Work based on this was published as
Chemical Physics Letters Vol 192, Number 1, p 122. 24 April 1992
Electronic and Geometric Structure in Silver Clusters
George Alameddin, Joanna Hunter, Douglas Cameron
and Manfred M. Kappes
Northwestern University, Department of Chemistry, Evanston, IL 60208, USA
One-photon ionization mass spectra were recorded for silver clusters (generated by pulsed laser vaporization) throughout the 4.92 to 5.96 eV energy range. Results include: (i) the observation of electronic structure effects to Agx, x<440 and (ii) the determination of vertical ionization potentials for most x<100 and x=138. Data are discussed in terms of various model calculations incorporating particle-size-dependent electronic/geometric structure and compared to analogous measurements of cold sodium and copper clusters.
Among metal clusters, understanding of particle-size-dependent electronic structure effects is most extensive for light alkalis - due to particular experimental the theoretical tractability [1,2]. The coinage metals can be regarded to first order as d-shell perturbed s1-electron clusters and therefore much of the semi-quantitative theoretical formalism used for alkalis can still be applied to them . On the other hand, there is presently much interest in developing predictive level quantum theoretical descriptions of the ground and excited states of these and more complicated transition metal clusters . A number of pioneering experiments resolving the details of electronic and geometric structure, notably photo-detachment spectroscopy from mass selected anions  and photodissociation spectroscopy on mass selected cluster cations  have already provided useful input. In contrast, comparatively little particle specific information has been available for neutral coinage metal clusters in gas-phase, excepting ionization potential brackets for small clusters [7,8], limited laser spectroscopy on a number of trimers [9,10] and Cux reactivity probes . Here we present IP determinations for silver clusters over a significantly wider particle size range than previously accessed. A companion paper presents photoionization probes of cold copper clusters in a similar size range .
A two stage differentially pumped molecular beam machine containing cluster source and detector chambers, separated by an externally positionable skimmer, was used in these experiments. Silver clusters were generated by laser vaporization  using a General Valve Series 9 pulsed valve modified for low temperature operation and run a 10 pps with helium, helium/argon, argon, nitrogen, helium/nitrogen or neon carrier gas at 10 bar . Target rods or foils of silver with natural isotopic distribution were vaporized by focused excimer laser (308 nm, 17 mJ/pulse, 10 ns pulsewidth) irradiation. Various conical nozzle and extender tube geometries were used. To generate clusters at a number of different internal excitation levels, nozzles were surrounded by a flow-through cooling mantle. When flowing liquid N2 through this, clusters formed using helium/argon (5%), argon or pure nitrogen expansions were cold enough to manifest extensive carrier gas complexation . There was no indication of such complexation for room temperature source operation.
Pulsed neutral beams were collimated by a 1 mm diameter 30o cone angle skimmer, approximately 5 cm downstream from the nozzle. Ions formed in the source were deflected off the beam center line by a 2 cm2 metal plate at a potential of -50V mounted 5 mm away from the molecular beam axis downstream from the skimmer. Neutral silver clusters were ionized with BBO I and II frequency-doubled excimer-pumped dye laser radiation. Resulting ions were detected with a 1 m drift tube Wiley-McLaren TOFMS oriented collinear to the neutral beam and equipped with dual microchannel plates. After preamplification, ion counts were read into a PC 386-based multichannel scaler board having 50 ns channel width.
Necessary digital delays were generated with an SRS DG535 variable delay generation. Other dimensional quantities of interest were: 58 cm physical separation between cluster source and detector ionization region and for room temperature source operation: 350 µs lag time between valve trigger and its opening; typical valve open times of 210 µs; 100-200 µs delays between valve opening and vaporization laser trigger; typical <50 ns firing delays between laser trigger and light emission with a superposed <50 ns jitter (for both vaporization and ionization excimers); 400-500 µs pulsed beam temporal widths at the detector ion source (comprising a <100 µs wide metal cluster bearing part) and about 420-440 µs (for He carrier) delay between vaporization and ionization laser triggers. The UV ionization laser was typically focused into the TOFMS ion source with a 20 cm focal length lens. Part of the incident ionizing radiation was split off to a fast photodiode which in turn triggered the mass spectrometer time base. Typical mass spectra were the result of 2000 pulse iterations.
Ionization laser fluence was kept below the threshold for multiphoton ionization as determined in previous studies of related transition metals . Given the collinear orientation of the TOFMS, ion arrival times at the multichannel plates following the ionization pulse depend also on neutral beam velocity. In converting ion arrival times into a linear mass scale we used a non-linear least squares fit procedure based on the electrostatic equations describing ion flight times for our experimental configuration. The assumption of equivalent velocity for all clusters simultaneously ionized was found to be adequate (within the limitations imposed by the isotropic distribution and the time resolution of the multichannel scaler) by comparing extrapolated to observed ion arrival times for large clusters (x<150). Note that this assumption does not negate clusters-size-dependent velocity slip effects which were observed .
All ionization potentials were determined using helium seed gas for which the heaviest detectable photo-ion signals corresponded to a cluster size of x = 200.
