Density Functional Theory Investigation on the Nucleation and Growth

Aug 22, 2014 - Department of Biotechnology and Chemistry, Tver Technical University, Tver 170026, Russian Federation. •S Supporting Information...
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Density Functional Theory Investigation on the Nucleation and Growth of Small Palladium Clusters on a Hyper-Cross-Linked Polystyrene Matrix Antonio Prestianni,† Francesco Ferrante,† Esther M. Sulman,‡ and Dario Duca*,† †

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Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, Viale delle Scienze, Parco d’Orleans II, Ed. 17, 90128 − Palermo, Italy ‡ Department of Biotechnology and Chemistry, Tver Technical University, Tver 170026, Russian Federation S Supporting Information *

ABSTRACT: Density functional theory calculations were employed to investigate the nucleation and growth of small palladium clusters, up to Pd9, into a microcavity of the porous hyper-cross-linked polystyrene (HPS). The geometries and the electronic structures of the palladium clusters inside the HPS cavity, following the one-byone atom addition, are affected by a counterbalance between the Pd− phenyl (Pd−Φ) and Pd−Pd interactions. The analysis performed on energetics, cavity distortions, and cluster geometries indeed suggest that the cluster growth is dominated by the Pd−Φ interactions up to the formation of Pd4 aggregates, whereas the metal−metal interactions actually rule the growth of the larger clusters. The elasticity of the hyper-cross-linked polystyrene matrix also plays an important role in the cluster development processes.

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INTRODUCTION Supported metal nanoparticles on nanostructured polymeric matrices currently seem a valid alternative to the application of more common heterogeneous catalysts already employed in several processes also of industrial interest.1−4 Both inorganic and carbonaceous supports indeed show catalytic instability, which is often caused by the difficulty of exactly controlling either the size distribution or the morphological properties of the metal particle.5,6 The pores inherently existing inside the macroscopic structure of certain polymers, on the other hand, can control the growth, and hence the sizes and shapes, of the metal nanoparticles.7 In this way, the catalytic efficiency of metal crystallites supported on porous polymeric materials could be positively influenced.8,9 As an example, platinum nanoparticles supported on hyper-cross-linked polystyrene (HPS) have been shown to act as a very stable and active catalyst for the wet air oxidation of phenol without any formation of hazardous side byproducts.10 Noticeably, other catalysts, such as unsupported Fe nanoparticles or SnO2/SiO2 nanocomposite aggregates, when employed in the same reaction were considered inadequate because of the occurrence of an intrinsic instability increased by leaching phenomena. The HPS matrix used in the catalytic example discussed above was introduced as a new material more than 50 years ago11 and soon became a promising structured polymeric material of use in catalysis. HPS polymers are characterized by small pores, leading to very high specific surface area.12 They are stable also at relatively high temperatures and can swell in © 2014 American Chemical Society

almost any liquid medium while their cavity sizes can be to some extent modulated by simply varying the polymeric synthesis conditions. Because of these features, HPS matrices are primarily considered as peculiar organic polymeric materials to be employed for supporting metal nanoparticles,13,14 the features of which are of great interest in characterizing resulting catalytic systems in both the industrial fine chemical and green chemistry fields.10 In particular, it was demonstrated that HPS can be efficiently employed to control either the growth or the shaping of Co, Ru, Pd, and Pt nanoparticles13,15,16 while the use of HPS in catalysis has proven to be effective in the synthesis of vitamin intermediates,7 selective hydrogenation of acetylene alcohols,17,18 and, most noteworthy, in oxidation of carbohydrates15,16 and phenols.10 Despite the great amount of work exploring the structural and morphological properties as well as the catalytic activities of the HPS-supported metal nanoparticles, very little is known regarding the particular interactions between the support and the metal atoms, probably because of the extreme complexity of the HPS matrix, which has eluded a systematic and detailed characterization. In this work, we investigate at the atomistic level the nucleation of a palladium cluster inside a cavity of hyper-crosslinked polystyrene, monitoring the cluster growth until the Received: June 25, 2014 Revised: August 21, 2014 Published: August 22, 2014 21006

