Effect of Charge and Phosphine Ligands on the Electronic Structure of the Au8 Cluster.

In this work, we use density functional theory calculations with a hybrid exchange-correlation functional and effective core pseudopotentials to determine the geometry of bare and phosphine-protected Au8 nanoclusters and characterize their electronic structure. Au8 clusters were bonded to four and eight PH3 ligands in order to evaluate the effect of ligand concentration on the electronic structure, while different positional configurations were also tried for four ligands attached to the cluster. We show that the neutral clusters become more nucleophilic as the ligands bind to the clusters at stable sites. The ground-state planar configuration of Au8 is maintained depending on the concentration and position of ligands. The effect of ionizing to the +2 charge state results in disruption of planar geometry in some cases because of inoccupation of a molecular orbital with the Au-Au bonding character. Natural bond order charge analyses showed that Au atoms oxidize upon ionization, instead of phosphine. The net positive charge makes the clusters more electrophilic with a capacity to absorb electrons from nucleophiles depending on the concentration and position of ligands and on the concentration of low-coordinated gold atoms. Besides, ionization energies and electron affinities were calculated through different mechanisms, finding that both variables are much higher for charged systems and change inversely with the concentration of ligands.

Introduction

Since the first publication about the unexpected catalytic activity of gold nanoparticles by Haruta[1] and Hutchings,[2] studies on gold clusters have been increasing significantly. The efficient catalytic activity of gold-based catalysts, as demonstrated by the CO to CO2 oxidation at low temperatures, is related to the small size of the clusters as catalyst deactivation occurs with cluster sintering.[3] The interplay between the size and the geometric configuration of gold nanoclusters becomes relevant when clusters are very small. Phase transformations are expected due to interactions of gold clusters with reducing chemical environments and charge transfers; in these environments, cluster nuclearity may change as a result of chemical reactions, such as ligand exchange.[4] Furthermore, 3D configurations are expected to vanish favoring the stabilization of planar geometries for small clusters; this transition is likely to occur in gold clusters with a total number of atoms between 10 and 14 atoms.[5] Nevertheless, other reports have identified the change switch from the planar structure to 3D at Au8 where different levels of the theory predict either the dominant planar (D2) geometry or at less common nonplanar structure (D2).[6] Theoretical calculations have attributed the stability of planar geometries to relativistic effects in the heavy gold atom that results in reduction of the s–d energy gap and s–d hybridizations and orbital overlaps with neighbor atoms.[7] Narrow gold cluster size distributions can be achieved through a combination of nucleation procedures, such as depositing size-selected gold nanoclusters on metal oxide or carbon substrates[8,9] or using metal–ligand complexes as precursors;[10,11] specific geometries are also achievable by substituting metals with other types of metallic atoms in order to suppress isomerization.[12] Therefore, the electronic structure and catalytic behavior of gold clusters can be defined at the synthesis stage.

Small catalyst nanoparticles can be synthesized through deposition on metal oxide substrates via metal evaporation,[13,14] although this type of process results in wide size distributions of gold nanoclusters.[14] Alternatively, the cluster deposition may take place from liquid solutions of atomically precise nanoclusters,[15,16] which yields narrower distributions. As a result of liquid phase synthesis processes, ligands bind to outer gold atoms of the nanoparticles to form charged complexes of ligand-protected clusters. Typical protecting ligands include thiols, amines, polymers, and phosphines. Despite stability issues related to weak Au–P bonds, water-soluble phosphine/gold complexes are commonly produced because phosphine favors the nucleation of narrow size distributions of ligand-protected gold clusters, as mentioned above. In addition to tuning their size by binding with ligands, gold clusters also find new stable geometries when they interact with ligand molecules, which are explained by charge transfers resulting from ligand–gold interactions that weaken Au–Au bonds.[17] Ligands are often removed to generate bare metal clusters with exposed sites for enhanced catalytic activity through certain techniques such as calcination in a controlled atmosphere,[10] heating under vacuum,[18] and low-temperature chemical reactions with peroxides.[11] The catalytic activity of these nanoparticles is related to the cluster size and geometry and their electronic structure, which is influenced by the absence, concentration, and configuration of attached ligands.

