)8+ in Figure 6c. The Ag5(H2O)5+ cluster shown in Figure 6d has four primary Ag−O interactions. The center silver atom is fully coordinated by other silver atoms. The Ag6(H2O)6+ cluster has Ag−O coordination through each ligand and is shown in the graphic included in the Abstract. The anion silver clusters are characterized by coordination of water ligands through H with the silver. Clusters of anion silver atoms with 3−6 water ligands are shown in Figure 7. There are strong H bonding interactions between the water ligands, and the corresponding typical Ag−H distances are given in Table 1. The structures for larger anion clusters become more complex. The Ag2(H2O)6−cluster has two groups of three ligands that interact with each silver through Ag−H coordination, as shown in Figure 8a. The Ag4(H2O)4− cluster in Figure 8b is the first anion structure observed to show Ag−O coordination in addition to Ag−H coordination. Earlier calculations40 found a stable cluster having only Ag−H coordination, but the cluster in Figure 8b is more stable. The Ag3(H2O)6− cluster in Figure 8c has only Ag−H coordination. The Ag5(H2O)5− cluster in Figure 8d has one ligand coordinated by Ag−O. The typical intermolecular distances are given in Table 1.

Figure 8. Equilibrium structures for (a) Ag2(H2O)6−, (b) Ag4(H2O)4−, (c) Ag3(H2O)6−, and (d) Ag5(H2O)5−.

The standard free energy of hydration (ΔG0) at 298.15 K and energy of hydration (ΔE0) at 0 K for forming gaseous silver−water clusters from the corresponding silver cluster and monomer water molecules were calculated. The resulting values are shown in Table 2 for the favored structures discussed in the figures for each charge state and correspond to the initial solvation by water. Generally the trends in these energies with cluster size are monotonic with few exceptions. Successive additions of water ligands to the most stable silver−water clusters of the same charge give a more positive free energy value, while the energy term becomes more negative. Differences in the energy and free energy values in Table 2 are due to temperature-dependent terms and the entropy 11815


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Table 2. Hydration Free Energies (ΔG0) at 298.15 K and 1 atm and Energy (ΔE0) at 0 K for Agn(H2O)m (kcal/mol) Formed from Corresponding Charge States of Agn with mH2O and Calculated Using PBE1PBE Functional with SDD+aug-cc-pvTZ Basis Sets with BSSE Correctiona neutral

a

cluster

ΔG

Ag(H2O) Ag(H2O)2 Ag(H2O)3 Ag(H2O)4 Ag(H2O)5 Ag(H2O)6 Ag(H2O)8 Ag2(H2O) Ag2(H2O)2 Ag2(H2O)3 Ag2(H2O)4 Ag2(H2O)5 Ag2(H2O)6 Ag2(H2O)8 Ag3(H2O)3 Ag3(H2O)4 Ag3(H2O)6 Ag3(H2O)8 Ag4(H2O)4 Ag4(H2O)6 Ag4(H2O)8 Ag5(H2O)5 Ag6(H2O)6

4.1 8.0 10.3 13.1 16.1 20.6 21.1jj 2.2 4.2 9.0 12.3 16.9 12.3 14.6jj 5.5 7.3 10.7 4.9cc 8.0 13.2 17.8jj 20.6jj 22.0jj

0

positive ΔE0

ΔG

−1.0 −5.5 −12.7 −19.5 −26.0 −31.7 −47.8jj −5.7 −12.4 −16.6 −23.3 −27.9 −43.3 −57.7jj −23.0 −30.5 −47.6 −69.7cc −32.1 −43.8 −56.6jj −25.4jj −33.4jj

−23.3 −42.6 −48.3 −52.0 −54.1 −53.6 −50.4jj −13.9 −24.2 −26.4 −27.8 −28.0 −28.2 −31.3cc −25.0 −24.8 −18.8 −27.5cc −17.8 −8.9 −21.0cc −16.8jj −8.5jj

0

negative ΔE0

ΔG

−29.3 −56.9 −70.9 −84.4 −95.1 −103.8 −119.0jj −21.8 −40.5 −51.9 −63.0 −72.1 −81.4 −100.7cc −52.1 −61.7 −76.2 −102.0cc −53.4 −66.6 −94.4cc −61.4jj −61.2jj

−2.3 −5.1 −3.9 −5.4 −4.8 0.4 1.1jj −1.2 1.0 2.5 5.1 8.1 11.0 4.3cc 6.3 6.1 9.9 1.1cc 13.0 18.4cc

−9.1 −17.3 −26.3 −38.5 −47.4 −51.5 −66.7jj −7.7 −15.2 −23.9 −30.1 −36.9 −44.5 −67.7cc −19.4 −30.5 −46.5 −72.3cc −25.7 −33.8cc

10.3jj

−36.7jj

0

ΔE0

Entries calculated with jun-cc-pvTZ are denoted by jj, those calculated with cc-pvTZ are denoted by cc.

of H interactions with the silver. The cluster shown in Figure 2b has two chains, each containing three ligands which curl toward the silver to provide Ag−H interactions. If this interaction is removed and the ligands that are H bonded and not having Ag−O bonds point away from the silver, the resulting isomer is less stable in energy and free energy by 10.1 and 9.6 kcal/mol, respectively. The Ag3(H2O)6 cluster, as in Figure 3b, has a more symmetrical isomer similar to the Ag3(H2O)4 cluster, which is 6.8 kcal/mol less stable. The Ag4(H2O)6 cluster has two other isomers with different water orientations that are less stable by 2.5 kcal/mol. Similar effects are found for the anion clusters dependent on chain ligand orientations. The most abundant isomers were observed for the positive clusters. Several examples are given in Table 3 where the relative energy ΔE0 is given, and we employ a notation x-y-z to denote the number of ligands in first and successive spheres. This notation is not completely adequate because of different orientations of H bonded ligands which will be denoted by letters. The relative energy shows a preferred collinear coordination of O to silver cation as exemplified in the figures. In the case of Ag(H2O)4+, the preferred second sphere ligands are trans to one another compared to the isomer 2−2D in which the ligands are cis and 0.2 kcal/mol less stable. When both second sphere ligands are attached to the same first ligand, the energy for 2−2F is 2.2 kcal/mol less stable. For Ag(H2O)5+ the 2−3 structure is most stable and the 3−2 structure has many different orientations of the second sphere ligands relative to one another, as shown for many entries. The Ag(H2O)6+ isomer is most favored at the 2−4 geometry, but one entry shows that the orientation of second sphere water ligands can lead to an energy penalty. For Ag2(H2O)4+ the most

