Metal clusters abundance spectrum

The abundance spectrum of Na clusters from Knight et al. s work [4] is shown in Figure 8.1a. Sharp drops are clearly seen after A = 8, 20, 40, 58 (and 92). Later on, mass spectra of other alkali metal clusters showed similar features [5-8]. Particularly interesting is Martin et al. s [8] work, which extended the observed mass spectrum for alkali clusters up to A = 2500. Katakuse et al. measured the abundance spectra of noble metal clusters Cu, Ag, and Au, and found sharp drops after A = 3,9,21, 35, 41, 59, 93. .. [9,10]. Since alkali, Cu, Ag, and Au atoms all have one s electron each in the outermost valence shell, and experiments were performed on cationic clusters of the noble metals, drops in abundance occur at the same number of valence electrons in all these clusters. 

Sharp drops after certain sizes in the abundance spectrum indicate enhanced stability of these clusters compared to neighboring sizes. We will try to understand this phenomenon from the behavior of valence electrons in the clusters by invoking simple quantum mechanical models. The simplest model one uses for valence electrons inside a bulk metal is the free-electron theory valence electrons of all the atoms are free to move over the entire volume occupied by the solid [11]. One can use a similar free electron model in case of metal clusters. As the simplest approximation, shape of the cluster can be taken as spherical, and the electrons strictly confined within the sphere. In this hard sphere model, the Schrbdinger equation describing the valence electrons is... 

These two clusters are both diamagnetic derivatives of formally M" " metals, but they have very different structures and spectroscopic properties. The Cu Sn9 ion has a centered Cu atom in a D3h - type Sn9 cluster however, the solid-state structure has only approximate C2v symmetry [44]. Regardless, the complex is fluxional in solution giving a single Sn resonance at — 1,440 ppm with J( Sn-" Sn) = 85 Hz. The remarkable feature of the spectrum is the well-resolved coupling to the quadrupolar Cu atom ( Cu, 69.1% abund., I = 3/2 ... 

The relative intensities of all subspectra of the different isotopomers reflect the molar fraction of the different isotopomers, as predicted from the natural abundance of the metal isotopes. The observed spectrum is then the sum of the spectra of each isotopomer weighted by its own relative intensity. Formulae and programs have been proposed to calculate these normalized probabilities for platinum [22,23] and for tin [24,25]. Such calculations can be extended to heteronuclear clusters [25]. Though the number of isotopomers increases rapidly with the size of the cluster, only a small number of them provides subspectra with significant intensities. 

What is the mechanism of met-car formation Collecting information on that problem requires identification of the metal-carbon subspecies sufficiently stable to be considered as intermediates in the construction of met-cars. Since the beginning of met-car history, the mass spectrum obtained from photoionization of the neutral MmC clusters (M = Ti, V) has provided information about the most prominent peaks in the region of intermediate mass - combinations at (w, ) = (4,8), (5,10), (6,12) and (7, 13) are noticeably more abundant than the adjacent metal carbon clusters (Fig. 6b). 

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