However, experimental characterization of the electronic structure in this type of system is still a major challenge, and specific information for ligand-protected Au (X < 10) clusters is still limited. The optical absorption spectrum of thiolated Au25 clusters showed molecular-like transitions because of quantum size effects.[19] Similarly, electrochemical characterization of small gold nanoparticles has revealed electron localization and molecule-like electronic behavior and nonzero highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gaps uncharacteristic of bulk metals.[20,21] However, electrodynamic models are not reliable for nanoparticles with sizes below 5 nm. The superatom model has been used to study the stability and electronic structure of ligand-protected gold nanoparticles at energy levels around the HOMO–LUMO gap, explaining delocalization, orbital contributions near the gap and structural stability due to occupation of superatom orbitals.[22] The superatom complex model is employed to predict the stability of structures according to their closed shell requirements. The model has evolved to present a unified view for ligand-protected gold clusters as superatom complexes regardless the ligand nature such as thiolate, phosphine, and halide ligands.[23] Thus, for single-shell clusters, the filling of subshells in an aufbau fashion, that is, 1S2|1P6|1D10|2S21F14|2P61G18|2D103S21H22|..., predicts exceptional stability for spherical structures with 2, 8, 18, 34, 58, 92, and so forth delocalized electrons (n*). For (LAX) systems, the formula is n* = NνA – M – z, wherein N denotes the number of atoms of the metal cluster (of type A), and ν denotes the corresponding atomic valence. As already known, νA = 1 for gold clusters because the delocalized electrons are mainly derived from the 6s atomic orbitals. M denotes the number of electron-localizing (or electron withdrawing) ligands—L—(assuming here a withdrawal of one electron per X), and z is the overall charge on the complex. In general, phosphine is considered a weak ligand, which only leads to a steric stabilization of the metal cluster surface. Density functional theory (DFT) calculations have predicted the HOMO–LUMO gap of Au11 and Au13 clusters protected by thiol and phosphine ligands stabilized by halogen or thiolate ligands. The stability was predicted through the satisfaction of an electronically closed shell superatom complex. The gaps were computed as 1.5 and 1.8 eV for ligand-protected Au11 and Au13 clusters, respectively, and attributed to the localization of electrons belonging to the conduction band by bonding of gold atoms with ligands.[24] For cluster sizes closer to our interest, based on the Au(X) cluster series (n = 6–9; X = PH3, PMe3, and PPh3),[25] a modified electron counting rule for delocalized electrons for charged phosphine-protected gold clusters: n* = NνA – M – z + CT, where CT means charge transfer, was proposed. For the case of the Au8(PH3)2+ (m = 7 and 8) clusters, this formula led them to calculate 7.7 and 7.2 delocalized valence electrons with Bader charges and 7.6 and 7.4 delocalized valence electrons with NPA charges, respectively. This means numbers differ from the number expected as calculated with the counting rule without the CT effect (n* = 6). Mollenhauer and Gaston mainly support this modification on the differences observed between the molecular orbital diagrams and projected local density of states of the bared clusters and the gold clusters protected by phosphine ligands. Nevertheless, more detailed information about molecular orbitals at energy levels below HOMO is needed for a complete electronic structure characterization, which is not achievable through the superatom model. Although other computational and theoretical works have studied ligand-protected clusters of different sizes[26,27] and have predicted the effect of ligands chemical composition[24] and orientation[22] on the electronic structure and stability, information about the influence of concentration and position of ligands in Au clusters on the electron transition variables and catalytic activity clusters has not been extensively reported.

In this work, we use DFT calculations with the hybrid exchange–correlation functional and effective core pseudopotentials (ECPs) to determine the geometry of bare and phosphine-protected Au8 nanoclusters and characterize their electronic structure. The electronic density of states (DOS), charge distributions, orbital occupation and energetics, electron affinities (EA), and ionization energies (IE) are calculated for the optimized structures, which were confirmed as minima.

Computational Methods

DFT calculations are performed as implemented in the Gaussian09 program.[28] M06[29] was chosen as the exchange–correlation functional, which belongs to the family of the generalized gradient approximation (GGA) that includes second derivatives of the electron density (meta-GGA).[30,31] This functional has been used in previous studies for the characterization of the Kohn–Sham wave functions of gold clusters[18] because its parameterization was carried out to represent chemical properties of transition metals.[32] The M06 functional has been also employed to describe activation energies for molecule oxidation on Au8 clusters, specifically.[33] Despite this article does not intend to evaluate activation energies, the prediction of the catalytic behavior is still a motivation to conduct this study. Therefore, M06 represents a proper choice that leaves a room for the continuity of this work. It is known that local spin-density approximation functionals predict better bond lengths in transition-metal dimers than GGA, meta-GGA, and hybrid functionals; however, they also significantly overestimate binding energies.[27] The DZ basis set with 9s and 5p primitive Gaussian functions (D95)[34] is selected to expand the electron wave functions for phosphorous and hydrogen atoms, whereas the Wood–Boring quasirelativistic pseudopotential (MWB)[35] is used to represent the core electrons of gold atoms, as defined by the Stuttgart–Dresden (SDD)[36−39] ECPs formalism. A very tight convergence criterion for the solution of linear equations is used along with self-consistent field iterations, while the ionic positions are optimized thorough the so-called “Berny” algorithm[40,41] with a tight force cutoff. Kick[42] software is used to generate potential-starting geometries of the bare Au8 cluster through a stochastic search over the potential energy surface (PES). A concise explanation of what the Kick code is and its main characteristics are detailed in the Supporting Information. The most stable geometry found for the bare Au8 cluster is initially optimized, and PH3 molecules are then put in the proximity of gold atoms in selected symmetrical positions. The gold atoms are classified as either two-fold (outer) and four-fold (inner) according to their coordination and position in the ground-state planar configuration of the Au8 cluster; thus, there is a maximum of eight binding sites in the planar bare cluster (four outer and four inner). In order to analyze the effect of ligand concentration and position, 4 × PH3 and 8 × PH3 ligands are bonded to the Au8 clusters; in the case of 4PH3, the four ligands are put close to either all outer or all inner binding sites and then optimized, whereas all binding sites (outer and inner) are occupied in the optimizations of clusters with 8PH3 ligands.

Although ligands as large as Ph2P(o-tolyl)[11] and PPh3[43,44] are employed to stabilize experimentally gold clusters, we chose the smaller PH3 ligand because it is suitable enough for mimicking the results expected with PPh3 as reported in previous studies.[45−47] For example, for Au(PX3) (X = H, Me, and Ph) systems, electronic parameters such as charge transfer and the HOMO–LUMO gap have been found with very similar values, demonstrating that the ligand change has nearly no influence on the cluster structure and nature. On the other hand, the steric stabilization provided by the phenyl part of triphenylphosphine is neglected by using PH3 ligands,[48] which in turn would require a better description of the dispersion due to π interactions. As a consequence, the binding energy changes up to 5 and 11 kcal/mol when the dispersion correction is included for neutral and plus one-charged Au–PPh3 and Au2PPh3 complexes.[48] However, we did not consider an additional dispersion correction for our DFT method because we were looking for structural changes and electronic behavior and qualitative energy trends.