change on hydration multiplied by temperature. The entropy changes on hydration can play an important role in determining preferred structures. The energies in Table 2 are for the aug-cc-pvTZ basis set on O and H atoms for most clusters. Data for the jun-cc-pvTZ or cc-pvTZ basis sets were entered in the table for some larger clusters in cases where optimization with the larger basis sets was not achieved. For reference, detailed comparisons of values for the different basis sets using silver−water clusters containing up to six ligands were made. The cc-pvTZ values differed on average by −5.0 kcal/mol for ΔG0 and −3.9 kcal/mol for ΔE0 versus values with aug-cc-pvTZ basis sets. For jun-cc-pvTZ, the average ΔG0 values were more negative by −1.5 kcal/mol, while average ΔE0 values differed by less than 0.1 kcal/mol. The jun-cc-pvTZ basis gives values very close to those obtained with the aug-cc-pvTZ basis. Several different starting configurations were used with the cc-pvTZ and jun-cc-pvTZ basis sets to find stable alternate structures with coordinates contained in the Supporting Information. Some examples for the less stable cases are interesting. The simple cluster Ag(H2O) has isomers with H or O bonded to Ag, as noted earlier.40 The O bonded isomer is most stable using the energy at 0 K or free energy at 298.15 K, as found using the low-frequency correction. Chains of H bonded water molecules are very important for neutral and anion clusters where the orientation of molecules along the chain can lead to different isomers. Consider Ag(H2O)3, as in Figure 1a, where if the chain of ligands avoids the Ag−H interaction the energy is 5.3 kcal/mol less stable. Another example is Ag(H2O)4 where different orientations of the water molecules along the chain lead to isomers 0.5 and 0.9 kcal/mol less stable. The Ag2(H2O)6 cluster shows the important effect 11816


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a small charge to the silver atoms. Representative values of various clusters are given in Table 5. The tables indicate that

Table 3. Comparison of Relative Energy (ΔE0) (kcal/mol) for Isomers of Cation Silver−Water Clusters cluster

orientation

relative energy

Ag(H2O)3+

2−1 3−0 2−2 4−0 2−2F 2−2D 2−3 3−2A 3−2B 2−2−1 3−2F 2−4 4−2 2−4C 3−3 2−2 4−0 3−1 2−2C 2−4 2−4B 3−3 4−2 5−1

0.0 1.3 0.0 4.9 2.2 0.2 0.0 3.4 2.5 1.0 2.4 0.0 4.5 2.5 3.7 0.0 3.6 4.8 4.0 0.0 3.6 0.0 4.2 3.0

Ag(H2O)4+

Ag(H2O)5+

Ag(H2O)6+

Ag2(H2O)4+

Ag2(H2O)6+ Ag3(H2O)6+

Table 5. Average Charges on Ag and O Atoms in Various Silver−Water Clusters Calculated by NBO Method59 cluster Ag(H2O)6 Ag(H2O)8 Ag2(H2O)6 Ag2(H2O)8 Ag3(H2O)6 Ag4(H2O)6 Ag5(H2O)5

Table 4. Calculated Bond Energy at 0 K for a Water Ligand Bound to Ag(H2O)n−1 (kcal/mol) for Different Basis Sets versus Experiment27 n

aug-cc-pvTZ

jun-cc-pvTZ

cc-pvTZ

exptl

28.6 25.4 11.8 11.3 8.8 6.9

27.8 25.5 11.4 11.4 8.7 8.6

28.3 25.7 13.6 12.2 10.1 9.8

31.3−32.7 26.3−30.1 14.8 11.5−13.9 13.6 13.4

−0.98 −0.99 −0.96 −0.98 −0.97 −0.94 −0.95

cation 0.79, 0.72, 0.43, 0.38, 0.25, 0.18, 0.16,

−0.95 −0.97 −0.98 −0.96 −0.96 −0.95 −0.95

anion −0.91, −0.89, −0.49, −0.53, −0.34, −0.27, −0.21,

−0.98 −0.98 −0.98 −0.95 −0.97 −0.94 −0.97

ionization results in most of the electron being withdrawn from silver, and electron acceptance places a large part of the electron on silver. The use of average charges on the silver atoms can be misleading for some clusters. The Ag3(H2O)6 cluster has silver atom charges of 0.08, 0.13, and −0.30 on the three silver atoms in the cluster. Examination of the structure in Figure 3b shows that the positive charge is associated with silver atoms bonded to water ligands through O. The third silver atom has the negative charge and interacts primarily with the H of water ligands. Similar effects are found in other neutral clusters such as Ag4(H2O)6 and Ag5(H2O)5 where the silver atom bonded to one oxygen has a positive charge unlike the other silver atoms in the cluster. The adiabatic change in Gibbs free energy upon ionization is calculated as the difference in free energy of the most stable neutral and cation clusters of the same size at room temperature. The trend is to smaller free energies required for ionization with increasing water ligands shown in Table 6 and is due to the polarization induced by the ligands. These values are rather insensitive to basis set, so some of the higher members were calculated with the lesser basis sets. The changes caused by the presence of water ligands are largest for the single atom and decrease as the number of silver atoms increases. The free energy value for even-sized clusters having the same ratio of H to Ag is larger than that of corresponding odd sized clusters with the exception of Ag(H2O). The effect of water solvent on the ionization free energy is determined by utilizing a self-consistent reaction field calculation with the SMD method.47 The difference in cation and neutral solvation energy provides corrections from gas to liquid phase which are added to the gas-phase value to get the corresponding aqueous value. As expected, the liquid-phase polarization for the charged clusters is greater than that for neutral clusters, leading to a greater decrease in value in aqueous phase. This effect can amount to 2−3 eV, as shown for the data in Table 6. A significant oscillation between even- and odd-sized silver clusters persists in the ionization free energy in the solvent. The odd−even oscillation in gaseous ionization free energy is manifest within a series of clusters with fixed numbers of water ligands and is well-known in bare silver clusters. This effect is illustrated using data calculated with the jun-cc-pvTZ basis on water for several clusters. For Agn(H2O) the values are 6.55, 6.87, 5.19, 5.96, 5.37, and 6.20 eV for n = 1−6. Corresponding values for Agn(H2O)2 are 5.57, 6.34, 4.83, 5.64, 5.03, and 5.70 eV, while for Agn(H2O)4 the values are 4.95, 5.85, 4.28, 5.35, 4.29, and 5.16 eV for n = 1−6. This oscillation in ionization free energy persists with hydration in each series. The hydration energies for neutral and charged clusters also show this effect.

