A practical law to predict the appearance sizes of multiply charged rare-gas and molecular clusters

Abstract A dimensionless law depending on cluster size N is derived from the Rayleigh limit expressed in reduced Lennard-Jones (LJ) units to predict the critical sizes n c ( z ) of clusters carrying z positive charges. This relationship provides suitable estimates of n c ( z ) ( z = 2 - 4 ) for rare-gas clusters, including neon clusters whose predicted critical sizes deviate from experimental expectations by less than 12% for different choices of LJ parameters. An extension to 11 nonpolar and 15 polar molecular clusters, from dimers to aromatic hydrocarbons, is achieved that demonstrates the broad applicability of the formula despite inaccuracies for highly polar systems.