The procedure is performed for bare and ligand-protected clusters with excess and lack of electrons in the systems with the purpose of analyzing the oxidation effect on the catalytic activity and for the calculation of ionization variables. Furthermore, the set of simulations was repeated for doubly charged systems (2+), with eight ligands and the two possible configurations for four ligands and with lack and excess of electrons for ionization energy (IE) and EA calculations. Ligand–cluster binding energies were also calculated for neutral and doubly ionized systems as Eb = (Esystem – (Ecluster + Eligand))/N, where N is the number of ligands. All energies included in the binding energy equation are obtained after a full optimization is performed and a global minimum is found. The binding energy calculated for charged ligand-protected clusters takes the optimized energy of the charged unprotected cluster as a reference along with the optimized energy for the neutral phosphine. Vibrational frequency calculations are performed to ensure that the minimized structures correspond to true minima.

The adiabatic IEs and EAs are calculated from the energies of the optimized structure of the reference system (Esystem) and the energies of the optimized clusters in excess or lack of one electron (+1e– and −1e–, respectively). This means that a new minimum is found in PES after an electron is added or removed from the reference systems. IE and EA are calculated according to the following equations

Results and Discussion

Bare Au8 Clusters

DFT calculations were performed initially on bare Au8 clusters; the initial geometry was set to be planar according to theoretical works reported elsewhere and conformational searches were performed through the methods implemented in Kick software for exploration of the PES.[42] After the total energy minimization, the ground-state configuration resulted in a planar configuration (D4) in agreement with previous reports.[5,6] The geometry of the optimized bare cluster is characterized by an inner set of atoms arranged in a four-fold hollow (square) configuration with sides of 2.865 Å, while the remaining four gold atoms relax outside the perimeter of the inner square with each outer gold atom lying equidistant (2.865 Å) to two inner gold atoms to form a three-fold hollow (triangle) (Figure a). The natural bond orbital (NBO) charge analysis represented in Figure a shows that despite the initial neutrality of the bare cluster, the negative charges are slightly shifted toward the core of the cluster, leaving the outer gold atoms with a small net positive charge. These results start hinting about possible stable binding sites for ligands because PH3 behaves as a nucleophile. Figure b shows the total electron DOS (TDOS) including the partial contribution of each type of orbital to the total density (PDOS). Unlike bulk gold, an energy gap between the HOMO and the LUMO is expected in small clusters such as Au8. This is observed in Figure b, where the TDOS line, and therefore all PDOS lines, vanish through the Fermi level opening a band gap of ∼2.8 eV; this feature is in agreement with reports demonstrating nonzero gaps for gold nanoclusters, which increase as the clusters become smaller.[21,22,49] As expected from the electron configuration of gold, the S type of orbitals represent a major contribution to the HOMO and LUMO, as seen from the red line approaching the black line at the HOMO energy level in Figure b. Conversely, the green line almost superimposes the black line in the range −12 to −7 eV, indicating that D orbitals have the greatest contribution at eigenvalues at lower energy levels. It can be observed from the inset of Figure b that both the HOMO (left) and LUMO (right) of the neutral Au8 cluster have a significant presence around the outer gold atoms, which defines potential sites to act as ligand receptors.

Figure 1

Bare Au8 cluster (a). Optimized structure, bond lengths, and NBO charges (b). TDOS and partial contribution of different type of orbitals. The original discrete DOS functions are broadened with a normalized Gaussian function with a full width at half-maximum value of 0.3 eV. The inset figures correspond to the HOMO (left) and LUMO (right) molecular orbitals.

Au8(PH3)4,8 Clusters

The optimized structure of the Au8 neutral cluster was used to investigate binding of different number of phosphine ligands to various binding sites, as shown in Figure . For all calculations, the PH3 ligands were initially placed with the P atoms lying within a bonding radius with Au atoms, with the H atoms pointing in the opposite direction. It was initially assumed that energy minimization through the PES would result in an overlap of Au and P atomic orbitals to form Au–P bonds. On the contrary, DFT optimizations showed that the formation of Au bonds depends on the concentration of ligands around the cluster and that the stability of the planar geometry of the neutral cluster is related to both the concentration and the binding sites of ligands surrounding the cluster. For instance, the Au8 cluster bonded to eight phosphine ligands (Au8(PH3)8) maintains the initial planar geometry. However, the phosphine ligands in the proximity of inner gold atoms lose the Au–P bond redefining the orientation of phosphine, with three of the four P atoms optimized to be pointing outward from the gold cluster (Figure ). The low stability of the inner position is confirmed by the optimized geometry of the Au8(PH3)4-inner, which causes a cluster core rearrangement to nonplanar geometry before phosphine could relax at the vicinity of gold atoms initially located at inner sites. In the case with the four ligands attached to outer binding sites (Au8(PH3)4-outer), there is negligible reorganization from the initial cluster geometry, and a great structural stability can be inferred from this symmetrical configuration with four ligands closely interacting with outer gold atoms (Figure ). The NBO charge distribution reported in Figure a already evidenced electrophilic binding sites at outer gold atoms. Thus, phosphine ligands with an unshared pair of electrons are attracted to these sites rather than more nucleophilic inner gold atoms, which explains the binding energy per ligand −0.76 eV obtained for Au8(PH3)4-outer, the most negative value found for neutral systems (Figure ). Furthermore, the presence of LUMO around outer Au and away of inner Au atoms (right inset in Figure b) provides insights about the instability of Au8(PH3)4-inner. Although it has been demonstrated that highly coordinated gold atoms can accept a lone pair of electrons from phosphine,[47] the high coordination of inner gold atoms leaves less empty states to be occupied by the free pair of electrons from PH3, compared to the outer gold atoms. This forces either phosphine ligands to relax at outer Au sites maintaining the cluster geometry or the cluster to reconstruct in order to find the ground state. This reconstruction lowers the energy significantly yielding a binding energy of −0.75 eV for Au8(PH3)4-inner, very similar to Au8(PH3)4-outer. At high concentration of ligands [i.e., Au8(PH3)8], the occupation of outer sites makes the inner sites very unstable, leading to a steric repulsion of ligands instead of a structural reconstruction of the planar cluster, as seen in Figure . The binding energy per ligand calculated for Au8(PH3)8 is consequently the less negative for the neutral systems, −0.58 eV.