stable 2−2 orientation has ligands H bonded to the first sphere ligands and orientated away from the silver. When the second sphere ligands orient more toward the silver, the structure becomes less stable. The same effect for the second sphere ligands is found for Ag2(H2O)6+. The data for Ag3(H2O)6+ show that structures with three Ag−O bonds are optimal. There are limited experimental data to compare to the hydration energy values in Table 2. Experimental gas-phase bond energies27 at 0 K for successive addition of water to Ag(H2O)n−1+ for n = 1,6 are available. The calculated data without the zero point energy was employed to prepare the data in Table 4. There are two sets of experimental data that

1 2 3 4 5 6

neutral −0.01, −0.02, −0.06, −0.02, −0.03, −0.06, −0.03,

cover a small range of values, but the agreement with experiment is reasonable for the three basis sets, and generally the calculated values are low. The agreement with calculation supports the assignments of calculated structures for this cation. A natural atomic charges population analysis59 was carried out to understand the charge distribution in the silver−water clusters. Analysis indicates that in all neutral clusters a small electron charge is transferred to silver from the water ligands. This is consistent with the picture that lone pair ligands transfer 11817


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The neutral clusters have the hydration energies −0.9, −5.6, −7.8, −7.9, −4.3, −4.5, and −4.1 kcal/mol in the series Agn(H2O) n = 1−7. The oscillation is not readily apparent but can be uncovered according to a procedure60 which indicates relative stability of a cluster compared to the average of its one atom larger and smaller counterparts. This measure of stability (Mn) of an n atom cluster is obtained from eq 3.

Table 6. Adiabatic Free Energy Change for Ionization (ΔG) Calculated with PBE1PBE for Gas Phase and Aqueous Phase Using SMD Method (eV) and Aqueous Reduction Potential (E0) for Silver−Water Clusters (V) at Room Temperature gas phase

aqueous phase

cluster

ΔG

ΔG

E0

Ag(H2O) Ag(H2O)2 Ag(H2O)3 Ag(H2O)4 Ag(H2O)5 Ag(H2O)6 Ag2(H2O) Ag2(H2O)2 Ag2(H2O)3 Ag2(H2O)4 Ag2(H2O)5 Ag2(H2O)6 Ag3(H2O) Ag3(H2O)3 Ag3(H2O)4 Ag3(H2O)6 Ag4(H2O) Ag4(H2O)4 Ag4(H2O)6 Ag5(H2O) Ag5(H2O)5 Ag6(H2O) Ag6(H2O)6

6.55 5.50 5.20 4.91 4.70 4.52 6.87 6.35 6.03 5.83 5.62 5.81 5.18 4.36 4.26 4.41 5.95 5.26 5.36 5.37 4.21 6.20 5.26

3.17 2.82 2.80 2.79 2.72 2.70 4.14 4.01 4.03 3.98 3.92 4.11 2.39 2.40 2.40 2.53 3.47 3.41 3.59 2.97 2.57 3.82 3.69

−1.11 −1.46 −1.48 −1.49 −1.56 −1.58 −0.14 −0.27 −0.25 −0.30 −0.36 −0.17 −1.89 −1.88 −1.88 −1.75 −0.81 −0.87 −0.69 −1.31 −1.71 −0.46 −0.59

Mn = ΔE0(n + 1) + ΔE0(n − 1) − 2ΔE0(n)

(3)

Here ΔE0(n) is the hydration energy at 0 K of a cluster with n silver atoms. The resulting stability values are Mn = 2.5, 2.1, 3.7, −3.7, and 0.6 kcal/mol for n = 2−6 and show an oscillation that is consistent with greater adsorption energy at even sized neutral clusters. The corresponding values oscillate for the cation clusters according to Mn = −5.0, 0.0, −1.1, 0.7, and −3.9 kcal/mol for n = 2−6. The corresponding values for the anion clusters are Mn = −0.8, 0.2, −1.4, 1.0, and −0.4 for n = 2−6. The hydration energy is greatest at odd-sized charged clusters. These trends become washed out in some series of clusters with more ligands attached to the silver cluster, as discussed in the Supporting Information. The odd−even effect has long been known and is attributed to the greater stability of closed versus open shells. These silver−water clusters are only partially solvated molecules that lack water molecules in more distant solvation spheres. These clusters offer an opportunity to calculate the silver cluster solvation free energy change corresponding to changing solute from gas phase to aqueous in standard states through use of the implicit cluster−continuum method.50,53−58 The total solvation free energy for bare silver neutral and charged ions is calculated with eq 2. The use of calculated gas-

Table 7. Free Energy of Solvation for Silver−Water Clusters of Various Charge at 298.15 K Calculated Using Cluster− Continuum Method with SMD and the PBE1PBE Functional with SDD and aug-cc-pvTZ and jun-cc-pvTZ Basis Sets (kcal/ mol) aug-cc-pvTZ

jun-cc-pvTZ

species

cluster

neutral

positive

negative

neutral

positive

negative

Ag

Ag(H2O) Ag(H2O)2 Ag(H2O)3 Ag(H2O)4 Ag(H2O)5 Ag(H2O)6 Ag(H2O)8 Ag2(H2O) Ag2(H2O)2 Ag2(H2O)3 Ag2(H2O)4 Ag2(H2O)5 Ag2(H2O)6 Ag3(H2O) Ag3(H2O)3 Ag3(H2O)4 Ag3(H2O)6 Ag4(H2O) Ag4(H2O)4 Ag4(H2O)6 Ag5(H2O) Ag5(H2O)5 Ag6(H2O) Ag6(H2O)6

1.0 7.1 6.9 10.0 12.5 16.3

−104.3 −105.4 −107.1 −104.4 −103.3 −99.9

−47.8 −43.2 −40.7 −41.6 −39.3 −32.7

−5.2 0.7 0.2 4.7 7.9 5.3 −5.2 −1.8 1.9 5.1 −7.4 −2.2 2.8 −2.2

−84.1 −81.2 −81.4 −77.8 −76.1 −74.3 −77.4 −77.6 −73.9 −67.9 −73.6 −68.7 −59.8 −68.4

