Among metal clusters, the understanding of size dependent electronic structure effects is most extensive for small alkalis because of their experimental and theoretical tractability. Many experiments have probed the properties of alkali metal clusters.^{18 19} In experiments related to the work described here, optical photodepletion spectroscopy has been used to study Na₃, Na₄, and Na₈.²⁰ The coinage metal clusters have not been as extensively investigated, but are similar to alkali metal clusters and can be regarded as s1 electron clusters perturbed by the underlying d shell.²¹ Stability patterns found in the abundance spectra of alkali metal clusters have also been observed for singly and multiply charged silver clusters.^22,23,24 A number of experiments have been performed on deposited silver clusters using various optical techniques^25,26 and electron microscopy. ²⁷ Gas phase silver clusters have been studied by photodetachment^28,29 and photoelectron^30,31 spectroscopy. Vibrational resolution has been obtained up to Ag₃³² and ionization potential brackets for a few clusters are already available.³³ There is also some work on silver cluster reactivity³⁴ and AgI derivatives.³⁵ Clusters smaller than Ag₁₀ have been modeled theoretically with high level calculations.^36,37

However there is still a need for a consistent set of size specific measurements on the ionization potentials (IP) of these clusters – especially cold clusters rather than those generated from sputtering sources. This would be a step in the important direction of understanding bonding in more complicated transition metal systems. Some of the research that is presented here has been published recently³⁸ but this account gives a more detailed description. In addition the following chapter describes a successful quantum mechanical model that explains the features observed in the ionization potentials of silver clusters. This model should also be applicable to other s1 metal clusters.

Figure 3.1 shows a typical mass spectrum of silver clusters obtained from the apparatus described in the previous chapter. The spectrum does not represent the underlying neutral cluster distribution which probably has far less structure.³⁹ Instead the structure is a result of the ionization efficiency of individual clusters at this wavelength. Due mainly to the isotopic distribution of silver, peaks cannot be resolved beyond approximately Ag₁₅₀, although structure is still visible in the mass spectra out to at least Ag₄₀₀.³⁸

Figure 3.1. Mass spectrum of silver clusters by photoionization using focused light at 235nm. The carrier gas is helium and the source is at room temperature. The ion abundance discontinuities correspond to changes in the ionization potentials. A 'shell' pattern exists that divides the peaks into sections: Ag₉-Ag₂₀, Ag₂₁-Ag₃₄, etc., as noted. A prominent even/odd pattern is also visible from Ag₂₁-Ag₄₃. (12-21-5.xlc) <full image>

Upon absorption of a photon it is possible that the cluster fragments. This has been observed for both silver cluster cations⁴⁰ and anions²⁸. In the determination of cluster ionization potentials, fragmentation is not likely to interfere for the following reasons. First, fragmentation below the IP would not effect the mass spectrum. Second, a fragmentation analysis that is based on simple kinetic arguments and ab initio binding energies shows that with the energy remaining after ionization (<2eV) fragmentation rapid enough (<1µs) to disturb the measurements is unlikely except for the smallest (n<7) clusters. (See the chapter on photofragmentation for more details.) Only fragmentation in competition with ionization would perturb the mass spectra and this is not expected to be significant near threshold.⁴¹

Cluster IP's were found to change if the clusters were generated with a liquid nitrogen temperature source rather than a source at room temperature. The ionization threshold became sharper at lower temperatures and the resulting IP was often higher. This is shown in the figures that follow. Under cold conditions the source could produce argon or nitrogen complexes suggesting that the internal temperature of these clusters is lower than those produced at room temperature. A sample mass spectrum is shown in Figure 3.2.