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actually chosen by selecting a cavity whose volume could be comparable to that of the cluster with the largest size we wanted to consider, namely that of a Pd9 cluster. Therefore, this cavity is representative of a HPS nanopore capable of giving rise to very small metallic clusters, separating them from the surroundings, and inhibiting their indefinite growth. The choice of this particular cavity, which of course cannot, in general, be considered representative of an average HPS cavity, has been also ruled by pragmatic issues, such as the necessity of maintaining the size of the model system in the ONIOM procedure as small as possible. The chosen cavity is, in fact, well-defined by a relatively small cross-linked portion of the starting HPS model fragment. Conversely, cavities like those occurring in more compact regions of the polymer (e.g., those in the upper part of the HPS shown in Figure 1) are too large and/or defined by too many coiled chains. In detail, the cavity here chosen has a C76H77 stoichiometry and is composed by two coiled fragments of polystyrene (PS) chain. One is formed by two styrene residues and the other by six styrene residues, kept together by XL units. On the whole, there are five XLs connecting benzene moieties while two Φ rings do not participate to the formation of any XL. A final Φ ring belongs to another chain fragment, which is not included in the cavity model and is bonded to the remaining part of the main structure through 2 XLs, placed in meta position to one another. The cavity is schematically shown in Figure 2, where the Φ rings are numbered for later reference.

room saturation of the cavity is reached. The aim is to evaluate the influence, in terms of interactions between the phenyl rings and the palladium atoms, of the cavity walls both on the properties and on the nucleation and growth processes of the clusters. To our knowledge this is the first high-level atomistic investigation of a system involving metal clusters embedded into such a large support fragment.

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CONSTRUCTION OF THE MODEL HPS and the Choice of the Cavity. A model of porous hyper-cross-linked polystyrene has been generated following the algorithm reported by Ferrante et al.19 Briefly, taking a linear polystyrene chain, a given percentage (namely, 40%) of phenyl (Φ) rings were provided with potential cross-linkers, i.e., methyl moieties with virtual dangling bonds, simulating −CH2Cl groups. After the relaxation of the linear polymeric chain, performed by United-Atoms AMBER molecular dynamics (MD),20 a cross-linking step was undertaken. Along this step, a geometry inspection of the relaxed polymer was performed and cross-link (XL) units between couples of Φ rings were put whenever preset distance and orientation criteria were satisfied. The resulting macromolecule was then relaxed again by some picosecond MD runs; thus, the cross-linking step was turned on anew. These cycles were repeated until 90% of the original potential cross-linkers gave rise to actual cross-links. The HPS fragment was finally subjected to a 20 ns MD relaxation and, in order to pass from the united-atom to the allatoms modeling description, which is clearly suitable for more detailed investigations, the stoichiometric amount of hydrogen atoms was added to the relaxed structure. Although here we focused on pristine HPS properties, the described algorithm is easily adjustable to build up polymeric systems including additional chemical functions (e.g., acid or basic groups) and/ or local morphological properties. These features will be exploited in future studies. From the macromolecule generated in this way, an approximately 1700 atom portion has been tailored. This contained the topological cavity, which has been the object of the present investigation. The surrounding HPS fragment, whose tridimensional structure is reported in Figure 1, has been

Figure 2. Schematic representation of the HPS cavity, hosting the Pdn clusters: Φ rings involved in the interactions with the Pdn are numbered from 1 to 5, being the reference Φ unit indicated as 1. Bond lengths and angles are distorted for the sake of clarity.