−36.1 −29.6 −28.6 −27.2 −23.3 −19.3 −34.2 −30.3 −27.1 −23.7 −29.7 −24.0

−3.8

−67.6

−28.2

1.4 6.1 5.6 8.2 10.4 13.5 13.2 −6.2 0.3 −0.9 3.0 5.8 2.8 −5.6 −2.3 0.3 3.5 −7.7 −2.8 1.3 −2.6 10.2 −4.1 7.0

−103.5 −106.0 −107.6 −105.6 −104.8 −103.8 −102.2 −84.4 −82.4 −82.4 −79.3 −77.9 −76.1 −77.5 −78.1 −75.1 −70.1 −73.8 −68.7 −62.1 −68.6 −65.2 −67.8 −57.7

−47.1 −44.1 −44.0 −41.3 −41.3 −35.0 −36.5 −36.4 −31.5 −29.8 −28.4 −25.4 −21.8 −34.7 −31.3 −28.3 −22.7 −29.9 −25.7 −20.9 −31.0 −18.7 −28.5

Ag2

Ag3

Ag4

Ag5 Ag6

−30.7

11818


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Ag(H2O)6+ were relaxed in the SMD calculation, and this led to a 2−3 kcal/mol stabilization. The low frequencies were modified, as described in the text, to attempt to correct for deviations of the harmonic model from the anharmonic nature of these vibrations. The correction reduces the entropy, and this changes the free energy of hydration. The magnitude of this effect is small and averaged over 48 clusters in the aug-cc-pvTZ calculation amounts to a 0.94 kcal/mol reduction per water ligand in −ΔG0. The correction to the energy at 0 K is negligible. More detailed studies with anharmonic methods could examine this effect. No corrections were made for less stable isomers studied that can yield a configuration free energy term for equilibrium mixtures. This procedure is probably weakest for the large clusters where various configurations for H bonded ligands are possible and several configurations might be possible, but the scope of such a study could be very large. These calculations include no relativistic effects beyond the effective core potential. Relativistic effects have been examined for Ag(H2O) as well as several other complexes of lone pair ligands with coinage metal atoms.61 Several basis sets were considered and yielded increases and decreases in the interaction energy due to relativistic effects. With the same basis the Ag(H2O) cluster was calculated to be 0.22 kcal/mol less stable in the relativistic calculation, and the authors concluded that relativistic corrections for Ag and Cu complexes were an order of magnitude less than those for Au complexes. Another relevant point in their benchmarking studies was that the DFT method with the PBE0 functional, which is denoted PBE1PBE in the present paper, reproduces relative stability of a range of metal ligand complexes quite well. In separate calculations the inclusion of spin−orbit coupling decreased the Ag2 interatomic distance by only 0.001 Å and therefore were not included in calculations for larger clusters.31 Because of these results and the already large scope of this work, relativistic calculations were not undertaken. Several modes of water coordination to silver clusters were noted to depend upon charge. Chains of ligand molecules connected by H bonds were noted for neutral and anion clusters. Both Ag−O and Ag−H coordination were found for neutral and anion clusters, while only Ag−O coordination was found for cations. The thermodynamics of silver−water clusters in the gas phase indicate their formation is possible under various conditions. The Ag(H2O) clusters are weakly stable, as shown by the ΔE0 value of −1.0 kcal/mol compared to values for higher analogues in Table 2. The free energy values at room temperature are positive and limits the gas-phase neutral clusters to lower temperatures at equilibrium. Adding more water ligands to these clusters leads to more negative ΔE0 values promoting their stability. Similar behavior is found for diatomic Ag2(H2O) which has a more negative ΔG0 value than monomer, indicating a higher stability. Both cation and anion silver−water clusters have exergonic free energy values for hydration, indicating their favorability for forming. The first ligand is bound more strongly than successive ligands, as shown in the data of Table 2. The properties of gas-phase silver−water clusters were used to calculate silver cluster solvation in the aqueous phase. The solvation free energy of neutral clusters was calculated to be positive for many cases in Table 7, and this value becomes more positive with increasing numbers of water ligands. For this reason, neutral clusters with one water ligand were considered to best represent the neutral cluster in the aqueous

phase free energy of hydration of the clusters, solvation free energies for silver−water cluster, as well as constants to adjust for standard state were employed in this cycle. The SMD method47 in Gaussian 09 was employed, recognizing that the relative values are important as well as the absolute values in Table 7. The silver cluster solvation energy values are dependent upon the size of the silver−water cluster used to calculate for each charge state. The trends in values for monomeric silver solvation energy are a decrease in solvation or less stable aqueous-phase species with number of water ligands for neutral and anion silver−water models, while for positive silver ion the extent of solvation goes through a maximum at Ag(H2O)3+. The positive values observed for neutral cases indicate less stability in the aqueous phase than gas phase. Silver cations are more favorably solvated than the corresponding anions. The trends are to a smaller solvation ability as the silver cluster size increases for positive and negative charge states. The largest calculated value of the Ag+ solvation free energy by this method with Ag(H2O)3+ is −107.1 kcal/mol, which compares with the experimental free energy of −102.8 to −107.0 kcal/mol for silver ions recently quoted.38 There is good consistency between the results for the two basis sets, and generally the jun-cc-pvTZ basis gives 1−2 kcal/mol more favorable solvation energies.

■

DISCUSSION While every effort has been made to perform the best possible calculation within the DFT approach, it is well-known that approximations still exist and errors sometimes cancel. The calculated bond energies of water ligand to silver ion in various degrees of hydration compared to experiment in Table 4 show reasonable agreement and consistent trends, but there are some differences. The density functional itself may be partly responsible. In the Supporting Information the hydration energy values at 0 K were compared for various common functionals for small silver−water clusters used in prior work.40 The averaged values of −ΔE0 follow the trend PW91 > M06L > TPSS > PBE1PBE > B3LYP with differences of 1.4, 2.5, 2.7, and 4.5 kcal/mol from the most favored PW91. This comparison is oversimplified because trends in values also depend upon cluster charge, but the ordering does suggest examining calculations with PW91 for the bond dissociation energies. The values 29.5, 28.0, 13.5, 12.6, 9.9, and 9.4 kcal/mol for n = 1−6 were found for comparison to data in Table 4 using the jun-cc-pvTZ basis and show that improved agreement with experiment can be obtained. Perhaps functionals yielding even better agreement could be found, but such a study is beyond the scope of this work. The calculated Ag+ free energy of solvation at room temperature agrees well with experiment, as indicated before. There is some uncertainty associated with the experimental data; therefore, some caution is observed. Table 7 also does show that there is good agreement between the aug-cc-pvTZ and jun-cc-pvTZ basis set calculations for solvation free energy, and this supports the use of this more simplified basis for larger clusters. There is a dependence of solvation free energies upon the degree of cluster hydration, which reflects some issues in the method at this cluster size range and suggests use of calculated values in a range. In the solvation energy calculations the gas-phase geometry was used in the aqueous phase. This neglects further relaxation and could lead to some underestimation of values. Some small clusters like Ag(H2O)4+ or 11819


