Article pubs.acs.org/JPCA
Superatomic S2 Silver Clusters Stabilized by a Thiolate−Phosphine Monolayer: Insight into Electronic and Optical Properties of Ag14(SC6H3F2)12(PPh3)8 and Ag16(SC6H3F2)14(DPPE)4 Lars Gell,† Lauri Lehtovaara,† and Hannu Hak̈ kinen*,†,‡ †
Department of Chemistry, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland
‡
S Supporting Information *
ABSTRACT: The electronic structure of two recently crystallographically solved, thiolate−phosphine protected silver clusters Ag14 and Ag16 are analyzed via density functional theory (DFT) and their optical excitations are analyzed from timedependent DFT perturbation theory. Both clusters can be characterized as having the S2 free-electron configuration in the metal core, which is the first time such a configuration is confirmed for structurally known ligand-protected noble metal clusters. However, their different core shapes and ligand layer induce significantly different optical spectra. Performance of gradient-corrected DFT functionals is discussed and it is shown that the asymptotically correct Leeuwen−Baerends LB94 functional reproduces the optical spectrum of Ag14 in a good agreement with experiment. Choice of the functional becomes important for clusters where the optical transitions are dominated by the electron-rich ligand layer.
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systems is very general; it was first introduced in the theory of nuclear structure in 1950s19−21 and later for electron clusters in semiconductor quantum dots in 1980s.22 These concepts were extended to monolayer-protected noble metal clusters in 2008 via an analysis of several then-known crystal structures of thiolate (SR), thiolate−phosphine (SR− PR3), and halide−phosphine (X−PR3) stabilized gold clusters.4,5 A formal count of free-electrons left in the metal core can be obtained by a very simple formula where each gold atom is considered as s-monovalent and each thiolate or halide as one-electron withdrawing ligand. The total charge of the cluster, if nonzero, needs also to be taken into account.5 Several new crystal structures of Aux(SR)y clusters have been reported after 2008, and many of them show nonspherically deformed metal cores with free electron numbers altered from the spherical magic numbers by geometry (for recent reviews see refs 23 and 24). The stability of the Aux(SR)y clusters is determined by a combination of electronic structure, atom packing, and the chemical and steric ability of the organic surface to block oxidation. The free-electron counting scheme of ref 5 has been shown to work also for main group metals; e.g., the structurally known cluster Al50Cp*12 (Cp* = pentamethyl cyclopentadienyl C5Me5)25 was shown to have a spherical shell filling up to 138 electrons with the highest
INTRODUCTION Understanding how size, shape, and composition affect physical and chemical properties of metal nanoclusters stabilized by a ligand monolayer has been a long-standing major challenge in materials chemistry.1−8 Although certain “magic-size” bare metal clusters display reduced activity for surface reactions in the gas phase,2 virtually any metal particles of nanometer-size dimension remain reactive and will ultimately coalesce to larger colloidal particles or will be oxidized in ambient conditions. To keep the particles in highly dispersed form, the reactive surface has to be passivated by a molecular overlayer of suitable ligands. Such chemistry is well developed for many transition, noble, and main group metals. The existence of free electrons in metals leads to prominent quantum confinement effects depending on the size and shape of the confining potential. The ensuing electron shell structure has given rise to the “superatom” concept, where enhanced shell effects and energy gaps between degenerate shells have been observed in gas-phase metal clusters leading to an enhanced electronic stability of the magic clusters.9−13 The concept was modeled first with spherical electron-gas (“jellium”) models14,15 where shell closing numbers correspond to filling angular momentum shells in the order of 1S2 1P6 1D10 2S2 1F14 2P6 1G18 ... giving rise to the magic electron number series 2, 8, 18, 20, 34, 40, 58, .... Changes in shape and dimensionality of the problem give rise to other magic electron numbers, such as 6 and 12 for 2D systems and 14 for a strongly prolate-deformed 3D system.16−18 Inclusion of atomistic structure introduces additional effects for clusters of freeelectron metals. The concept of shell structure in fermionic © XXXX American Chemical Society
Special Issue: A. W. Castleman, Jr. Festschrift Received: February 3, 2014 Revised: March 4, 2014
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dx.doi.org/10.1021/jp501185q | J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Figure 1. Structure of the PBE-optimized (a) Ag14(SC6H3F2)12(PPh3)8 (1) and (b) Ag16(SC6H3F2)14(DPPE)8 (2) clusters. Both clusters may be described as having a Ag6 core, but the overall symmetry of 2 is lower than that of 1. Although the octahedral core of 1 is clearly visible in (a), the core of 2 in (b) is best described as a planar four-atom rhombus capped below by two additional silver atoms. Colors: Ag, gray; S, yellow; P, green; organic rest, cyan sticks.