3.1 Mass spectra
Figures 1 and 2 show typical silver mass spectra obtained under a variety of source an ionization conditions. The underlying neutral abundances are likely near monotonically varying functions of particle size . Therefore, observed mass spectral discontinuities are indicative of variations in cluster-size-dependent photoionization efficiency at the probe wavelength, which can to first order be correlated with size-dependent variations in vertical IP. Note that ionization-induced fragmentation is likely insignificant near threshold in this system .
Due to a combination of isotopic broadening and limited experimental mass resolution, individual silver cluster ions could only be resolved to x<150, however atomically unresolved abundance discontinuities were still observed to much higher masses. Following smoothing of the high mass data sets, the positions of step like IP discontinuities were parameterized to yield the cluster sizes and errors listed in table 1.
3.2 Ionization potential determinations
Information on vertical IPs was obtained by acquiring a set of mass spectra at 1.0 nm wavelength increments throughout the 208 to 255 nm range for both room temperature and flowing liquid N2 source operation. After data reduction, photoionization efficiency (PIE) curves were generated for all ionizable clusters x<=100. In addition we provide an IP bracket for x-138. Vertical ionization potentials as shown in figure 3 were interpreted by extrapolating linear near threshold regions of these PIE curves to their intersection with the baseline. The signal to noise at which PIE curves were obtained does not allow for a more elaborate deconvolution procedure . Error bars reflect uncertainties in this linearization procedure and depend on the S/N of the component mass spectra as well as the post-threshold energy range accessible. Lower IP limits are shown where the appearance threshold lies above the available ionization energy range (208 nm = 5.96 eV). In all cases the respective appearance thresholds fall within the tabulated errors. Ongoing are similar measurements for Agx 100<x<150 as well as the determination of IP brackets for a number of even larger species. These will be reported in a future publication together with a detailed discussion of the dependence of near threshold PIE on cluster internal excitation and source block temperature .
Experiments are compared to both simple and self-consistent spherical jellium calculations from reference 20 which were parameterized for sodium.
Figure 3.Vertical ionization potentials plotted as a function of cluster size. () liquid N2 source, () room temperature source. Shown for x<100 are IP values assigned by linearization of PIE curves. Several clusters were not ionizable within the available energy range.<full image>
4.1 Global trends in ionization potentials
Vertical IPs were among the first metal cluster dynamic response properties to be accessed in particles specific gas-phase measurements [22,23]. Consequently extensive literature exists on IP prediction/rationalization by way of model calculations. The classical limit has been particularly well studied, stimulated by early alkali cluster data sets which were globally consistent with the IP expression for a metal sphere, derived using an electrostatic image charge Ansatz :
WF = IP - (3/8) e2/R
Here WF is the polycrystalline metal work function and R is the sphere radius equivalent to the volume of an x-atomic metal cluster . It has since been shown that the correct classical electrostatic expression follows from the calculation of a metallic sphere charging energy :
WF = IP - (1/2) e2/R
A classical electrostatic description of IP data sets in terms of spherical metal droplets is limited by [26-28]: (i) non-spherical actual equilibrium structures (which may furthermore differ for same sized neutrals and cations), (ii) non-uniform intracluster valence electron density distributions, (iv) discontinuous electronic state densities and (v) poorly defined polycrystalline work functions, which represent the correct macroscopic limit for only fluid metal droplets.
More detailed model calculations of electronic/geometric structure no exist for s1-electron metal cluster neutrals and ions at various computational levels (and in various size ranges). Most complete are ab initio quantum-mechanical treatments, feasible only for small clusters, which are accurate enough to be used for the interpretation of optical response measurements on Lix, Nax [26,29], LixNay [26,30] as well as more recently Agx+ and Agx- [26,31]. Less complete but accessing the full particle size range are semi-classical determinations of sphere charging energies using jellium/density functional approaches [32-34]. Compared to (2), these still neglect non-spherical symmetry and electronic level structure pertaining to real molecules but now include particle-size-dependent electron kinetic and exchange correlation energies. A commonly quoted semi-classical result, which assumes uniform ion core spacing and extrapolates to the correct classical expression at large R  is
WF = IP - (1/2) e2/(R+a)
where a is the element specific extent of (cluster radius independent) electron spillout. Figure 4 compares silver cluster ionization potentials determined for flowing liquid nitrogen conditions to global expressions (1)-(3). Such comparison is most meaningful for near spherical clusters, where any remaining deviations from (3) reflect: (i) molecular radii which do not scale linearly with N1/3 and (ii) the neglect of discrete electronic level structure. In this context it is of interest to note that the IPs for clusters which in quantum jellium treatments are regarded as near-spherical (Ag34, Ag40, Ag58, Ag92 and Ag138 ) following equation (3) moderately well.