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These conclusions for exergonic changes upon aggregation or silver ion addition are consistent with experimental observations of neutral and positive clusters larger than monomer in aqueous solution.5−7,11,19,20 It is clear that reaction of neutral clusters with one another or with silver ion are in competition and the conditions of the experiment can determine the dominant path. This competition was found in the pulse radiolysis experiments19−22 where in the absence of excess silver ions large neutral clusters were formed. An interesting cluster of dipositive tetratomic silver was found in the radiolysis experiment was thought to form by reaction 7.

phase. The charged silver ions have negative free energies of solvation in water. Increasing numbers of water ligands cause the values to be less favorable for solvation, except for the Ag(H2O)n+ series which is most negative at n = 3. Experiments suggest five or six ligands coordinated to the silver ion in solution, and this calculated result seems at variance, but the difference in solvation free energy with four or five ligands are small and within the errors likely in the calculation. The solvation free energies given in Table 7 reflect the solubility of silver clusters on transfer from gas to aqueous phase at standard states. While calculated values depend upon the degree of hydration of the silver−water computational cluster, the trends at constant hydration are interesting. The entries in Table 7 are rather complete for one or four water ligands and show that solubility decreases with size for anion and cation silver clusters because the trend is to more positive solvation free energy value with increasing size. This accords with expectations based upon the classical Gibbs−Thompson equation. The behavior of neutral silver clusters is different because the free energy becomes more negative with increasing size. The solubility is increasing over the range 1−4 atoms and remains favorable at larger sizes. This behavior is different than that expected from classical continuum models of nucleation and is worthy of further study. The energetics of some possible reactions of aqueous-phase silver−water clusters can be calculated by expressing the free energy Gsoln(S) of solute S in the aqueous phase Gsoln(S) = Ggas(S) + ΔGsolv*(S) + ΔGss

2Ag 2+ → Ag4 ++

The calculated aqueous free energies for Ag4(H2O)4+2 and Ag2(H2O)2+ were used to determine the free energy change of −53.0 kcal/mol for reaction 7 driven by solvation and supporting the plausibility of this reaction even though like charges are combining. The structure of this tetratomic cluster was pyramidal with one water ligand attached to each silver atom. The reduction potential of silver clusters containing 1−3 atoms has been estimated and measured for Ag5 in water.19,20 The reported values are −1.8 V for n = 1, −0.1 V for n = 2, −0.9 V for n = 3, and −0.2 V for n = 5 versus the bulk experimental value 0.799 V. Here, the reduction potential is calculated using differences in neutral and cation solution free energies following procedures worked out for various systems.62,63 The one-electron reduction potential (E0) in volt units is found by subtracting the value of the standard hydrogen electrode potential, taken as 4.28 eV, from the free energy values in aqueous solution and is given in Table 6. A dependence on the number of ligands in the cluster is found within the range −1.1 to −1.6 V for n = 1, −0.1 to −0.4 V for n = 2, −1.9 to −1.8 V for n = 3, −0.8 to −0.9 V for n = 4, −1.3 to −1.7 V for n = 5, and −0.4 to −0.5 V for n = 6. The trend in values shows an odd−even oscillation and provides rough agreement with the previous estimates, but they indicate negative potentials throughout this size range, indicating difficult reduction. Experiments12,17,18 show that mild reducing agents do not reduce silver ions in solution for a period of time and that a catalytic center must be present to initiate reduction in the form of a seed particle of silver. The calculated reduction potentials of small silver cations are sufficiently negative such that hydroquinone, having an experimental reduction potential12 of 0.70 V, could form only a small amount of silver atoms. In the presence of a silver center, designated Agn, the unstable silver atom Ag(H2O) might be adsorbed and stabilized by eq 8

(4)

where Ggas(S) is the gas-phase free energy of solute S, ΔGsolv*(S) the calculated solvation energy of solute upon transfer from gas phase 1 mol/24.46 L to liquid at 1 M, and ΔGss a correction for standard state differences established to be 1.89 kcal/mol. Using eq 4, a measure of the ability of aqueous neutral clusters to aggregate can be considered through the reaction nAg(H 2O) → Ag n(H 2O)n

(5)

for which the calculated ΔG values are −34.5, −49.6, −85.5, −105.4, and −144.0 kcal/mol for n = 2−6. The strong negative free energy change indicates a driving force for aggregation. This comparison is made for clusters with equal numbers of silver atoms and water molecules. There are few steric barriers for aggregation of Ag(H2O) or Ag(H2O)2 or even more hydrated units that can readily combine. For example, the Ag(H2O)3 cluster shown in Figure 1a can dimerize to Ag2(H2O)6 in Figure 2a, forming a silver−silver bond with only minor movement of the ligands. The free energy change for Ag(H2O)3 dimerization is −37.2 kcal/mol. Comparable trends are found for aggregation of Ag(H2O)2 and Ag2(H2O)4. An alternative reaction of neutral clusters is with the silver ion. Consider the reaction Ag n(H 2O) + Ag(H 2O)3+ → Ag n + 1(H 2O)4 +

(7)

Ag(H 2O) + Ag n → Ag n + 1(H 2O)

(8)

in order to accomplish one reduction cycle. The adiabatic changes in free energy are calculated to be −27.0, −11.0, −32.0, −24.0, −35.0, −17.0, and −34.0 kcal/mol for n = 1−7 and indicate that a considerable stabilization is possible for the otherwise unstable aqueous silver atom. Under this mechanism, an unstable silver atom produced by reduction becomes stabilized by adsorption to the existing small silver particle. A more detailed examination of the stabilization mechanism can be based upon eq 6 where a silver ion in the form Ag(H2O)3+ first adds to a catalytic center Agn(H2O) in aqueous solution to form a cation Agn+1(H2O)4+. The cation can accept

