Alkali metal clusters ionization potential

Electronic shell effects are well known in clusters of the monovalent metals alkali and noble metals. The experimental ionization potential of alkali metal clusters [25] decays with R following Eq. (1), but superimposed to this average behavior there are pronounced drops between cluster size N and N -i- 1 for some particular values of N, namely N = 8, 18, 20, 40, 58, 92,... 

As the cluster grows the number of electronic shells increases and the energy gaps between shells become smaller. Surprisingly enough, shell effects are still reflected in the behavior of the ionization potential of very large alkali metal clusters. 

Ionization Potentials. Ionization potentials have been measured for small alkali metal clusters183-185 as a function of cluster size. The ionization potential decreases with cluster size (approximately 5eV at M2 down to 3.5 eV at M14) but even for 14 atom clusters the value is far above the 2.3 eV found for the work function of bulk metal. 

This is a severe drawback in the case of equilibrium studies of metal molecules since, as a rule, such molecules are minor vapor components and maximum sensitivity is required for their thermodynamic evaluation. However, very precise ionization potentials can be measured using photoionization spectroscopy (5,28). Berkowltz (28) reviewed early work concerning alkali metal dimers. Herrmann et al. ( ) have measured the ionization potentials of numerous sodium, potassium and mixed sodium-potassium clusters. For most of these clusters the atomization energies of the neutral molecules are not known. Therefore, the dissociation energies of the corresponding positive ions cannot be calculated. 

The transition from the atom to the cluster to the bulk metal can best be understood in the alkali metals. For example, the ionization potential (IP) (and also the electron affinity (EA)) of sodium clusters Na must approach the metallic sodium work function in the limit N - . We previously displayed this (1) by showing these values from the beautiful experiments by Schumacher et al. (36, 37) (also described in this volume 38)) plotted versus N". The electron affinity values also shown are from (39), (40) and (34) for N = 1,2 and 3, respectively. A better plot still is versus the radius R of the N-mer, equivalent to a plot versus as shown in Figure 1. The slopes of the lines labelled "metal sphere" are slightly uncertain those shown are 4/3 times the slope of Wood ( j ) and assume a simple cubic lattice relation of R and N. It is clear that reasonably accurate interpolation between the bulk work function and the IP and EA values for small clusters is now possible. There are, of course, important quantum and statistical effects for small N, e.g. the trimer has an anomalously low IP and high EA, which can be readily understood in terms of molecular orbital theory (, ). The positive trimer ions may in fact be "ionization sinks" in alkali vapor discharges a possible explanation for the "violet bands" seen in sodium vapor (20) is the radiative recombination of Na. Csj may be the hypothetical negative ion corresponding to EA == 1.2 eV... 

If the octahedral and icosahedral 13-atom nickel clusters are representative, an inhomogeneous magnetic field is not a good tool for separating isomers of transition metal clusters. This result is reminiscent of the fact that geometry plays no strong role in the ionization potential variation of alkali clusters (80). However, many calculations must be made before we can be definitive here. 

The ionization potentials (IPs) of ammonia clusters containing alkali metal atoms, such as Li [10], Na [8] and Cs [9], have been reported by Hertel s and Fuke s groups. These clusters have been prepared by pickup sources coupled with a heated oven (Na and Cs) or a laser-vaporization source (Li). The IP(n) values decrease almost linearly with (n-f 1) , which is approximately proportional to the inverse of the cluster radius. Although the IPs of free atoms are different (5.392, 5.139 and 3.894 eV for Li, Na and Cs, respectively), those of the clusters (n > 5) are almost the same irrespective to the metal atoms. The intercept at (n + 1) 0... 

The mono-valent metals have also been found to show a certain type of periodicity dominated by an odd-even alternation. One example of the odd-even alternation is abundance spectra, where the even clusters are more abundant than the neighbouring odd ones. Ionization potentials have also been measured for clusters of Cu [99] to be higher for the even than for the odd sizes. Fig. 11. In addition to the odd-even alternation in the ionization energies, as shown in the figure there is an additional periodicity with high values for sizes 20, 34 and 40, which are the very numbers found for clusters of alkali elements. Values obtained are strongly dependent on the temperature of the cluster and a prerequisite for resolving this type of odd-even alternation is that the clusters are sufficiently cold. 

Experiments on noble metal clusters (Cun, AgN, Aun) indicate the existence of shell-effects, similar to those observed in alkali clusters. These are reflected in the mass spectrum [10] and in the variations of the ionization potential with N. The shell-closing numbers are the same as for alkali metals, that is N = 2,S,20,40, etc. Cu, Ag and Au atoms have an electronic configuration of the type nd °(n + l)s so the DFT jellium model explains the magic numbers if we assume that the s electrons (one per atom) move within the self-consistent, spherically symmetric, effective jellium potential. 

It was mentioned in Sect. 4 that electronic-shell effects appear in the mass abundance [10,43], ionization potentials [88], and electron affinities [89] of noble metal clusters that are very similar to those observed for alkalis. These can be readily interpreted within the spherical jellium model if we treat the noble metal atoms as monovalent, that is, each atom contributes its external s-el tron only. Even more, odd-even effects are also observed for small N in the properties mentioned above, and have been explained by Penzar and Ekardt [32] within the context of the spheroidally deformed jellium model. 

It is noteworthy that the NH4 radical has the /g (4.65 eV) [12] close to those of alkali metals (see Table 1.2) and thus can be regarded as a quasi-metal. For homo-atomic clusters of metal atoms, M , the ionization potentials (U) decreases with the increase of n and ultimately approaches the work function bulk metal, according to Eq. 1.7 [13],... 

Nonstoichiometric alkali halide clusters X Y with X = Na, Li, K and Y = Cl, F containing single and multiple excess electrons have been extensively studied experimentally " and theoretically " as prototypes of possible metal-insulator transitions and segregation into metallic and ionic parts in finite systems. Hydrogenation of lithium clusters has also been investigated but considerably less than alkali halides (cf. Ref. 36 and references therein). Of course the ground state properties such as ionization potentials (IPs) were first available for both halides and hydrides. In the case of the optical probes the visible region was until recently experimentally more easily accessible than the infrared and therefore the data were incomplete. 

E. Eliav, U. Kaldor, and Y. Ishikawa, Ionization potentials and excitation energies of the alkali-metal atoms by the relativistic coupled cluster method, Phys. Rev. A 50, 1121 (1994). 

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