Figure 2

Initial and optimized structures of Au8 clusters protected by PH3 ligands at different concentrations and positions. The charge of these systems is zero. Yellow spheres correspond to gold atoms, whereas orange and white spheres represent phosphorous and hydrogen atoms of the phosphine, respectively. Binding energies per ligand (Eb) are reported for each configuration.

It is worth noting that Au8(PH3)4-outer and Au8(PH3)4-inner clusters have very different structures but almost degenerated, the first one maintained the planar structure of the gold cluster but the second one is evidently 3D geometry. Then, the degeneracy should be expected to appear for different configurations at a saturated regime as observed in this case when four ligands are considered instead of the eight ligands to saturate the eight gold atoms. An example of the SH2 and PH3 ligand effect is reported by Guedes-Sobrinho et al.[47] in a DFT study of three configurations of Au55 and Pt55 nanoclusters: icosahedron (ICO), cuboctahedron, and the low-symmetry putative global minimum configuration, which has been called distorted reduced core (DRC). Interestingly, the DRC structure as the most stable at the gas phase becomes nearly degenerated in energy in comparison with the ICO structure when protected by 18 ligands, which they attributed to an enhancement in the stabilization induced by the release of the core strain energy.

The electron DOS decomposed into individual contributions of all atoms in Au8(PH3)4-outer and is plotted along with the total electron DOS (TDOS) in the Figure . The green line represents the overlap of the partial DOS (OPDOS) of phosphorous onto the gold. As seen in Figure , the HOMO has the Au–P antibonding character because the green line becomes negative at the HOMO energy level. The shape and location of the HOMO (inset molecular orbital at bottom) corresponds to an antibonding molecular orbital mainly located around the outer Au atoms and P atoms. The LUMO (inset molecular orbital at top-right), on the other hand, has the nonbonding character between gold atoms, which is confirmed by the OPDOS becoming zero at the LUMO energy level. The LUMO does not affect the bonding nature of the ligated cluster unless reduction takes place. Besides the HOMO, the electronic state of the HOMO – 1 also presents the antibonding character, as indicated by the negative green peak at about −5.5 eV in Figure . These two antibonding molecular orbitals are occupied, and one would expect the cluster to structurally collapse as a result but this does not occur after optimization. Nearly degenerate bonding molecular orbitals at lower energy levels are then responsible for keeping the structural integrity of Au8(PH3)4-outer, as inferred from the positive green peak between −10 and −11 eV. One of those molecular orbitals is shown in the inset of Figure (top left), where not only the bonding character between Au and P atoms is verified but also electron delocalization among gold atoms that provides a bonding interaction between outer and inner gold atoms and significant structural stability. Because these bonding orbitals are beneath the HOMO energy, it is expected that the structure of Au8(PH3)4-outer will maintain its highly symmetrical planar structure upon chemical oxidation because excitation from antibonding states will not affect the Au–P bonding interactions. Reduction, on the other hand, may cause some kind of structure deformation or Au bond stretch/breaking because nonbonding empty electron states would become filled or partially filled. The DOS plots for Au8(PH3)4-inner are reported in the Supporting Information and show the three Au–P antibonding states at the HOMOs (HOMO, HOMO – 1, and HOMO – 2); this supports the poor binding between Au and P in the inner configuration compared to the outer configuration in Au8(PH3)4.

Figure 3

Electron DOS for the optimized structure of Au8(PH3)4-outer. Inset molecular orbitals correspond to the bonding orbital 65 with an energy of ∼−10.70 eV (top left), the antibonding HOMO (bottom), and the LUMO (top right), showing nonbonding character between Au and P. The OPDOS (green line) represents the overlap DOS between the Au and P atoms.

The partial and TDDOS curves for Au8(PH3)8 are shown in Figure . The highest energy levels including the LUMO, the HOMO, and the state just under the HOMO are all antibonding between the Au and P atoms (i.e., the green OPDOS line is negative). Similar to Au8(PH3)4-outer, lower energy molecular orbitals are the ones responsible for holding the planar geometry of Au8(PH3)8 through strong binding between Au and P, and inner and outer Au. However, those energetically close states spread under the high TDOS peak in Figure (−11 to −9.5 eV) also present contributions from overlap of phosphorous and hydrogen molecular orbitals, as seen from the cyan and blue lines overlapping in that range. From the optimized structure of Au8(PH3)8 reported in Figure , it is inferred that only one of the inner phosphine ligands is forming a bond with a gold atom. This is confirmed by the inset molecular orbital shown in Figure at left bottom, which clearly showcases the bonding overlap between particular P and Au atoms and is supported by the green line becoming slightly positive at that energy level. No other bonding molecular orbitals involving inner phosphine ligands are seen, which confirms the instability of these binding sites, especially when outer positions have been filled. A second OPDOS is drawn in Figure , corresponding to the overlap of molecular orbitals of outer and inner gold atoms and aims to account for structure stability defined by Au-inner/Au-outer interactions. This purple line becomes positive at states near the HOMO, defining a bonding interaction between outer and inner gold. The density surface of the HOMO shown in the inset of Figure (top) indicates that this molecular orbital is indeed overlapping outer and inner gold atoms covering the three-fold hollow sites formed by two inner gold and one outer Au. The source of planar stability at high concentration of phosphine ligands might be related to the geometrical symmetry of this high energy molecular orbital, although it is necessary to remark that the purple line becomes negative between −5.5 and −8 eV defining antibonding interactions at lower energy levels.