(6)

where the form of the silver cation chosen has three water ligands. The calculated free energy change values are −7.6, −22.9, −22.3, −25.0, and −24.8 kcal/mol for n = 1−5. The comparable reaction with Ag(H2O)5+ yields values −6.5, −3.2, and −16.1 kcal/mol for n = 1−3; therefore, both approaches promote an equilibrium to the right. Calculations for cation clusters containing dimer or larger silver units also indicate exergonic reactions with the silver atom by reactions like eq 6. 11820


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The Journal of Physical Chemistry C an electron from the active form of hydroquinone (HQ−), which is the anion.12 This reaction can be written Ag n + 1(H 2O)4 + + HQ− → Ag n + 1(H 2O)4 + HQ

oscillation with size and are sufficiently negative that such aqueous clusters are difficult to reduce. The gas-phase structures provide properties for aqueous solvated clusters through use of the cluster−continuum model and were used to determine solvation free energies for silver clusters up to six atoms in aqueous solutions. Good agreement with experiment was found for Ag+. There is a strong driving force for aggregation of neutral silver−water clusters to form larger aggregates that competes with silver ion reaction leading to formation of positively charged clusters in solution and the doubly charged tetramer. These results based upon free energy calculations are consistent with observed reactions of aqueous neutral and positive clusters under various conditions and support the use of these silver−water clusters as reliable models for corresponding particles in the aqueous phase. The neutral silver clusters in aqueous solution are possible catalysts for adsorbing silver ions or atoms and accepting electrons from mild reducing agents such as hydroquinone in solution. The growth to larger clusters through stabilizing action by silver catalyst in the presence of weak reducing agents is supported by these calculations.

(9)

Using the methods of this report, the calculated adiabatic free energy needed to ionize the hydroquinone anion is 4.98 eV in aqueous solution, which according to the standard hydrogen reduction potential cited above agrees well with the reported reduction potential of 0.70 V.12 Using this value, the calculated free energy changes for eq 6, and the free energy changes for ionization in Table 6, the overall free energy change for the reaction Ag n(H 2O) + Ag(H 2O)3+ + HQ− → Ag n + 1(H 2O)4 + HQ (10)

is calculated to be +15.1, +36.9, and +14.1 kcal/mol for n = 1− 3. This is the free energy change to convert a silver ion to an atom on the catalytic center and oxidize hydroquinone. These values compare to the bulk silver value calculated from the reduction potentials of −2.3 kcal/mol and indicate a more favorable reaction at larger particles. The reaction at small particles proceeds because the hydroquinone oxidation product undergoes an irreversible reaction.12 The alternate pathway in which the steps of electron and silver ion addition to the catalytic center are reversed leads to the same result, but the two possibilities are not distinguished in this work. Aqueous silver anion nanoclusters have been invoked in experimental studies3,4 involving the superoxide O2− radical reduction of silver ion whose first step is the transfer of an electron to silver nanoparticles via reaction 11. O2− + Ag n → Ag n− + O2

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b01648. Results of small silver−water cluster calculations exploring effects of various basis sets and density functional; coordinates of equilibrium structures of silver−water clusters calculated using the PBE1PBE functional with SDD pseudopotential and basis on Ag and cc-pvTZ, jun-cc-pvTZ, and aug-cc-pvTZ basis on O and H (PDF)

(11)

The free energy change to remove the electron from the O2− radical is calculated to be 3.6 eV in aqueous solution and is smaller than that for the comparable hydroquinone reaction. Nevertheless, the initial electron transfer in this reaction lends support to the possibility of the same first step in the hydroquinone example discussed above.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

■

ORCID

Roger C. Baetzold: 0000-0002-4246-8117

CONCLUSIONS The equilibrium structures, hydration free energies, reduction potentials, and solvation free energies of silver clusters in three charge states containing up to six silver atoms and eight water ligands were determined using density functional theory with the PBE1PBE functional at 298.15 K. The basis sets, density functional, and various approximations were tested and compared favorably to experimental silver−water bond strength in the Ag(H2O)n+ series. The bond strengths decrease with number of ligands, and calculated values trend well with experiment, confirming the collinear calculated structure. Positively charged silver−water clusters have Ag−O coordination, the largest exergonic hydration free energies, and the greatest solvation. Neutral silver clusters display primarily Ag− O coordination with additional water ligands forming H bonds to these ligands and terminating in a chain ligand with Ag−H coordination. The neutral clusters are weakly solvated but show increasingly negative free energy of solvation up to four atoms, indicating more favorable solubility with size. Negatively charged silver clusters show Ag−H coordination and contain chains of ligands connected by H bonds and one instance of Ag−O coordination in the larger clusters. The calculated reduction potentials for Agn+ for n = 1−6 have an odd−even

Notes

The author declares no competing financial interest.

■

ACKNOWLEDGMENTS The author thanks Dr. R. S. Eachus, a former colleague at Eastman Kodak, for many discussions and collaborations concerning silver particles and other aspects of photosensitive materials. No external funding was involved in this work.

■

REFERENCES

(1) Batley, G. E.; Kirby, J. K.; Mclaughlin, M. J. Fate and Risks of Nanomaterials in Aquatic and Terrestrial Environments. Acc. Chem. Res. 2013, 46, 854−862. (2) Sotiriou, A. A.; Meyer, A.; Knijnenburg, J. T. N.; Panke, S.; Pratsinis, S. E. Quantifying the Origin of Released Ag+ Ions from Nanosilver. Langmuir 2012, 28, 15929−15936. (3) Jones, A. M.; Garg, S.; He, D.; Pham, A. N.; Waite, T. D. Superoxide-Mediated Formation and Charging of Silver Nanoparticles. Environ. Sci. Technol. 2011, 45, 1428−1434. (4) Garg, S.; Ma, T.; Miller, C. J.; Waite, T. D. Mechanistic Insights into Free Chlorine and Reactive Oxygen Species Production on Irradiation of Semiconducting Silver Chloride Particles. J. Phys. Chem. C 2014, 118, 26659−26670. 11821