Modeling Pdn Growth. The palladium clusters’ adsorption and growth inside the cavity described in the preceding section were investigated, applying the algorithm sequence summarized in the following: (i) First, a palladium atom was placed in several positions of the cavity, in particular atop the Φ rings whose normal to the plane was directed inside the nanopore; geometry optimization was performed in all cases and the most stable configuration was chosen as the starting one for nucleation. (ii) A second Pd atom was added near the first nucleus, and the resulting structure was subjected to a new geometry optimization, thereby obtaining the most stable interaction geometry between the cavity atoms and the linear Pd2 species. (iii) From the third Pd atom onward, a growing number of geometries were taken into account for positioning

Figure 1. Hyper-cross-linked polystyrene portion and the cavity chosen for the nucleation and growth of the palladium clusters. 21007

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the nth atom and, after geometry optimizations−testing various structural arrangements for any involved cluster−the most stable one was chosen as a starting point for the addition of the (n + 1)th Pd atom, until the final Pd9 cluster was obtained. In all the calculations, 3 different spin multiplicity states (i.e., singlet, triplet, and quintet) were considered. The nature of minima in the potential energy hyper-surface of all the geometries involved in the algorithmic sequence above was checked by the inspection of the harmonic vibrational frequencies and by the energy-based discrimination, considering the energy values corrected for the zero-point vibrational contribution. To compare the cluster growth in the cavity with the same Pdn particles in the isolated state, the structure and the spin multiplicity states of the latter were also studied by in vacuo optimizations, starting from the geometry adopted by the different Pdn clusters in the cavity. Computational Details. All the calculations on the different Pdn/HPS systems were performed by the Gaussian 09 suite of programs,21 without freezing any atomic position during the geometry optimizations. This was accomplished by means of a DFT:MM ONIOM procedure,22 in which the model system was devised by the n atoms of the considered palladium cluster (n = 1−9) plus the 149 HPS atoms of the cavity detailed in Figure 1; the real system is the whole Pd/HPS system, which has stoichiometry PdnC847H840. The high-level calculations, on the model system, were performed by the (unrestricted) B3LYP functional in conjunction with the Coulomb attenuated method (CAM-B3LYP)23 joined with the Los Alamos National Laboratory (LANL2-DZ) effective core potential for the palladium atoms and the D95V basis set for all the lighter atoms. The low-level (i.e., the real system) was, on the contrary, managed by the universal force field.24 The couple CAM-B3LYP plus LANL2-DZ was also employed for the investigation of the Pdn clusters in the isolated state. As mentioned in the preceding section, the calculations involving the palladium clusters were carried out by considering the singlet, triplet, and quintet spin multiplicity states. It is, in fact, known that the quintet state is the maximum spin multiplicity of a Pdn cluster with n ≤ 9.25,26 When relevant, the basis set superposition error was estimated by means of the counterpoise procedure.27 Of course, the metal cluster adsorption and shaping that experimentally occur generally on a support and specifically on HPS is pretty far from the one-by-one atom addition model here proposed. However, supposing a smooth and rapid reduction of the metallic precursor and hypothesizing that the metal reduction is not affected by the leaving substituents of the same metallic precursor, it is reasonable to think that what is produced along the optimization in the calculations here presented could roughly reproduce the clustering and shaping processes of the palladium atoms. At this point, it is worthwhile to discuss the reliability of the computational method (DFT functional plus basis set for the high level ONIOM procedure) adopted in the present work by comparing its performances in estimating the Pd−phenyl interaction energy with the results obtained by other methods. Granatier et al.28 reported an extensive investigation on the interaction between benzene and three transition metals (Pd, Ag, Au). The presumably highly accurate CCSD(T)/ANORCC-VTPZ BSSE-corrected potential curve was taken as the benchmark and hence compared to the corresponding curves obtained either by second-order Möller−Plesset perturbative approaches or by DFT methods employing exchange-

