The rare-earths are known to have intriguing changes of the valence, depending on chemical surrounding or geometry. Here we make predictions from theory that combines density functional theory with atomic multiplet-theory, on the transition of valence when transferring from the atomic divalent limit to the trivalent bulk, passing through different sized clusters, of selected rare-earths. We predict that Tm clusters show an abrupt change from pure divalent to pure trivalent at a size of 6 atoms, while Sm and Tb clusters are respectively pure divalent and trivalent up to 8 atoms. Larger Sm clusters are argued to likely make a transition to a mixed valent, or trivalent, configuration. The valence of all rare-earth clusters, as a function of size, is predicted from interpolation of our calculated results. We argue that the here predicted behavior is best analyzed by spectroscopic measurements, and provide theoretical spectra, based on dynamical mean field theory, in the Hubbard-I approximation, to ease experimental analysis.
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