An analytic relationship between size and ionization potential of transition-metal clusters

Based on the effective coordination number (ECN) model, we have constructed an analytic expression for the size dependence of ionization potentials (IPs) for transition-metal clusters. An approximate formula of the surface ratio as a function of cluster size for the close-packed structures has been fitted from the icosahedral-like structures. The IPs of Con, Yn, Nbn, Nin are calculated and compared with experiments as well as with the prediction of the conducting spherical droplet (CSD) model. It is found that the present approach agrees with experiment much better than the CSD model.