correlation functionals capable of treating dispersion interactions. With regards to the Pd−benzene interactions, those authors, at the CCSD(T) level, found for the most stable system a BSSE-corrected binding energy (BE) of 82.4 kJ mol−1, parallel to a geometry in which the Pd atom was placed in the midpoint of a C−C bond. The Pd-midpoint C−C equilibrium distance was 2.11 Å, corresponding to a Pd−C distance (dPd−C) of 2.23 Å. They also noted that the utilized dispersion-corrected exchange-correlation functionals overestimated the binding energies.28 In preliminary studies, we performed geometry optimizations of palladium−benzene systems, using either CAM-B3LYP or two M06-family functionals (namely, M06L29 and M062X30). The functionals above were associated both to the LANL2+D95V basis set, having double-ζ quality, and to the more extended cc-pvtz-PP+cc-pvtz combination, which is composed by the polarized triple-ζ basis set of Dunning,31 for the H and C atoms while an effective core potential, having a valence basis set qualitatively equivalent to that used for the lighter atoms, was employed for Pd.32 When the triple-ζ basis set is used, the CAM-B3LYP BSSE-corrected binding energy is closer (BE = 80.2 kJ mol−1, dPd−C = 2.19 Å) to the homologous CCSD(T) value than anyone otherwise obtained, considering the different methods applied. The M06L and M062X functionals indeed predicted too strong (BE = 121.5 kJ mol−1, dPd−C = 2.15 Å) and too weak (BE = 66.7 kJ mol−1, dPd−C = 2.30 Å) Pd−benzene interactions, respectively. These trends clearly mirror those revealed by Granatier et al.28 With the double-ζ basis set, the agreement with the CCSD(T) benchmark is worsened but the trend is unchanged: BE = 64.5, 103.6, 58.8 kJ mol−1 and dPd−C = 2.25, 2.21, 2.39 Å, according to CAM-B3LYP, M06L, and M062X, respectively. In the present work the use of a double-ζ, instead of the higherquality triple-ζ basis set was, in any case, necessary because of the sizes of the treated systems, even if they were embedded within an ONIOM approach.

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RESULTS AND DISCUSSION Pd/HPS: Metal−Metal and Metal−Support Mutual Conditioning Effects. In the very first step of the clustergrowing procedure, one palladium atom was placed at the center of the HPS cavity and the structure was optimized without any constraint. In this system, the Pd atom adsorbs on a Φ unit forming two cross-links in meta position, that is, it adsorbs on a three-substituted benzene ring. This special Φ ring will be used as a reference throughout. In the relaxed configuration, the Pd atom is placed in an almost symmetric bridge position between two carbon atoms of the Φ moiety, with Pd−C distances of 2.32 Å and one angle of 99° with respect to the phenyl plane. These values are very close to the corresponding ones formed in the isolated Pd−benzene system. A number of trials were performed in order to place the second palladium atom in its initial orientation with respect to the first Pd atom and the reference Φ ring. The most stable geometry found for the Pd2/HPS system shows one palladium atom that remains in an asymmetric bridge position on a C−C bond, being dPd−C1 = 2.21 Å and dPd−C2 = 2.38 Å, while the other Pd is placed atop a carbon atom of the same reference Φ moiety at a distance dPd−C6 = 2.25 Å. The Pd−Pd bond length (dPd−Pd) is 2.75 Å, which is ca. 0.25 Å larger than the dPd−Pd value found in the isolated Pd2 species, treated at the same level of calculation. It is worth noting that the Pd2/HPS system has a 21008

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Figure 3. Top panels: geometry of the Pd3 clusters in the singlet and triplet multiplicity states, when isolated and inside the HPS cavity (bond lengths in angstroms, angles in degrees). Bottom panels: schematic representations of the interaction distances among the involved Φ rings of the HPS cavity with the palladium atoms of a Pd3 cluster in the singlet (a) and triplet (b) states and of a Pd4 (c) cluster. PS and XL represent polystyrene chain and cross-link, respectively.