Figure 4

Electron DOS for the optimized structure of Au8(PH3)8. Inset molecular orbitals correspond to the bonding orbital with an energy of ∼−10.50 eV (bottom left) and the antibonding HOMO (top).

Figure shows the electrostatic potential mapped onto the total electron density of the bare Au8 cluster and all three ligand-protected clusters. With a planar geometry of the Au atoms, the electronic charges are symmetrically distributed along the defined plane. The electrostatic potential surface for Au8 confirms the higher EA of outer gold atoms compared to Au atoms forming the inner square. The positive electrostatic potential represented by the dark blue regions delimits electrophilic zones, where the cluster is susceptible to chemical attack by nucleophiles such as phosphine. As discussed above, outer gold sites are the most stable sites for phosphine binding providing strong Au interaction and stabilizing the planar geometry. When the symmetrical planar structure is maintained, the charges coming from the unshared pair of electrons of phosphine distribute over the planar cluster creating nucleophilic areas at the hollow sites of the cluster, as shown by the red regions of the electrostatic potential of Au8(PH3)8 and Au8(PH3)4-outer in Figure . Neutral Au8(PH3)4-inner does not keep the symmetrical planar structure of the cluster with occupied outer sites, and therefore, its irregular binding behavior leads to a limited charge transfer from the ligand to the gold cluster. The smaller red region of the electrostatic potential of Au8(PH3)4-inner is indicative of less reduction of gold atoms upon interaction with phosphines in comparison with Au8(PH3)8 and Au8(PH3)4-outer. Furthermore, the surface profiles of the electrostatic potential reported in Figure also provide clues about the different chemical behavior that may exist among clusters with different concentrations and configurations of ligands. Planar ligand-protected clusters present a larger and more exposed negative region of the potential on which electrophiles, or positively charged species, can approach from perpendicular directions to the cluster plane. The surface of the planar clusters (Au8(PH3)8 and Au8(PH3)4-outer) becomes a reduction site capable of providing electrons, which principally come from the phosphine ligands. Consequently, it is expected that the ionization energy diminishes as the concentration of ligands bonded to gold atoms of the cluster increases, as will be discussed later. Au8(PH3)4-inner, on the other hand, presents a limited negative electrostatic potential sterically obstructed by ligands bonded to out-of-plane gold atoms, making it less active for reduction of molecules. However, it is important to remark the small range of the color map of the electrostatic potentials (−0.07 to 0.07), which evidences a not too strong potential but rather shows a slight charge redistribution as a consequence of Au–PH3 interactions.

Figure 5

Electrostatic potential mapped on the electron density surface of the bare Au8 cluster and all three ligand-protected clusters.

Doubly Ionized Au8(PH3)4,8 Clusters

The synthesis of phosphine-stabilized Au clusters in the liquid phase results in ionized clusters, an example being Au8(PPh3)82+[43] and Au8(PPh3)82+.[50] These structures have the gold atoms in 3D geometry; thus, Au8(PPh3)72+ exhibits an icosahedron-five-vertices shape, while Au8(PPh3)82+ shows a bicapped centered chair shape. The synthesis of the charged ligand-protected Au8 clusters with less number of ligands has led to clusters with six ligands such as [Au8(dppp)4Cl2]2+, dppp = 1,3-bis(diphenylphosphino)propane.[51] Its single-crystal X-ray diffraction analysis of the hexafluorophosphate salt revealed that the cluster core had di-edge-bridged bitetrahedral geometry. This permitted it to exhibit a prolate shape, which is in accordance with n* = 4. Besides, in 2013, Kobayashi et al. synthesized a series of [core + exo]-type Au8 clusters bearing two alkynyl ligands on the exo gold atoms [Au8(dppp)4(C≡CR)2]2+ by the reaction of [Au8(dppp)4]2+ with alkynyl anions.[52] The [Au8(dppp)4]2+ (dppp = 1,3-bis(diphenylphosphino)propane)[51] cluster synthetized for the first time by Kamei et al. founded that the cluster core adopted edge-shared tri-tetrahedral motifs based on the X-ray crystallographic analysis of its structure.[51] Calculating n*, its value is n* = 6; this is an oblate distortion explained by the s2p4 molecular orbitals according to the superatomic complex model.[23]

Despite the information above and the usual way to obtain the start geometries for modeling the charged ligand-protected clusters, that is, from the X-ray data, we choose to start from the neutral and flat gold structure.

In order to study the electron structure and predict the chemical behavior of ionized clusters, two electrons are removed from each one of the optimized neutral systems studied previously. The deficit of electrons results in a geometry modification of Au8(PH3)8, which is not observed in the corresponding neutral system (Figure ). The lack of two electrons and the consequential inoccupation of the HOMO produce a gold cluster prone to lose its planar stability in the presence of phosphine ligands at unstable binding sites, which is supported by recent studies with Au4 where the positive charge induces 2D–3D geometry transitions.[53] This result is expected from the analysis of DOS and molecular orbitals of the equivalent neutral clusters. Figure shows the HOMO as a bonding molecular orbital between outer and inner Au, whereas the rest of overlap states (purple line) correspond to nonbonding or antibonding orbitals. Losing two electrons results in total inoccupation of the bonding HOMO and the consequential loss of structural symmetry in Au8(PH3)8. The high stability of Au8(PH3)4-outer is proven as its geometry remains unaltered by the positive charge. The high bonding character between gold molecular orbitals at low energy levels (−10.70 eV) shown in Figure contributes to maintain the symmetrical planar structure of Au8(PH3)4-outer upon ionization. Similar to the neutral systems, the outer configuration produces the lowest Au–PH3 binding energy among all charged ligand-protected clusters, with −2.29 eV, as shown in Figure . Conversely, the charged Au8(PH3)4-inner cluster keeps planar geometry slightly different from the initial configuration but with most of phosphines optimizing attached to outer gold atoms or with inner gold atoms moving closer to the phosphine to stabilize the Au–P bond at inner positions (Figure ). The charged inner configuration produces a higher binding energy per ligand (−1.97 eV) compared to the outer configuration but still lower than the binding energy per ligand of Au8(PH3)8 (−1.71 eV). As described earlier, the binding energy of charged systems is calculated, taking the energy of the charged unprotected cluster as a reference along with the energy of the neutral phosphine. This calculation represents a fair approximation to the exact binding energy because the two electrons removed from the ligand-protected clusters come principally from gold atoms, resulting in a net loss of nearly two electrons in the metal cluster (Figure ). This approach is also in agreement with previous computational studies for ligand-protected Au clusters.[11,54]