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The Journal of Physical Chemistry C (5) Richards, V. N.; Rath, N. P.; Buhro, W. E. Pathway from a Molecular Precursor to Silver Nanoparticles: The Prominent Role of Aggregative Growth. Chem. Mater. 2010, 22, 3556−3567. (6) Takesue, M.; Tomura, T.; Yamada, M.; Hata, K.; Kuwamoto, S.; Yonezawa, T. Size of Elementary Clusters and Process Period in Silver Nanoparticle Formation. J. Am. Chem. Soc. 2011, 133, 14164−14167. (7) Thanh, N. T. K.; Maclean, N.; Mahiddine, S. Mechanisms of Nucleation and Growth of Nanoparticles in Solution. Chem. Rev. 2014, 114, 7610−7630. (8) Sosso, G. C.; Chen, J.; Cox, S. J.; Fitzner, M.; Pedevilla, P.; Zen, A.; Michaelides, A. Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations. Chem. Rev. 2016, 116, 7078−7116. (9) Gentry, S. T.; Levit, S. D. Stochastic Control: Transition from Differentiated to Undifferentiated Kinetic Growth in Ag Nanoprisms. J. Phys. Chem. C 2009, 113, 12007−12015. (10) ten Kortenaar, M. V.; Kolar, Z. I.; Tichelaar, F. D. Formation of Long-Lived Silver Clusters in Aqueous Solution by Anodic Dispersion. J. Phys. Chem. B 1999, 103, 2054−2060. (11) Berim, G. O.; Brim, L. I.; Ruckenstein, E. Mobile Monomers and Dimers in Precipitation Kinetics: a Microscopic Approach. J. Phys. Chem. B 2017, 121, 854−862. (12) James, T. H. The Theory of the Photographic Process, 4th ed.; Macmillan Publishing Co., Inc.: New York, 1977. (13) Hamilton, J. F.; Baetzold, R. C. Catalysis by Small Metal Clusters. Science 1979, 205, 1213−1220. (14) Fayet, P.; Granzer, F.; Hegenbart, G.; Moisar, E.; Pischel, B.; Woste, L. Latent-Image Generation by Deposition of Monodisperse Silver Clusters. Phys. Rev. Lett. 1985, 55, 3002−3004. (15) Baetzold, R. C. Effect of Size on Electron Transfer to Silver Clusters. J. Phys. Chem. C 2008, 112, 13070−13078. (16) Vajda, S.; White, M. G. Catalysis Applications of Size-Selected Cluster Deposition. ACS Catal. 2015, 5, 7152−7176. (17) Gentry, S. T.; Fredericks, S. J.; Krchnavek, R. Controlled Particle Growth of Silver Sols through the Use of Hydroquinone as a Selective Reducing Agent. Langmuir 2009, 25, 2613−2621. (18) Jana, N. R.; Sau, T. K.; Pal, T. Growing Small Silver Particle as Redox Catalyst. J. Phys. Chem. B 1999, 103, 115−121. (19) Henglein, A. Physicochemical Properties of Small Metal Particles in Solution: ″Microelectrode″ Reactions, Chemisorption, Composite Metal Particles, and the Atom-to-Metal Transition. J. Phys. Chem. 1993, 97, 5457−5471. (20) Linnert, T.; Mulvaney, P.; Henglein, A.; Weller, H. Long-Lived Nonmetallic Silver Clusters in Aqueous Solution: Preparation and Photolysis. J. Am. Chem. Soc. 1990, 112, 4657−4664. (21) Ershov, B. G.; Janata, E.; Henglein, A.; Fojtik, A. Silver Atoms and Clusters in Aqueous Solution: Absorption Spectra and the Particle Growth in the Absence of Stabilizing Ag+ Ions. J. Phys. Chem. 1993, 97, 4589−4594. (22) Mostafavi, M.; Lin, M.; Wu, G.; Katsumura, Y.; Muroya, Y. Pulse Radiolysis Study of Absorption Spectra of Ag0 and Ag2+ in Water from Room Temperature up to 380 °C. J. Phys. Chem. A 2002, 106, 3123− 3127. (23) Khatouri, J.; Mostafavi, M.; Belloni, J. Kinetics of Electron Transfer in Solution Catalyzed by Metal Clusters. In Photochemistry and Radiation Chemistry: Complementary Methods for the Study of Electron Transfer. Wishart, T., Nocera, D., Eds.; ACS: Washington, DC, 1998; pp 293−314. (24) Khatouri, J.; Mostafavi, M.; Amblard, J.; Belloni, J. Ionization Potential of Clusters in Liquids. Z. Phys. D: At., Mol. Clusters 1993, 26, 82−86. (25) Belloni, J. Photography: Enhancing Sensitivity by Silver-Halide Crystal Doping. Radiat. Phys. Chem. 2003, 67, 291−296. (26) Chi, C.; Xie, H.; Li, Y.; Cong, R.; Zhou, M.; Tang, Z. Photoelectron Imaging of Ag−(H2O)x and AgOH−(H2O)y (x = 1,2, y = 0−4). J. Phys. Chem. A 2011, 115, 5380−5386. (27) Rodgers, M. T.; Armentrout, P. B. Cationic Noncovalent Interactions: Energetics and Periodic Trends. Chem. Rev. 2016, 116, 5642−5687.