optimized structure characterized by a bond length of 2.417 Å. If we accept the energy value above as benchmark, our CAMB3LYP/LANL2DZ level BEPd−Pd result (69 kJ mol−1), which becomes 56 kJ mol−1 by BSSE corrections, suggests to us that the method selected for this work is reliable also for describing Pd−Pd interactions. Going back finally to the Pd2/HPS system, the energetic and geometric properties characterizing adsorption, together with the discussion above, seem to indicate that the Pd−Φ interactions prevail on the Pd−Pd interactions so that the singlet state of the Pd2 cluster inside the HPS could be stabilized with respect to the triplet state because of the favorable strong interactions of the palladium moiety with the phenyl ring. The hosting hyper-cross-linked polystyrene cavity begins to deform when the third palladium atom is added to the Pd2/ HPS system. In the isolated form, the Pd3 cluster shows the triplet spin multiplicity state and the geometry of an isosceles triangle: dPd−Pd = 2.56 (×2), 2.78 Å. In the singlet state, its geometry becomes that of an equilateral triangle with dPd−Pd = 2.55 Å. In the isolated state and at the computational level here employed, the difference in the ZPVC energies between the triplet and the singlet spin multiplicity states is 46 kJ mol−1. The Pd3 cluster, when inside the HPS cavity, assumes the geometry of a slightly distorted isosceles triangle, dPd−Pd = 2.80, 2.86, 2.96 Å. This likely takes place for the occurrence of a balance between the Pd−Pd and Pd−Φ interactions. This issue will be of extreme importance in the following discussion. The Pd3 cluster clearly interacts with four Φ rings, as detailed in Figure 3. Two of these interactions are of Pd−C2 bridge-type; the other two are of Pd/C atop-type. As already observed in the Pd2/HPS system, an inversion in the singlet−triplet stability order is found for the Pd3/HPS system; the singlet spin multiplicity state is now 48 kJ mol−1 more stable than the triplet state. This evidence can likely be interpreted as follows: As shown by Figure 3, the structure of the Pd3 cluster inside the HPS cavity is sensibly distorted with respect to those of both the triplet and singlet state geometries of the isolated Pd3. On the other hand, in the former, when the singlet state is considered, the average distance between the Pd atoms of the cluster and

singlet spin multiplicity in its ground state. If the same calculation is performed by considering a triplet multiplicity, a structure is obtained that is 104 kJ mol−1 less stable. In the latter structure, the Pd2 moiety interacts with the reference Φ ring through just one Pd atom, having Pd−C distances of 2.55 Å while the other Pd is placed at Pd−C distances larger than 2.7 Å. Furthermore, the Pd−Pd bond length is now 2.53 Å, i.e., very close to that of the isolated Pd2. The bonding properties for many transition-metal dimers are up to now unclear. Among these, the bond in the Pd2 molecule seems to be one of the least understood, even though a large number of experimental and computational investigations concern the study of the palladium dimer. It is outside the scope of this article to report an extensive section about the Pd2 molecule; however, the work of Schultz et al.33 is worth mentioning here as a source of deeper discussion regarding this topic. Furthermore, to point out some interesting issues originating from mass spectrometry and effusion experiment results,34 it should be mentioned that the Pd2 species would seem to be weakly bound aggregates with a bond length of 2.57 Å and binding energies in the 70−110 kJ mol−1 range. The latter appears, in particular, to be the correct range of values in aggrement with more recent investigations. The Pd2 molecule should actually prefer a ground state with triplet multiplicity,35,36 and recently the 3∑+u ground state has indeed been confirmed by laser-induced fluorescence experiments,37 which also gave an estimated bond length of 2.47(4) Å and a vibrational frequency of 211.4 cm−1. The CAM-B3LYP/ cc-pvTZ-PP approach fixed the values at 2.486 Å and 211.4 cm−1 for the bond length and stretching frequency, respectively, which became 2.504 Å and 215.9 cm−1 when the LANL2DZ basis set was used. The agreement with the experimental data of Qian et al.37 is remarkable, although it is almost certain that some error cancellation did occur along with the calculations. In regard to the binding energy characterizing Pd2 species (BEPd−Pd), there is some skepticism33 about the recommended experimental value of 24 ± 4 kcal mol−1 (100 ± 17 kJ mol−1), based on molecular parameters obtained from a ground state wrongly described as 1∑+g .38 At variance with that, it was indeed suggested to use as the benchmark the CCSD(T)/MQZ-sc value of 16.9 kcal mol−1 (71 kJ mol−1), being the corresponding 21009