Figure 3.2. Mass spectrum of silver clusters generated at liquid nitrogen source temperatures with 5% argon /He carrier gas. Ag9 easily forms complexes with the argon. These complexes are not seen for room temperature measurements. An even/odd effect in the pure clusters is also evident.<1004-08.tof><full image>

To determine cluster ionization potentials, mass spectra were acquired over the energy range 208 to 255nm (5.96–4.86eV) at 1nm increments using the apparatus described previously. For each cluster size, graphs were made of the cluster signal as a function of the ionizing photon energy. These photoionization efficiency (PIE) curves were then used to estimate the cluster ionization potentials by drawing a straight line through the most linear portion of the curve and then noting its intercept with the x-axis. Example PIE curves for two clusters with long tails into the red end of the spectrum, Ag₉ and Ag₂₁, are shown in Figure 3.3. PIE curves were made for all clusters whose IP was within the observable range out to Ag₁₀₀. There are definite variations in the length of the PIE curves with cluster size. Ag₃₁ and Ag₄₉, for example, have long tails. Some of these features are explained using a distorted sphere cluster model described in the next chapter.

Figure 3.4 shows the result of the linearization procedure for both room temperature and cold source conditions. The cold cluster IP's are also tabulated in the appendix. There is more detail in the ionization potential pattern under cold source conditions since the 'thermal' tails become shorter and the curves steeper. The clusters Ag₂, Ag₄, Ag₆, and Ag₈ have IP's above the accessible range of the doubled dye laser.

The error bars are approximately +/-0.15 eV. More emphasis is placed on the overall pattern than on the absolute values due to the arbitrary nature of linearizing the PIE curve to one IP value. Because of variation in the signal coming from the molecular beam and the long tails on some of these curves, the absolute value of the ionization potential assigned to the cluster has a significant uncertainty that was difficult to estimate. However the linearization procedure was applied consistently and the relative error between clusters is small. These relative errors are indicated in Figure 3.4 as error bars. Three sets of experiments were performed with the source at room temperature and one set with the source near liquid nitrogen temperature. The repeated experiments gave consistent results.

This work can be compared to the electron impact ionization of silver clusters, Ag₂ – Ag₃₆, which gives higher IP's than the photoionization measurements reported here.⁴² Another photoionization study of Ag₃ however, gives a value in agreement with the results presented here.⁴³ The reason for the discrepancy is uncertain but could be attributed to fragmentation that occurs with electron impact ionization or the higher efficiency of photoionization.

For comparison to s1 metal clusters, the radius can be approximated with R=rsN1/3 where N is the cluster nuclearity and rs is the radius of the volume of an electron in the bulk.⁴⁴ Some improvement can be made to this approximation for small clusters by adding to the cluster radius an additional constant amount attributed to the electron 'spill-out'.⁴⁴ If this classical IP term is subtracted from the measured IP's, the remaining intrinsic IP can be compared for various materials. Figure 3.5 makes this comparison with silver, sodium, and copper. Deviations from the properties of a classical metallic sphere could be attributed to a number of effects, for example (1) non-spherical structures and perturbations to the electron density caused by the ion cores, (2) variation in the atomic spacing with cluster size, (3) size dependent interaction with the underlying d-electrons and (4) effects related to the quantization of valence electronic energy levels. As will be shown in the next chapter, most if not all the observed features can be attributed to non-spherical structures and quantization of the valence electrons. Certain clusters that are considered to be spherical due to their closed-shell electronic structure are expected to approximate the behavior of metal spheres. These are sizes 8, 20, 34, 40, 58, 92, and 138.

Figure 3.5. "Intrinsic" components of the vertical ionization potentials for cold Ag_n from this work, Cu_n from [⁴⁷,⁴⁸,⁴⁹], Na_n from [⁵⁰]. The similarities of the local features to these curves are visible. Spherical shell closings are noted in bold face. Values shown here correspond to IP-WF-½e2/(R+a). Work functions WF are from [⁴⁹], and the electron spill-out radius a is from [⁴⁴]. Further details are given in [³⁸]. (File:ns.xls) <full image>

To show that these patterns differ from other non-s1 metal systems, Figure 3.6 gives the ionization potentials of nickel and niobium clusters.^{52 53}