(28) Zhao, S.; Li, Z.-H.; Wang, W. N.; Liu, Z.-P.; Fan, K.-N.; Xie, Y.; Schaefer, H. F. Is the Uniform Electron Gas Limit Important for Small Ag Clusters? Assessment of Different Density Functionals for Agn (n ≤ 4). J. Chem. Phys. 2006, 124, 184102−184107. (29) Sierraalta, A.; Anez, R.; Alejos, P. Performance of Density Functional Methods. Some Difficult Cases for Small Systems Containing Cu, Ag, or Au. J. Phys. Chem. A 2013, 117, 2619−2628. (30) Chen, M.; Dyer, J. E.; Li, K.; Dixon, D. A. Prediction of Structures and Atomization Energies of Small Silver Clusters, (Ag)n, n< 100. J. Phys. Chem. A 2013, 117, 8298−8313. (31) Duanmu, K.; Truhlar, D. G. Validation of Methods for Computational Catalyst Design: Geometries, Structures, and Energies of Neutral and Charged Silver Clusters. J. Phys. Chem. C 2015, 119, 9617−9626. (32) Fox, B. S.; Beyer, M. K.; Bondybey, V. E. Coordination Chemistry of Silver Cations. J. Am. Chem. Soc. 2002, 124, 13613− 13623. (33) Lee, E. C.; Lee, H. M.; Tarakeshwar, P.; Kim, K. S. Structures, Energies, and Spectra of Aqua-Silver (I) Complexes. J. Chem. Phys. 2003, 119, 7725−7736. (34) Iino, T.; Ohashi, K.; Inoue, K.; Judai, K.; Nishi, N.; Sekiya, H. Infrared Spectroscopy of Cu+(H2O)n and Ag+(H2O)n: Coordination and Solvation of Noble-Metal Ions. J. Chem. Phys. 2007, 126, 194302− 194313. (35) Shimodaira, Y.; Miura, T.; Kudo, A.; Kobayashi, H. DFT Method Estimation of Standard Redox Potential of Metal Ions and Metal Complexes. J. Chem. Theory Comput. 2007, 3, 789−795. (36) Blumberger, J.; Bernasconi, L.; Tavernelli, I.; Vuilleumier, R.; Sprik, M. Electronic Structure and Solvation of Copper and Silver Ions: A Theoretical Picture of a Model Aqueous Redox Reaction. J. Am. Chem. Soc. 2004, 126, 3928−3938. (37) Fulton, J. L.; Kathmann, S. M.; Schenter, G. K.; Balasubramanian, M. Hydrated Structure of Ag(I) from SymmetryDependent, K- and L- Edge XAFS Multiple Scattering and Molecular Dynamics Simulations. J. Phys. Chem. A 2009, 113, 13976−13984. (38) Rao, L.; Cui, Q.; Xu, X. Electronic Properties and Desolvation Penalties of Metal Ions Plus Protein Electrostatics Dictate the Metal Binding Affinity and Selectivity in the Copper Efflux Regulator. J. Am. Chem. Soc. 2010, 132, 18092−18102. (39) Wu, D.; Duan, S.; Liu, X.; Xu, Y.; Jiang, Y.; Ren, B.; Xu, X.; Lin, S. H.; Tian, Z. J. Phys. Chem. A 2008, 112, 1313−1321. (40) Baetzold, R. C. Silver−Water Clusters: A Theoretical Description of Agn(H2O)m for n = 1−4; m = 1−4. J. Phys. Chem. C 2015, 119, 8299−8309. (41) 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, et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. (42) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (43) Andrae, D.; Haussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-Adjusted Ab Initio Pseudopotentials for the Second and Third Row Transition Metal Elements. Theor. Chim. Acta 1990, 77, 123− 141. (44) Papajak, E.; Truhlar, D. G. Convergent Partially Augmented Basis Sets for Post−Hartree−Fock Calculations of Molecular Properties and Reaction Barrier Heights. J. Chem. Theory Comput. 2011, 7, 10−18. (45) Yepes, D.; Seidel, R.; Winter, B.; Blumberger, J.; Jaque, P. Photoemission Spectra and Density Functional Theory Calculations of 3d Transition Metal−Aqua Complexes (Ti−Cu) in Aqueous Solution. J. Phys. Chem. B 2014, 118, 6850−6863. (46) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. (47) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric 11822


Article

The Journal of Physical Chemistry C Constant and Atomic Surface Tension. J. Phys. Chem. B 2009, 113, 6378−6396. (48) Ribeiro, R. F.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Use of Solution−Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation. J. Phys. Chem. B 2011, 115, 14556− 14562. (49) Marenich, A. V.; Ding, W.; Cramer, C. J.; Truhlar, D. G. Resolution of a Challenge for Solvation Modelling: Calculation of Dicarboxylic Acid Dissociation Constants Using Mixed Discrete− Continuum Solvation Models. J. Phys. Chem. Lett. 2012, 3, 1437− 1442. (50) Riccardi, D.; Guo, H.-B.; Parks, J. M.; Gu, B.; Liang, L.; Smith, J. C. Cluster−Continuum Calculations of Hydration Free Energies of Anions and Group 12 Divalent Cations. J. Chem. Theory Comput. 2013, 9, 555−569. (51) Ho, J.; Klamt, A.; Coote, M. L. Comment on the Correct Use of Continuum Solvent Models. J. Phys. Chem. A 2010, 114, 13442− 13444. (52) Sutton, C. C. R.; Franks, G. V.; da Silva, G. First Principles pKa Calculations on Carboxylic Acids Using the SMD Solvation Model: Effect of Thermodynamic Cycle, Model Chemistry, and Explicit Solvent Molecules. J. Phys. Chem. B 2012, 116, 11999−12006. (53) da Silva, E. F.; Svendsen, H. F.; Merz, K. M. Explicitly Representing the Solvation Shell in Continuum Solvent Calculations. J. Phys. Chem. A 2009, 113, 6404−6409. (54) Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Aqueous Solvation Free Energies of Ions and Ion-Water Clusters Based on an Accurate Value for the Absolute Aqueous Solvation Free Energy of the Proton. J. Phys. Chem. B 2006, 110, 16066−16081. (55) Bryantsev, V. S.; Diallo, M. S.; Goddard, W. A., III Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/ Continuum Models. J. Phys. Chem. B 2008, 112, 9709−9719. (56) Pliego, J. R.; Riveros, J. M. The Cluster-Continuum Model for the Calculation of the Solvation Free Energy of Ionic Species. J. Phys. Chem. A 2001, 105, 7241−7247. (57) Gupta, M.; da Silva, E. F.; Svendsen, H. F. Explicit Solvation Shell Model and Continuum Solvation Models for Solvation Energy and pKa Determination of Amino Acids. J. Chem. Theory Comput. 2013, 9, 5021−5037. (58) Zhan, C.-G.; Dixon, D. A. Hydration of the Fluoride Anion: Structures and Absolute Hydration Free Energy from First-Principles Electronic Structure Calculations. J. Phys. Chem. A 2004, 108, 2020− 2029. (59) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899−926. (60) Jaque, P.; Toro-Labbe, A. Characterization of Copper Clusters Through the use of Density Functional Theory Reactivity Descriptors. J. Chem. Phys. 2002, 117, 3208−3218. (61) Pasteka, L. F.; Rajsky, T.; Urban, M. Toward Understanding the Bonding Character in Complexes of Coinage Metals with Lone−Pair Ligands. CCSD(T) and DFT Computations. J. Phys. Chem. A 2013, 117, 4472−4485. (62) Jaque, P.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Computational Electrochemistry: The Aqueous Ru3+|Ru2+ Reduction Potential. J. Phys. Chem. C 2007, 111, 5783−5799. (63) Thapa, B.; Schlegel, H. B. Calculations of pKa’s and Redox Potentials of Nucleobases with Explicit Waters and Polarizable Continuum Solvation. J. Phys. Chem. A 2015, 119, 5134−5144.

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SilverâWater Clusters: A Computation of Agn(H2O)m for n = 1â6; m

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