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the carbon atoms of the phenyl moieties is 2.37 Å (interaction with six centers, Figure 3a), while the same average distance in the triplet case is 2.52 Å (interaction with eight centers, Figure 3b). This points out that in the singlet state Pd3/HPS system the Pd−C distances are closer to those of the optimal value of 2.25 Å obtained, at the same level of calculation, for the Pd−C distances in the simple Pd−benzene aggregate. The Pd−Φ interactions in the Pd3/HPS system seem yet to play a primary role in determining the cluster geometry and its electronic structure, overcoming in magnitude the Pd−Pd interaction effects and shaping the cluster in an unexpected form. In order to quantify this aspect, it was attempted to compare the cohesive energy of the Pd3 cluster with the Pd−Φ interaction energy. This is of course only a crude estimation because a number of other presumably relevant issues−weak interactions with phenyl rings at larger distances and with other substituent groups, distortions of the cavity, and so on−should participate in ruling the true energetic behavior of the Pd3 cluster inside the cavity. The cohesive energy for Pd3 was estimated by using the general formula Ec = E(PdCP) − [E(Pdn)/n], where the counterpoised E(PdCP) energy was obtained by averaging the energy calculated for the n palladium atoms in the Pdn cluster when the other n − 1 atoms were defined as ghosts. Ec was 57.2 kJ mol−1 for the Pd3 cluster. According to the already discussed role of the Pd−Φ interactions in leading the growing and shaping of the palladium cluster inside the HPS cavity, this value is 7.3 kJ mol−1 smaller than the BSSE-corrected Pd−Φ binding energy, estimated at the same level of calculation in the Pd3/HPS system. The interaction parameters of the Pd4 cluster with the HPS cavity are reported in Figure 3c. In this case, though the triplet spin multiplicity of the isolated cluster is again lowered to singlet in the cavity, the energy difference between the two multiplicity states is reduced to ca. 30 kJ mol−1. In the Pd4 system, we can point out a clear tridimensional distortion of the cluster when it interacts with the Φ moiety constellation of the HPS cavity. We can indeed notice that the cluster has a structure significantly different from that shown in vacuo, which is trigonal-pyramidal in the triplet ground state and tetrahedral in the singlet state.39 In the cavity, the Pd4 cluster has conversely the geometry of a distorted and bended parallelogram, where each Pd atom shows seemingly very efficient interactions with two phenyl carbon atoms. The shape of this structure can be once again attributed to the effects of a balance between the metal−metal and the metal−phenyl interactions, with the latter presumably stronger than the former. The geometries of the Pdn (n = 5−9) clusters inside the HPS cavity are shown in Figures 4 and 5. It can be noticed that the number of Pd−Φ interactions increases as the cluster grows. Table 1 presents the results if we define ν(n,rs) as the cumulative number of Pd−C distances in a given Pdn/HPS system that are smaller than or equal to rs. Recalling that, at the computational level used here, the Pd− C equilibrium distance when a single metal atom interacts with the HPS matrix (Pd/HPS) is ca. 2.3 Å, this value can be taken as the initial point for rs. As can be observed, the ν(n,2.3) reaches a maximum at n = 4, then decreases in the range n = 5− 7 (where the average Pd−C distance is larger, as witnessed by the values of ν at higher rs), and finally for n = 8,9, turns back higher. These behaviors are, in our opinion, related to two important issues: (i) The local organization of the metal clusters on HPS is not a simple consequence of the hindered

Figure 4. Schematic representation of the interaction distances (in angstroms) between the palladium atoms of the Pdn clusters (n = 5−7) and the involved phenyl rings of the HPS cavity. PS and XL refer to polystyrene chain and cross-link, respectively.

Figure 5. Schematic representation of the interaction distances (in angstroms) between the palladium atoms of the Pdn clusters (n = 8,9) and the involved phenyl rings of the HPS cavity. PS and XL refer to polystyrene chain and cross-link, respectively.

space available to the Pd atoms inside a given cavity. (ii) Along the growing of the metal clusters inside the here selected cavity, the Pd−Φ interactions prevail upon the Pd−Pd ones up to Pd4 then, from Pd5 onward, the latter become predominant. As a consequence, the Pd4 cluster should be the largest supported metal fragment, which is strongly affected by the position of the 21010