Optimization was performed without any symmetry constraints until the residual forces on each atom were below 0.05 eV/Å. Angular momentum resolved projected density of states analysis was performed by projection of the Kohn−Sham orbitals to the center of mass of the clusters (projected density of states, PDOS).5 Optical absorption was calculated from the linear response time-dependent DFT (LR-TDDFT) as implemented in GPAW.39 Both PBE and LB94 functionals40 were used to evaluate the transition matrix. Individual absorption lines were folded into smooth spectra with a Gaussian broadening of 0.05 eV. The analysis of optical transitions was done using a recently developed method based on time dependent density functional perturbation theory TD‑DFPT.33,41 This allows for decomposition of a spectral feature (peak, shoulder) to contributions from individual particle-hole transitions in the Kohn−Sham basis (transition contribution map, TCM) as well as for a spatial visualization of the particle and hole densities involved in a particular spectral feature.
occupied shell having a significantly high angular momentum number L = 6.26 This count is obtained by considering the 3valent s2p-character of aluminum and the tendency of each Cp* ligand to withdraw one electron from the metal core. Thiolate-stabilized silver nanoclusters have been synthesized for several years as well, although their atomic-level characterization has been challenging due to the less-noble chemical character of silver that makes it more prone to oxidation than gold and induces degradation of the clusters during mass spectrometry or over prolonged times in ambient conditions.27−30 In 2013, the group of Nanfeng Zheng resolved successfully several silver cluster compounds protected by SR− PR3 or pure SR monolayer.31−33 Among them the Ag44(SR)304− cluster displayed a series of similar Keplerate M32 core structures with variant fluorinated arylthiols; additionally, gold−silver intermetallic compounds Au12Ag32(SR)304− were resolved as well. Each of those compounds fulfilled the 1S2 1P6 1D10 (18-electron) shell-filling rule of superatoms.33 Here we analyze (1) Ag14(SC6H3F2)12(PPh3)8 and (2) Ag16(SC6H3F2)14(DPPE)8 (DPPE = 1,2-bis(diphenylphosphino)ethane) that were among the first ligand-stabilized silver clusters that were structurally solved in 2013,31,32 and establish their electronic structure having an S2 type configuration of free electrons in the metal core, as expected from the counting rule.5 The optical absorption is calculated and compared to the experimental data, and the transitions are analyzed. It is shown that the long-range corrected LB94 functional is needed for realistic description of the optical spectrum in these clusters where the ratio of “active” free electrons in the metal core is low and the excitations are dominated by the electron-rich ligand layer. As far as we know, this is the first time when the smallest nontrivial shell-filling count of 2 free electrons is confirmed for a structurally known monolayer-protected noble metal cluster, although 2-electron systems have been suggested from earlier theoretical work for other metal−ligand compositions.34,35
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RESULTS AND DISCUSSION PBE-optimized structures of 1 and 2 are shown in Figure 1. In agreement with the structural interpretation from the crystal structure,31 the metal arrangement of 1 consists of two silver shells: an octahedral Ag6 shell inside a cubic Ag8. This arrangement of the silver atoms is remarkably similar to the conventional Ag14 unit cell of a face-centered cubic (fcc) crystal that is also the known bulk lattice structure of silver. The 12 thiolates passivate the 12 edges of the Ag8 cube in somewhat distorted fashion. The first-shell and second-shell silver atoms are coordinated to two and three thiolates, respectively. The eight PPh3 groups passivate the vertices of the Ag8 cube. The Ag−Ag bond lengths in the first shell are within 2.85−2.90 Å, with the average of 2.88 Å, slightly longer than 2.84 Å observed in the crystal structure (Table 1). This 1.5% overestimation of metal−metal bonds is typical for the PBE approximation. The Ag−S and Ag−P bonds are overestimated by 1−2% as well. Similar agreement between calculated and observed atom− atom distances is found also for cluster 2 (Table 1). This structure was described initially as having a low-symmetry Ag8 core with a nominal charge of 6+.32 Our analysis on the electronic states (discussed below) will show that the core is best described as Ag6 with a nominal charge of 4+, a planar four-atom rhombus capped below by two additional silver atoms, as shown in Figure 1b. Though clusters 1 and 2 are of