Figure 6

Optimized structures of charged ligand-protected clusters. The binding energies per ligands (Eb) are reported for each configuration.

Figure 7

NBO charges for neutral (top) and charged (bottom) ligand-protected Au8 clusters.

Although our approximation does not follow the common way to obtain the initial structure of the charged ligand-protected clusters, that is, from the X-ray data, the particular distances Au–Au and Au–P agree very well with the reported values from the X-ray data, see Table . However, the bicapped centered chair shape was not obtained, but a 3D geometry of the gold core was characterized. It is also worth noting that our % error is smaller in comparison with these specific results found by Mollenhaueer and Gaston who optimized the same type of the cluster but with triphenylphosphine.

Table 1

Selected Structural Parameters of the Au8(PH3)82+ Cluster and Their Comparison with X-ray Data

	data from this study		data from ref (25)		experimental data (ref (50))
	Au8(PH3)82+	% errora	Au8(PH3)82+a	% errora	Au8(PH3)82+b
Av. Au–Au	2.87 (−0.01)	0.3	2.78 (−0.10)	3.5	2.88
Min. Au–Au	2.69 (−0.03)	1.1	2.75 (0.03)	1.1	2.72
Max. Au–Au	3.13 (0.13)	4.3	2.85 (−0.15)	5.0	3.00
Av. Au–P	2.50 (0.01)	0.4	2.36 (−0.13)	5.2	2.49
Min. Au–P	2.49 (0.03)	1.2	2.34 (−0.12)	4.9	2.46
Max. Au–P	2.52 (−0.04)	1.6	2.44 (−0.12)	4.7	2.56

% error = (|computational data – X-ray data|/X-ray data) × 100.

Structural data of the optimized Au8(PH3)82+ cluster of ref (25).

X-ray data available at ref (50). Av., Min., and Max. represent mean average, minimum and maximum, respectively. Data between parentheses correspond to the difference between the data reported in a given column and the experimental data reported in the sixth column.

The NBO analysis of charges in Figure provides useful information about the effect of ligands on the potential chemical reactivity of Au8. As mentioned above, the ionization that results from the liquid phase synthesis comes principally from the oxidation of gold atoms, which become electrophilic centers prone to accept electrons from nucleophilic molecules. Furthermore, differences in the coordination number of these positively charged atoms define their EA and reactivity. Four phosphine ligands in inner positions result in the displacement of three ligands toward two of the four outer gold atoms [see Au8(PH3)42+-inner in Figure ]. This displacement leads to an increase in coordination of outer gold atoms, producing three and four coordination sites for outer gold atoms that initially had two coordination sites. Outer gold atoms that remained two-coordinate exhibited the most positive charge in the cluster (see Au8(PH3)42+-inner in Figure ), which turn them into a potential spot for adsorption of nucleophiles and electron transfer. Conversely, four ligands in outer configuration (see Au8(PH3)42+-outer in Figure ) relax at the initial positions increasing the coordination to outer gold atoms from two to three and creating a steric obstruction for axial binding of approaching molecules. Au8(PH3)42+-outer is expected to have a lower reactivity compared to Au8(PH3)42+-inner because the electron transfer pathways are enhanced in the inner configurations. The higher concentration of phosphine ligands provides the electrons to convert Au8(PH3)82+ into a less positive and nonplanar cluster with higher coordination of all its gold atoms. Therefore, the NBO charge analysis suggest that Au8(PH3)82+ is a weaker oxidizing agent than Au8(PH3)42+, regardless of the structural configuration. This information is supported by the electrostatic maps in the Supporting Information (Figure S2) in which positive charges are more homogeneously distributed than in Au8(PH3)42+, with Au8(PH3)42+-inner exhibiting the sharpest positive charge distribution among all the charged clusters and positive electrostatic zones around low-coordinated gold atoms. Similarly, the Mulliken population analysis reported in Figure S3 shows a qualitative agreement with the NBO charges, supporting the analysis of potential binding sites on charged clusters.

