Relationship between electron affinity/hardness and the clusters size of V_n/Cr_n clusters

The relationship between the electron affinities, the hardness and the clusters size was studied for Vanadium clusters and Chromium clusters. According to the Spheroidal Jellium Model, a new formula E_A (R) = W_∞-ae²/R-b/R² (R = r_sN^1/3), which relates to the relationship of E_A vs. n, is put forward with considering the polarization, the d-s hybridization in the atoms (or molecules) and the screening effect on the surface. Then the EA values at the infinite size are close to the metal's work functions, and an excellent fitness is obtained that the EA values are accorded with E_A (R) = W_∞-ae²/R-b/R² well even in small size clusters. Meanwhile, the clusters which changed to the bulk metallic clusters are began at V₁₈ and Cr₂₁, and the structures of some abnormal clusters V₅, V₇, V₉, V₁₃, Cr₆, Cr₁₀ and Cr₁₇ are analyzed in detail.