Calculation of ionization potential of small yttrium and lanthanide metal clusters

Our analytic formula for ionization potential (IP) of a metal cluster of given radius, R, is adapted to small size clusters with number of atoms n<40. The radius is defined as the distance between gravity center and the most remote atom surface. R was either calculated or determined experimentally with relative uncertainty of 3%. We have found that R(n) significantly fluctuates around 1.30 n1/3 for n<40. The calculated IP values for Yn and Cen small clusters indicate the valence transition from Z=3 to Z=2 at n=6 and 3, respectively, whereas Z=3 may be considered for Pr5 and perhaps for Pr6