Figure shows the electron density space of the HOMO (Figure a) and LUMO (Figure b) for the three charged clusters. The occupation of energy levels by remaining electrons determines the stability and activity of positively charged nanoclusters. According to the representation of the HOMO of Au8(PH3)42+-outer (Figure a), there is significant electron delocalization among outer and inner gold atoms which holds the symmetrical planar geometry and provides stability to charged Au8. The LUMO of Au8(PH3)42+-outer (Figure b), related to the EA, is mainly localized around outer gold atoms. However, the outer atoms are protected by PH3 ligands in this configuration, and a lower reactivity is expected because of steric obstruction for nucleophiles approaching the protected outer gold atoms. The HOMO (Figure a) and LUMO (Figure b) of Au8(PH3)42+-inner, has significant electron density around the lowest coordinated gold atoms, which were shown to keep the most positive charge. The low bond order along with the positive charge and lack of steric obstruction by PH3 ligands predicts a higher activity for oxidation for the inner configuration of the charged ligand-protected Au8. Molecules with unshared pairs of electrons approaching Au8(PH3)42+-inner will have the chance to form bonds by filling unoccupied molecular orbitals. Au8(PH3)82+ loses planar geometry and finds stability with large electron delocalization among gold atoms at the HOMO energy level [Au8(PH3)82+ in Figure a]. The LUMO of Au8(PH3)82+ (Figure b) presents high bonding overlap among gold atoms and antibonding Au–P overlap; this is also seen in the OPDOS in Figure (vide infra). The location of this molecular orbital has no easy access for approaching molecules that are willing to provide electrons because all PH3 ligands are bonded to each one of the gold atoms in a nonplanar configuration, creating a three-dimensional steric barrier. This is contrary to what is seen in neutral Au8(PH3)8, which has a planar configuration and PH3 ligands do not hinder species approaching the cluster from a normal direction to the plane. At the HOMO energy level, there is nonbonding and antibonding behavior evident between gold and phosphorous atoms, which suggest Au–P bonding orbitals are occupied at lower energy levels as occurs in the case of neutral ligand-protected clusters.

Figure 8

Molecular orbitals of charged ligand-protected Au8 clusters: (a) HOMO and (b) LUMO.

Figure 9

Total (black line), partial (Au: red line, P: blue line, H: cyan line), and overlap (OPDOS) partial DOS for charged ligand-protected Au8 clusters. The OPDOS (green line) represents the overlap DOS between the Au and P atoms.

The plot of the electron DOS reported in Figure shows the positive overlap of Au and P molecular orbitals at low energy levels for all charged ligand-protected clusters, as seen by the green line becoming positive well below the HOMO energy level (between −19 and −15 eV). This orbital overlap confirms the strong bonding between gold and phosphorous as a result of metal oxidation and increase of electrostatic interaction. As in Figure , the vertical dashed and dash-dotted lines in Figure show the location of the HOMO and the LUMO, respectively. It is noted that both the HOMO and LUMO are shifted toward lower (more negative) energy levels as the concentration of ligands also decrease, finding a minimum at the bare Au82+ cluster.

Charge Transfer and Its Relationship with the Cluster Stability

Employing the modified electron counting rule for delocalized electrons for charged phosphine-protected gold clusters proposed by Mollenhauer and Gaston,[25] the charge transfer was calculated for every analyzed system. The charge transfer from the ligand shell to the cluster is the lost charge by all phosphine molecules, see Table . As usually found, the atomic charge distribution depends on the method used. For example, the charge transfers calculated with NBO are bigger than the values obtained with Mulliken. However, the general analysis of the charge transfer, and therefore of the delocalized electrons and its relationship with the cluster stability, is mostly the same for both methods. As expected, the charged transfer was bigger in charged systems than in the corresponding neutral systems. Thus, the more the negative binding energy (more stable) was, more charge was transferred. Regarding the delocalized electron number, the expected numbers were n* = 8 and n* = 6 for neutral and charged systems because the phosphine ligand effect is considered only as steric stabilization. Nonetheless, considering the charge transfer, those numbers become different to whole numbers and higher than 8 or 6 and in all cases. We found a very similar value for the delocalized electron number (n* = 7.1, considering Mulliken charges) for Au8(PH8)2+ in comparison with the value calculated by Mollenhauer and Gaston (n* = 7.2, considering Bader charges). Then, it is possible to infer that the charge transfer mostly depends on the ligand numbers and the cluster charge more than on the observed specific 3D gold arrangement. It was also observed by Guedes-Sobrinho et al.[47] who explained the same stability of Au55 and Pt55 nanoclusters at the limit of 18 ligands (DRC and ICO structure) based on the charge transfer from phosphine ligands to the metal cluster as mentioned above.

Table 2

Employment of the Modified Counting Rule Proposed by Mollenhauer and Gaston[25]a

Mulliken				NBO
	CT	n*b	total Eb		CT	n*	total Eb
Au8(PH3)8	0.24	8.2	–4.6	Au8(PH3)8	0.86	8.9	–4.6
Au8(PH3)4-outer	0.02	8.0	–3.0	Au8(PH3)4-outer	0.67	8.7	–3.0
Au8(PH3)4-inner	0.07	8.1	–3.0	Au8(PH3)4-inner	0.79	8.8	–3.0
Au8(PH3)82+	1.06	7.1	–13.7	Au8(PH3)82+	2.15	8.2	–13.7
Au8(PH3)42+-outer	1.08	7.1	–9.2	Au8(PH3)42+-outer	1.30	7.3	–9.2
Au8(PH3)42+-inner	1.00	7.0	–7.9	Au8(PH3)42+-inner	1.45	7.5	–7.9

CT = charge transfer (in e), n* = delocalized electrons, and total Eb = total binding energy (in eV).

n* = NνA – M – z + CT. N = 8, νA = 1, M = 0, z = 0 or +2. See the explanation of these values in the text.

IEs and EAs

There is an intrinsic relationship between the energy values of molecular orbitals neighboring the Fermi level and some electron transition variables. The negative of the HOMO energy level is related to the vertical IE, whereas the negative of the LUMO energy approximates to the vertical EA.[55] Unlike, the adiabatic electron transition energies calculated by eqs and 2, the vertical IEs and EAs would be obtained from single-point calculations of systems with excess or lack of electrons. As seen from Figure and Table , the negative of LUMO energy of the cluster (related to the vertical EA) increases as the concentration of ligands decreases; this indicates that a stronger activity for oxidation is expected for lower ligand concentration and even stronger for the bare charged clusters. On the other hand, as the concentration of ligands increases, the negative of HOMO energy (related to the vertical IE) becomes lower, which means that less energy is required to remove an electron from the ligand-protected cluster, turning the cluster into a potentially active catalyst for reduction of electrophiles. It is important to remark that at some concentration of ligands (Au8(PH3)42+), the inner configuration presents a higher adiabatic EA than the outer configuration, which is expected from the higher concentration of low-coordinated and positively charged gold atoms present in the inner configuration, as reported in Figure . These results suggest that a less stable configuration might have better chemical reactivity if we consider that the outer configuration presents stronger Au–P binding. However, there is a negligible difference between the IEs of both structural configurations of Au8(PH3)42+, which means the band gap also differs from outer to inner configuration, as seen in Figure and Table .