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Table 1. Cumulative Number of Pd−C Distances, ν(n, rs), Smaller than or Equal to a Given Distance, rs, Present in a Cluster Having n Pd Atoms Inside the HPS Cavity

Even though systematic investigations on the properties of small palladium clusters are reported in the literature,26 we studied the Pdn (n = 1−9) clusters without the HPS matrix (in the following we will refer to these systems simply as in vacuo systems). Because a number of geometries are possible for the clusters, for the sake of direct comparison it was necessary to find the cluster structure that, for every n, is closer to the one adopted in the HPS cavity. To achieve this, the starting geometry for the in vacuo optimization was just that adopted by the clusters in the cavity. We already discussed exhaustively the Pd2 species. The adsorption on the HPS produces a singlet state where the bond length is increased by ca. 0.25 Å. Again, at the same level of theory the Pd3 cluster, which in the isolated state is an isosceles or equilateral triangle, in the cavity becomes a larger and less regular triangle because of the interaction of the vertex atoms with three different Φ rings (see Figure 3a,b). Furthermore, the geometries that the Pd4 and Pd5 clusters adopt in the cavity are fundamentally different from those adopted in vacuo, i.e., a distorted “butterfly” square versus a tetrahedron for Pd4, and a square pyramid instead of a trigonal bipyramidal species for Pd5. A descriptor of the change in the structural properties of the metallic clusters is illustrated in Figure 6, in which the Pd−Pd

rs (Å) 2.50

2.40

2.30

n

ν(n,2.5)

ν(n,2.4)

ν(n,2.3)

2 3 4 5 6 7 8 9

2 5 7 6 9 10 10 12

2 3 5 4 9 6 7 7

1 2 5 2 1 2 4 4

Φ rings in the HPS cavity now considered, whereas for all the Pdn systems the Pd−Pd interactions should exploit the atomistic level elastic properties of the HPS matrix, which in turn are affected by the growth of the same metal clusters. To give a quantitative form to the statements above, let us try to compare the cavity in a Pdn/HPS system to the same cavity deprived of the metal cluster. To this aim, we could define as descriptors the vectors centered on the Φ rings and normal to the plane defined by the same moiety. The filled (by a given palladium cluster) cavity structure to be inspected is overlapped to the bare cavity so that their reference phenyl rings 1 (see Figure 2) have the same spatial coordinates; for this comparison, the distances between the centers of corresponding phenyl rings (rc) and the orientation changes of their normal vectors are calculated. In particular, an orientation change (dN) is defined as the dihedral angle between the planes identified by the points e1c1c0 and c1c2e0, where e and c are the normal vector end point and the center of the phenyl ring, respectively, while the subscripts 1 and 0 indicate the cavity with and without the palladium cluster. If distortions were not occurring in the HPS cavity after the palladium embedding, rc and dN would clearly have a result of zero. Noticeably, because of the hyper-cross-linked nature of the support matrix, even small displacements of phenyl rings in a given portion of the cavity could result in large distortions of the whole geometry. The values of rc and dN are plotted for every phenyl ring belonging to the cavity of any Pdn/HPS system (n = 1−9) in Figure S1 of the Supporting Information. Even a single palladium atom inside the cavity can cause rc displacements of ca. 2 Å, but until Pd5 is formed these displacements are controlled and more or less constant with respect to the addition of new Pd atoms. Occasionally dN values are larger than 40°, while they are usually less than 20° and sometimes negligible. Major distortions are localized on the Φ rings numbered 8 and 9, which do not show any cross-link and are the most distant from the nucleation center. This fact would seem to indicate that small displacements of the Φ rings, which interact with palladium atoms, are amplified along the network and their effects are more pronounced in the HPS portions that are less entangled. As an example, when n > 4, the rc values for the Φ rings 8 and 9 are always larger than 5 Å and sometime exceed 10 Å. Pd Cluster Geometries Inside the HPS Cavity. Up to now we discussed adsorption, nucleation, and growth of palladium clusters on the HPS matrix taking the cavity as reference. Now, we analyze how the process proceeds if the clusters become the focal point of the observation.