4.2 Mass spectra and electronic structure
Major ion abundance discontinuities observed in both secondary ion  and electron impact  mass spectroscopic studies of silver clusters have been rationalized in terms of an electronic shell structure model, extensively applied to alkali metal clusters . Essentially equivalent to the quantum-mechanical problem of independent particles in a homogeneous spherical potential well and yielding eigenfunctions characterized by a main (n) and an angular momentum quantum number (l), this model rationalizes the dominant mass spectral ion abundance variations in terms of cluster stability and/or IP changes associated with filling of degenerate electronic levels (subshell closings) [20,40,41].
The major ion abundance discontinuities observed in this study all correlate with pronounced particle-size-dependent variations in vertical IP (see figure 3) and generally agree with the positions of subshell bunchings (n,l) predicted by both simple and self-consistent spherical jellium calculations (parameterized to the sodium Wigner-Seitz radius) [20,40,41]. However, there are a number of pronounced local IP minima (x=31,49) and maxima (x=74) which cannot be so rationalized - at least within a spherical shell model.
4.3. Correlation among IP data sets obtained for cold s1-clusters
Generally PIE curves become steeper, and thermal "tails" become shorter upon cooling the source block. As a consequence tabulated room and liquid N2 temperature IP values (figure 3) are significantly at variance, with liquid N2 temperature values generally higher. Cluster internal excitation is generally thought to scale linearly with, but not necessarily equilibrate to, source block temperature . We presently have no information on the dependence of valence isomer distributions on expansion conditions.
It is instructive to compare liquid N2 Agx IP determinations obtained using a helium carrier with measurements for sodium  and copper clusters  obtained in the same size range at (nominally) similarly low temperatures. As figure 5 indicates, the three data sets bear striking similarities both regarding general size trends and fine structure. They have in common:
(i) Extensive even-odd variations where clusters with even valence electron counts have somewhat higher IPs that their immediate neighbors. This is usually attributed to electron pairing/correlation effects .
(ii) A number of IP discontinuities consistent with spherical jelium model predictions (i.e. step-like drops in average IP following a "shell-closing").
Figure 5. "Intrinsic" components of the vertical ionization potentials for cold Nax , Cun [7,12,36] and Agn (this study). Tabulated numbers correspond to IP-WF-½e2/(R+a). Polycrystalline work functions were taken from reference , while element-specific spillout corrections are from reference . Note the high degree of correspondence between data sets. (File:ns.xls) <full image>
Within the spherical jellium paradigm there are however minor differences between elements: an IP drop at 40/41 appears smaller (relatively) in Ag than in the Cu and Na data sets; a strong 34/35 drop observed for Cu and Ag is not seen in Na. Small, element specific differences in the magnitudes of IP variations at purported subshell and shell closings have been rationalized as due to the depth, radial distribution and long range cutoff of the assumed mean field potential . Further inconsistencies among data sets include:
(a) local IP maxima at x=57 and 91 in Cu#1;
(b) local IP minima at x=31, 49 and 61 in both Ag and Cu but not Na data sets (where a minimum at x=47 is seen instead) and
(c) for Ag a local IP maximum near x=74.
The origin of these is presently unclear but in addition to element specific bonding, variations in internal temperature and/or isomer distributions may play a role.
4.4. Geometric structure
The highly structured IP size dependence observed for all three s1-metals in part reflects non-spherical geometry/topology of both neutral and positively charged clusters. A first approach to non-spherical structure in these systems has been to retain the quantum-mechanical jellium free electron model while topologically distorting the uniform background potential . Only spheroidal or ellipsoidal distortions have generally been considered, while minimizing total energy to find an optimum distortion for a specific electron count. This approach has provided limited insight into the stability, ionization potential and electron affinity fine structure observed for Nax 10<x<41 [46,47].
Optical response measurements on a number of small sodium and lithium clusters have established rigid ion core geometries, differing from symmetric pieces of either the bulk lattice structure or from fragments of icosahedra which more fully satisfy isotropic sphere packing requirements for low atom counts. Molecular orbital calculations on alkali clusters with x<20, indicate that this is essentially a consequence of Jahn-Teller distortion: the number of associated volume atoms is small enough such that valence electron correlation takes precedent over (high symmetry) ion core packing . However, for large enough electron counts, packing effects do eventually manifest themselves in terms of periodicities in IP indicative of closed shell icosahedral topologies . The situation is likely analogous for coinage metal clusters [48-51].
Gas-phase Cux (x<=120) reactivity measurements have provided evidence for icosahedral structures in many x>=70 . This is seemingly inconsistent with a spherical quantum jellium picture which globally describes the observed IP discontinuities. It has been shown, however, that while spherical jellium level degeneracies are lifted by lowering the symmetry of the potential to icosahedral , resulting electronic level "bunchings" still retain most of the global features found for the simpler spherical potential [35,52]. This is not the case for several other plausible cluster topologies/potentials (e.g., cuboctahedral). In future, it will be of interest to rationalize observed Agx IP variations in terms of detailed cluster geometries . Experimentally, isomer specific probes of even colder clusters are called for.
This work was supported by the National Science Foundation (CHE 9011641), the American Chemical Society (PRF 24413-AC5) and the Sloan Foundation.
#1 -- It is presently not clear whether Na91 manifests an IP maximum.
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