Table 3

Thermodynamic Data Calculated for Neutral and Ionized Au8 Clusters

	Eg (eV)a	–EHOMO (eV)b	–ELUMO (eV)c	IE (eV)d	EA (eV)e
Neutral
Au8(PH3)8	2.594	4.231	1.637	4.977	1.100
Au8(PH3)4-outer	2.414	4.355	1.941	5.282	0.990
Au8(PH3)4-inner	2.783	4.708	1.924	5.265	1.191
Au8	2.809	6.551	3.742	7.826	2.678
Charged
Au8(PH3)82+	3.239	9.973	6.733	10.399	6.010
Au8(PH3)42+-outer	2.723	11.549	8.827	12.576	7.973
Au8(PH3)42+-inner	1.893	11.427	9.534	12.380	8.598
Au82+	1.705	14.516	12.811	14.287	11.519

HOMO–LUMO gap.

Negative of the HOMO energy.

Negative of the LUMO energy.

Adiabatic ionization IE calculated with eq .

Adiabatic EA calculated with eq .

The HOMO–LUMO gap values for charged and neutral systems are reported in Table . The band gap values show an increasing conducting behavior in charged clusters as the concentration of ligands decreases. For neutral clusters, on the contrary, the band gap drops as ligand concentration increases, only if Au8(PH3)4 takes the inner configuration; however, neutral Au8(PH3)4-outer is the most stable of both Au8(PH3)4 configurations, and it yields the lowest band gap among all protected and unprotected neutral clusters. HOMO–LUMO gaps are more related to optical properties and electron conductivity than reactivity. The energy values of HOMO and LUMO by themselves provide more information about reactivity and capacity to transfer and absorb electrons. The second and third columns in Table report the negative of HOMO and LUMO, respectively. In general, the HOMO and LUMO present lower values for neutral clusters than for charged ones. This is explained from the amount of energy required to remove an electron from a neutral cluster, which should be lower than the energy to remove an electron from a positively charged system. Also, the amount of energy released upon electron absorption is expected to be larger for positively charged clusters in comparison with neutral ones. Adiabatic IEs and adiabatic EAs were also calculated and reported in the columns 4 and 5 of Table . As noted from the values reported for neutral systems, IE and EA are comparable to negative HOMO and LUMO, respectively. As seen from the data reported in Table , adiabatic electron transition variables and HOMO–LUMO energies yielded quite similar values, supporting the previous analysis of IE and EA as a function of concentration and configuration of ligands. The minimization of doubly charged clusters over the PES does not alter the qualitative general trend of increasing EA and IE as the concentration of ligands decreases. For Au8(PH3)42+ clusters, the inner configuration presented higher adiabatic EA, as expected from the negative values of the LUMO (i.e., vertical EAs). As mentioned above, the high EA is associated to the high concentration of low coordinated and positively charged gold atoms in a nonplanar configuration. This leads to the conclusion that the chemical reactivity of gold nanoclusters can be modified with specific ligand decorations, enforcing different cluster geometries and charge distributions. Theoretical results herein reported demonstrate that the electronic behavior and the capacity of small gold nanoclusters to absorb or donate electrons are influenced by the presence of phosphine ligands, their concentration, and spatial configuration. Therefore, it can be stated that the chemical activity of gold clusters can be altered thorough specific synthesis procedures in which the concentration of phosphine ligands is controlled.

Conclusions

DFT calculations were performed over neutral and charged Au8 clusters with phosphine ligands added at different concentrations and configurations. The bare neutral Au8 cluster has planar geometry with two- and four-folded gold atoms, with slight negative charges concentrating at two-coordinated atoms located at the outside corners of the planar cluster. These sites become centers of ligand binding as the phosphine transfers an unshared pair of electrons to the electrophilic corners of the cluster. The charge distribution in the unprotected neutral cluster hints that the binding behavior between clusters and four PH3 ligands in the outer configuration is the most stable ligand-protected cluster with the strongest binding per ligand. The strong binding stability was evidenced by the planar geometry kept by the Au8(PH3)4-outer cluster and confirmed by analyses of charge, electron density of molecular orbitals, and electronic DOS. In the cases where clusters maintained planar geometry, electrons provided by ligands distributed along the cluster plane located at hollow sites formed by gold atoms, making the clusters more nucleophilic. The energy degenerance for very different neutral structures was observed (outer and inner), but when those ligand-protected clusters were charged, the degenerance was lost; although in that case, the gold cluster structure remains very similar to the flat structure of the neutral Au8 cluster. Ionizing the ligand-protected cluster resulted in oxidation of gold atoms and destabilization of the planar geometry in the case of highest concentration of ligands due to the inoccupation of Au–Au bonding states at the HOMO energy level. Adiabatic IEs and EAs showed that both variables are higher for charged systems, as expected, and are consistent with HOMO and LUMO energies, respectively. Furthermore, it was shown that IE and EA decrease as the concentration of ligands increases in both charged and neutral clusters. These results provide the theoretical support to guide experimental strategies to adjust the electron density behavior of gold-based clusters, and therefore, their chemical activity.