Figure 6. Average bond lengths in the Pdn clusters (n = 2−9) in the isolated form and inside the HPS cavity. The most stable spin multiplicity state of the system is also indicated (S, singlet; T, triplet; Q, quintet).

average bond length differences between supported and unsupported (in vacuo) species are displayed. Figure 6 clearly shows that the major differences in the average Pd−Pd bond length actually occur in the Pdn clusters with n < 5. This is additional evidence that Pd4 is on the borderline of Pd−C on the Pd−Pd interaction predominance effects. When n > 5, even if distortions still occur, the clusters in the HPS cavity have the same geometries that they show in the isolated state. In particular, Pd6 has a typical octahedron geometry and Pd7 adopts an augmented triangular prism shape. It is to be noted that the larger Pd8 and Pd9 clusters, although in the cavity experience a multiplicity lowering (from quintet to triplet) with respect to the isolated state, have essentially the same geometry structure: the fusion between a square and a trigonal-pyramid with one common vertex (resembling a biaugmented triangular prism) for Pd8 and the same arrangement plus one Pd atom placed on a face of the square pyramid for Pd9. The latter saturated the considered HPS cavity, which 21011

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cannot be deformed anymore. This is also witnessed by the fact that for clusters larger than Pd7 there are not any changes regarding the Φ rings involved in the Pd−C interactions. Finally, according to the Mulliken scheme, an approximately 0.2 |e|/atom charge donation from the HPS to each Pdn cluster occurs upon interaction (see Figure S2 in Supporting Information). This issue was already observed also from computational studies on palladium clusters adsorbed on carbon nanotubes.40,41 Accordingly, the palladium atoms that mostly feel the effects of this charge donation are those with the larger coordination numbers. This allows one to infer that, beside the local topology of the metallic cluster sites that influences their coordination states and hence their chemical properties, the migration of electron density from the support to the metallic cluster certainly contributes to giving rise to the different behaviors among the cluster sites devoted to the catalytic substrate adsorption in a given heterogeneous reaction. This, in turn, is generally recognized as an important topic when the catalytic properties of very small metal clusters are exploited.42

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CONCLUSIONS

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +39-091-23897975. Fax: +39-091-590015. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the POLYCAT project (Modern polymer-based catalysts and microflow conditions as key elements of innovations in fine chemical synthesis), funded by the 7th Framework Programme of the European Community; G.A. CP-IP 246095; http://polycat-fp7.eu/.

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REFERENCES

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In a cavity topologically defined by a portion of hyper-crosslinked polystyrene, which had enough room to host one small cluster formed by a few metal atoms, the nucleation and growth of Pdn (n = 1−9) have been investigated by means of a DFT:MM hybrid approach with the aim of modeling the interactions occurring between the metal particles and the atoms forming the wall of a small HPS cavity. The atomistic level (local) elasticity of the HPS matrix allows the cavity to distort in response to the interactions between the phenyl rings and the palladium atoms already when the Pd cluster is nucleating. At this stage these Pd−C interactions seem to prevail over the metal−metal interactions, which instead become predominant, increasing the size of the growing metal clusters. The large number of under-coordinated metal atoms in a cluster surely affects its catalytic properties. The peculiar characteristics of every site of a cluster are determined by its geometry and electronic structure. In fact, the investigation reported in this work has demonstrated that, at least regarding small palladium clusters, the hyper-cross-linked polystyrene is not a mere support preventing particle sintering. Instead, its small cavities affect the cluster site properties, both the geometric and the electronic properties and hence the adsorption and the overall catalytic properties. The local effects of HPS on the metallic cluster properties could actually influence if not rule the interactions of the latter with the catalytic substrates in a reactor, an issue that can be exploited to control and hopefully improve the performances of some catalytic applications.

S Supporting Information *

Graphs reporting the data for the comparison between the empty HPS cavity and the same cavity when a Pdn cluster is adsorbed; Mulliken charges on the adsorbed palladium clusters; Cartesian coordinates of the optimized geometry of the Pdn/ HPS systems (only the portion formed by the cluster and the cavity). This material is available free of charge via the Internet at http://pubs.acs.org. 21012

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