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COMPUTATIONAL METHODS We used density-functional theory (DFT) with projector augmented waves (PAW) as implemented in the real-space grid code GPAW.36,37 Scalar-relativistic effects for silver are included in the PAW setup. Total energy calculations and structural optimization of the clusters were done with the PBE exchange−correlation functional,38 and the wave function and electron density were evaluated with a grid spacing of 0.2 Å. B
dx.doi.org/10.1021/jp501185q | J. Phys. Chem. A XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry A
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The computed energy gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO−LUMO gap) are 1.8 eV (690 nm) for 1 and 1.7 eV (730 nm) for 2. The large gaps reflect the small size, strong electron confinement, and molecular nature of the clusters. The projection of the single-particle density of states to angular momentum components reveals that the HOMO state of both 1 and 2 is of “superatomic” S-symmetry and localized mainly in the metal core (Figure 3), whereas the LUMO state has a different character in these clusters: the LUMO of 1 is a ligand state, whereas the LUMO of 2 is one of the metal-core superatomic P-orbitals. To get further insight into the character of the optical transitions of 1, we used time dependent density functional
Table 1. Characteristics Bond Lengths (Average Values, Å) in Clusters 1 and 2, Both from the Crystal Structure and for the Computed Relaxed Structures 1 1 2 2
(calculated, (crystal, ref (calculated, (crystal, ref
PBE) 31) PBE) 32)
Ag−Ag (core)
Ag−S
Ag−P
2.882 2.837 2.854 2.806
2.675 2.612 2.629 2.580
2.516 2.480 2.475 2.436
very similar overall size, their significantly different structures highlight the importance of the ligand shell, in particular the effects of the DPPE ligands in 2. Although the counting5 of free Ag(4s) derived delocalized electrons in the clusters will give the same number (2 electrons) for both 1 and 2, their different geometric structure and ligand shell give rise to differences in the electronic structure and optical properties, as will be shown next. Because both clusters have a rather small metal core and electron-rich ligands shells (phenyl rings both in thiolates and in phosphines), the ligand shell is expected to be involved in most of the optical transitions inducing potential chargetransfer character. It is well-known that the standard gradient corrected functionals such as PBE are usually inadequate to describe charge-transfer excitations; thus we compared the spectra computed by using PBE to those obtained from the asymptotically correct LB94 functional40 that is expected to perform better. The comparison of the PBE and LB94 spectra of both 1 and 2 is shown in Figure S1 (Supporting Information). Though the PBE and LB94 spectra are quite similar for 2, there are clear differences in the spectra for 1. Figure 2 compares the computed LB94 spectrum of 1 to the
Figure 3. Transition contribution map (TCM), electron state analysis, and particle−hole densities of the two prominent absorption features in the calculated LB94 optical spectrum of 1. (a) and (b) show the analysis of the features at 500 and 371 nm, respectively, shown by the arrows in the bottom right panels. Bottom horizontal and right vertical panels show the angular momentum analysis (projected density of states, PDOS) of the occupied (negative energies) and unoccupied (positive energies) electron states, respectively. The color coding of the PDOS analysis is shown in (b). The HOMO state is dominantly in the metal core and is of S-symmetry. The 4d-band of silver is found for energies
